I think all of our memories of stories are from being able to curl up with a book, hide under the duvet with the light on in the torch, that excitement of discovering an author for the very first time. On the internet you'll be told what to read, there'll be icons on the front page of things that say this is the author that you're reading now, the short story you're reading, but anyone who's read anything on the screen for a long period of time, I don't believe they'll create that bond that they will have with their very special books, those ones with their bookmark in.


Moving to the pool, Bemidji hosting Park Rapids. Kicking things off in the 200 individual medley, the race started out fairly close with the top three racers separated by less than two seconds after the first leg. But eventually, Park Rapids, Kazemir Simonson would pull away. He'd take first with a time of two minutes, 19 seconds. The Panthers, Marcus Benson and Bemidji's Luke Yards would fight for second. But Benson would win by 0.19 seconds, then in the 50 free. On the home stretch, Bemidji's Gabe Goodwin can't quite catch Spencer Fritzi of Park Rapids. He wins with a time of 24.08 seconds. Goodwin in second place. We don't have scores from that one, but the highlights look good. If you've enjoyed this segment of Lakeland News, please consider making a tax-deductible contribution to Lakeland Public Television.


Hi everyone, my name is Steph, this is Kiblet Joy and welcome to the third episode of the Reading Diaries. I did miss a couple of weeks because it's just been a little bit hectic. It's a perfect time to sort of just go through what I've been reading both in the classroom but also at home. So we're going to start off with a couple of texts that we've been using in the classroom as mentor texts. Before I do, we have been continuing our poetry reading and we are continuing our World Robot Read. Last week was a bit hectic, we didn't get as far through the World Robot as I would like so I think we're sitting around chapter 25-26 at the moment so we've still got a fair way to go. So this week we're going to be reading through some more chapters because we need to get a little bit further along but the class are really enjoying the World Robot. I think there is enough pitched at that level but also enough that extends them because there's a lot of oh what does that word mean or what is that and it's helping us to have some really good conversations around new words which is my favorite thing to do. We've spent a lot of time recently talking about making connections both text to self, text to world, text to text and we have been reading a variety of books to suit that including Don't Let the Pigeon Stay Up Late by Mo Willems which is just a classic and it's a really fun read about a pigeon who doesn't want to go to sleep and of course this is a really fantastic persuasive text and in fact I think we read this when we were talking about persuasive texts. We're talking about all the different authors purposes behind books. This book always makes kids laugh, it is funny and you can't help but read it with enthusiasm and joy because the pigeon is just a delightful character. We also read Market Day by Callie Galash which was a shortlisted book last year. It is one of my favorite picture books and it is about a young girl and her family who go to a market. The young girl is given a coin to spend at the market but she doesn't know what to spend it on. There are so many amazing things and she spends the entire day trying to decide and it's not until the family are leaving at the end of a long day they've had some dinner there, there's been music and dancing that she knows what to do with her coin and it is a beautiful story about thoughtfulness, about a love for markets and for the amazing people who sell things at markets like it's just a really glorious read and the color palette in it is just stunning. So I'll leave the CBCA review that featured this book on the screen so you can check it out if you haven't seen it already. We also read What Do You Do To Celebrate by Ashley Barton. This one is all about different celebrations around the world and each page features one child and their celebration. It doesn't tell us where on those double page spreads but at the end of the book we get to go through a list of where all of these children are from and what the celebrations are. This one does mostly feature Christmas celebrations but different Christmas celebrations around the world and there are other celebrations included as well. So there were lots of things that kids could connect to. It also invites a lot of close reading and close looking at text and inferencing because it never outrightly states exactly what the holiday is. You kind of have to make an inference on that before you check the back of the book. All right then moving into some other kids titles that I have been reading over the last little while including picture books, middle fiction, and young adult titles. The next two books are books that I bought for my niece particularly for my mom to have at her place. My mom's family is, or family background is, Italian. So we've been trying to hunt down some books. I'm trying to find a good book that talks about Anonna but I haven't been able to find a good one yet. So if you have any recommendations, leave them down below. But I did find these two. So there is my first 100 words in Italian which is great. This is super simple. It's really bright and colourful. The only thing I'll have to do in here is go through and change mom to mom because it was written by an American. So I'll just go through it. I'll make sure we have our Australian spelling in here. That's okay because it's our family book. We can do what we want with it. The other one that I really loved was Familiar and this one is Italian and English words for family. I'm going to have to do the same thing in this book. But it's really simple. It's just the English word and the Italian word for the different people in all the different members of families. And it is just so cute and bright and colourful. And I know my mom is going to really enjoy having these there because I think I talked about it last year. I did find some Persian books or Persian slash English books for my brother-in-law's family. But now we have some Italian ones. My mom does also have some other Italian books from when we were children. But some new ones Familiar are coming her way. I also found two more books about Ramadan and I have promised my class that I'll bring in some books because we have quite a few students whose family celebrate Ramadan. I've got two more books to add to the collection. The first one is Tell Me More About Ramadan. This one is by Bashar Karun. And it was a really lovely story of Leila who is wanting to learn more about Ramadan and explaining the purpose behind Ramadan and why they fast. And similarly there is Little Leila learns about Ramadan again in the same vein. Just a slightly different story. This one is slightly less wordy than Tell Me More About Ramadan. But both of them have really gorgeous illustrations and a really lovely message and narrative through them. So these will be added to my collection. I do have another video all about other books that I found last year for Ramadan. We'll have a little box for a little while so that kids can find them really easily. Then there are a couple of picture books that I just found randomly that I had in my collection but I have not actually read so I decided I should get on that. The first one is Bedtime Sorted by Jimmy Reese. And this one is a funny story about a dad who's trying to put his kids to bed. Jimmy Reese is an Australian comedian. He's really funny. And he also has three young children including a set of twins like the dad in the story. And dad thinks he's so successful at putting the kids to bed until they keep getting up and not going to sleep. So it is a really fun, very cute story. This one I will probably gift to my sister and to Mila so that they have a bedtime story when Mila is going through this stage. There is The Biscuit Maker by Sue Lawson. This is about a very busy neighbourhood where the neighbours don't really know one another until suddenly these amazing biscuits begin appearing and people love them until the biscuits stop and then they begin to wonder well where did they come from and why have they stopped? And it turns out that one of the elderly neighbours has been making these biscuits as a way of trying to build community but he falls ill and it comes down to one of the young children who realises what has happened and checks in on him. So it's a very lovely story. And then there is The Two-hearted Numbat by Ambulan and Ezekiel Quaimulana. This is a First Nations story about a numbat who has two hearts. One is his heart of feather which is light and playful and the other is the heart of stone which is fearsome and brave and the numbat feels that there is this disconnect between him and that he needs to just have one heart and so he goes to seek some advice and he's sent on a journey where he discovers that actually having the two hearts is an absolute bonus because it means that the numbat approaches situations from multiple perspectives and knows when to apply both his heart of feather and his heart of stone and that actually it's the two of them combined that make up his heart. It's really really lovely and the illustrations are so gorgeous. The final picture book that I am going to talk about is I Am Me, a book about authenticity by Susan Verde and Peter H Reynolds. This is a really great book about being yourself. I am trying to collect some more of the books in this series.  So I absolutely loved this book. It was so gorgeous and fun and then we move into some middle fiction and young adult titles. So I finally finally read the first book in the Polly and Buster series by Sally Rippon. This is The Wayward Witch and the Feelings Monster. I recently talked about this on my other channel. Polly is a witch. She's in magic school. She's in year five and she's terrible at spell making because she doesn't know that this is what it is but she's dyslexic. The letters swim on the page and she struggles to really concentrate on what is actually being asked of her to do and so her spells always go awry. Her best friend is Buster. He is a monster that lives next door and in this world witches and monsters are not supposed to get along, are supposed to be friends and so their friendship is frowned upon by just about everyone.  So when he's happy and joyful he's big and light and when he's sad he is small and gray. This is about them navigating that friendship about Polly realizing what true friendship is and that Buster has always stood by her and it also navigates prejudice in a lot of ways. Great dyslexia and some neurodivergent representation in here. I'm definitely looking forward to continuing this series very soon. I also read Our Home is Dirt by Sea, Australian Poems for Australian Kids. This is a collection that has been selected by Diane Bates. It is a wonderful little collection of Australian poetry for kids following a bunch of different categories from mostly me or an about me section, families, people, animals, sports school, and special times. They're short, they're fun, they're funny, and highly entertaining. And the last book that I'll talk about is Everything Under the Moon. This is a collection of fairy tales in a Queer Alight. This is edited by Michael Earp and illustrated by Kit Fox. This is a collection of queer re-imaginings or retellings of fairy tales or folktales. I've also spoken about this recently on my other channel. I didn't necessarily love every story in here but I did enjoy a lot of them and I thought they were really well done. It's a great collection. If you are looking for fairy tales for a young adult audience that do explore and represent a variety of queer experiences, lived queer experiences, this is a great collection. It does play on a lot of traditional fairy tales but also a lot of other folktales as well. And I can highly recommend the Gary Lonsborough, Lily Wilkinson, Helena Fox, and Alison Evans stories as some of my favourites from in here. So that is the end of my reading diaries for the last couple of weeks. I'm sorry that it's been so long but hopefully the variety of texts in here made up for it. In the comments I'd love to know what recent children's titles you have been reading and enjoying. Feel free to let me know down below. Otherwise, feel free to leave an emoji that you believe represents you down below. I hope that wherever you're on the world you're staying safe and healthy and I will see you in my next video. Thanks so much for watching. Bye everyone.


Assalamu alaikum. Welcome to lecture number two of the course on statistics and probability. In the last lecture, I can wait to you the organization and structure of this course. In addition, I discussed with you the nature of the discipline of statistics, the importance of statistics in different fields and also I picked up some technical concepts such as data, variables, measurement scales and errors of measurement. Today, we will be discussing the various steps involved in a statistical inquiry and in particular, we will be discussing the methods of data collection, both primary data and secondary data and also we will discuss at some length the concept of sampling. Students, koi bhi research jo hum real life data bhi based karna chahate hain us me kon kon se steps involved hote. Actually, it's quite a scientific method and you have to have a methodological approach toward this problem. So agar main isko list karne ghi koshish karun to hum yoon kais sakte hain. For any statistical inquiry, first of all, you would be very clear about the topic and the significance of the study. You should be absolutely clear about the objective of your study, exactly what it is that you are trying to find out and then of course, the methodology for data collection, the source of your data and also the sampling methodology as well the instrument for collecting your data. The tool by which you would collect your data is of the utmost importance. Then of course, once you have collected the data, you would proceed to the analysis of this data. You will draw results and conclusions and finally, recommendations based on your study. As far as the methodology for data collection is concerned, I just said to you ke teen cheeze hain jenke baare aapko bilkul clear hona chahiye. Sb se pehle, source of your data, yani wo statistical population jaha se aap data collect keringi. And then the sampling methodology, kyunke aksar obeishtar aap ke paas resources itne nahi hote, ke aap poori population se data collect kar sakhein and you have to resort to sampling. Or uske baad also equally important, saath hi saath the instrument, the method by which you would collect your data. So, I will begin the discussion from the third point and that is the instrument and then I will go to the first two points the population and the procedure for sampling. Students, kisi bhi statistical enquiry mein ye jo collection of data hai, this is one of the most important steps. You see the point is ke saara jo aapka analysis hai, jo baad me aapne bade bade sophisticated methods bhi aap uske upar apply karne, agar aapka data hi sahi nahi hai, toh how can you expect your results to be reliable and valid. So, is zimne mein, the first thing to understand is that we can differentiate between two types of data that we could collect the primary data and the secondary data. Data that have been originally collected and have not undergone any sort of statistical treatment are called primary data, yani duse lafzo mein wo data jo aap khud collect karenge, fresh data that is primary data. On the other hand, data that have undergone some sort of statistical treatment are called primary data. So, we have to be concerned by statistical methods at least once, that is data that have been collected, classified, tabulated and presented in some form for a certain purpose are called secondary data. As far as collection of primary data is concerned, students, there are a number of ways of doing that. We have direct personal investigation, indirect investigation, collection through questionnaires, collection through enumerators and also there is a method in which we have data collected through local sources. Subh se pehle, direct personal investigation ki baat karte hain. Students, yeh wo method hain ki jis mein researcher ya investigator jo hain, wo data ko khud personally collect karta hain. Kisi aur peh rely nahin karta. Aur chunke uska apna zati interest us research problem mein itna zyada hota hain, is liye iss tra se jo data collect kiya jata hain that is generally quite accurate. But of course, as you can understand this method you know in which the interviewer is, I mean the researcher is doing it himself, you know this method can prove quite costly and time consuming when especially when the area to be covered is vast. However, it is quite a useful method for lab experiments or for localized inquiries. Lekin iss mein ek problem aur bhi hai, ke although the researcher may be wanting and thinking that he is being very impartial and objective you know sometimes it is possible ke uska jo personal, ek personal inclination hai, personal ek jo bent of mind hai, personal way of thinking jo hai jise hum log personal bias kahange you know actually that might actually enter into the data and so the data that way may not be extremely accurate. The next method that I would like to discuss is the method of indirect investigation. Tek ye baz oka at aisa hota hai, ke aap information jen logon ke bari mein hasil karna chahate hain you know they are hesitant to provide that information to you. For example, aap sab jaanthi hain ke income log apni income ek dum se aap ke saath share nahi karna chahate. Ya khawateen ke bari mein, aam baat hai ke jee khawateen apni umar aap ko nahi bataan chahate. So this is just a small example to illustrate the point that sometimes actually it is it may not be possible for you to obtain the accurate information directly from the person's concern. As a situation mein you would be interviewing some third party who has knowledge about that particular you know about that about those people and about that phenomenon and you will be collecting data from these third parties in an indirect way. Eise kahte hain, indirect data collection. Lekin is may be we have to be very careful because sometimes it is possible that the third party may give you wrong information about this person deliberately. The next method is the questionnaire method. Eise kahender hain aap ek sawal naama tayar karthe hain aur usko hain administer karthe hain apni respondents ke upar and they are required to answer all the questions and to fill out the performer. Western countries mein jaha pe aur un sab countries mein jaha pe level of literacy aur education humare developing countries ke nispat bohot zyada hota hain. Sab se zyada aam tarika ye hain ke by mail you know they would send the question hain by mail aur aap to aap ko pata hain ke email aur in sab cheez ho ka zamana hain. Lekin developing countries mein as you know when there are so many people who are not able to read and write. Generally you would have a trained enumerator who would go to this respondent and he would interview the person aur jo unka jawabat unke jo honge ye hamara jo enumerator hain wo form ko bharega according to the answers given by the respondent. So in this manner the next method that I listed the method of trained enumerators ko link up ho jata hain questionnaire method ke saad. Kyuke jab trained enumerator bhi jata hain to ek sabal naama uske bas hota hain jise wo administer karta hain on the respondent. In sab methods ke lawa ek aur method is ka main zikar kiya that is the method in which we have the data collected locally from local sources. Iska asan example krop estimation ka hain jab aap ko krop ki krop ke baare main daza karna hota hain to aap jo local sources hain jo gaon ka number dar hain jo waha ke local concerned log hain un se aap information munga laite hain. Ye to hui baat primary data ki wo data jo aap khud collect karenge aap karenge. The other kind of data is secondary data and as I mentioned earlier this is that data which has already been collected by some organization. Iske andar hain maare pass hain uske categorize kar dehte hain mukh talif kategories mein. We have official sources, semi-official sources, publications of trade associations and chambers of commerce and such organizations and we also have research organizations. Official sources ki category mein governmental departments such as the statistics division, the provincial and federal bureaus of statistics or semi-official mein semi-government idare. For example, the railway board or the central cotton committee iss khasam ke idare uske andar shamil hota hain. Students ye to hui methods of data collection ki baat. Aayi aap hain us baat pe jaate hain jo maini pehle shroo mein kahi thi. The source of our data, yani data collect kaha se karenge? The population, the statistical population and then also the method of sampling. Iske andar sabse pehle dekhne ki tis ye hai ke why do we have to resort to sampling? Jaise ka maini pehle kaha. Of course, if we could conduct a complete census, a complete count that would be a perfect situation, an ideal situation is liye ke aap apni tamamthar population ko exhaust karenge aur ek ek element of the population se data collect karenge. But the problem is that this perfect and ideal situation is not available in real life. Very rarely is it possible to you to have access to the entire population. More often than not the study has to be conducted on sample basis. You samaj liye ke ye jo subject hai statistics ka, iska goal hi ye hai. The goal of the science of statistics is to draw conclusions about large populations on the basis of data collected on sample basis. Aap hum ye jo loves population hai, isko formally define karte hai. As you can see on the screen, a population is the collection of every member of a group possessing the same basic and defined characteristic, but varying in amount or quality from one member to another. We have two types of population, the finite population and the infinite population. Let me explain this point with the help of some examples. For a finite population, you could think of the IQs of all the children in a school, the heights of those children, their weights, their blood pressures, their body temperatures. Kehne ka maksat ye hai ke chunke o school ke andar un bachon ki tadaad, ek finite tadaad hai. Le haza aap unse related kisi bhi variable pe agar data collect karenge toh that will constitute a finite population. The other of course is the infinite population. For example, the barometric pressure, there are an infinitely large number of points on the surface of the earth and hence we can have an infinite number of readings of barometric pressure. Isziman mein samajne ki baat ye hai ke bahut si populations itne zyada large hoti hai ke even if they are agar hum rigorous, bahut hi zyada rigorously define karen, so hum keh sakein ke it's a finite population. Lekin chunke bo iskhadar large hai isliye for all practical purposes it is equivalent to an infinite population. Students ye toh dono examples main aapke saamne pesh ki, they were of what can be called existent populations. But then we could also talk about the hypothetical population. The population of all conceivable ways in which a certain event can happen. For example, all possible outcomes from the throw of a die. However long we throw the die and record the results, we could always continue to do so for a still longer period students. There is one other differentiation that we need to make and that is between the sampled population and the target population. Sampled population is that from which the sample is chosen. Whereas target population is that about which the information is sought. For example, suppose that we desire to know the opinions of the college students in the Punjab regarding the present examination system. Our population will in that case consist of the total number of students in all the colleges of the Punjab. But if suppose that on account of shortage of resources or time we are unable to conduct a survey of this kind on all the colleges and we select only five colleges scattered throughout the province. Then our target population consists of all the colleges whereas the sampled population consists of those five colleges that we have chosen. Students, the next question is how do we draw a sample from our population? This is the very first thing to note is that we have two methods of sampling basically the non-random sampling and random sampling. Statistics ki jo tamam tar jo teri hai, statistical inference ki jo teri hai that is based on the assumption that our sample is a random sample. In order to draw a random sample from a population, students the first thing we need is the complete list of our population which is technically called the frame. For example, the complete list of all the BCS students of the virtual university of Pakistan as on 15th of February 2003. Students as far as the sampling frame is concerned it should be kept in mind that as far as possible our frame should be free from various types of defects that can occur. It should not contain inaccurate elements, it should not be incomplete, it should be free from duplication and it should not be out of date. I have just given you an example that on 15th of February 2003 the list of all the students of the virtual university. So, the defects that I have mentioned you can understand that if the list contains some student who had previously enrolled but has now left or if the list contains the name of the same student twice then these are the kinds of errors that we must try to avoid. And as far as possible the frame should be complete, accurate and up to date. Now, let us talk about actual sampling. From this frame we need to draw an example. The first thing to keep in mind is that a sample is only a part of this population and therefore it can only represent the population to a certain extent. It cannot represent it fully and the goal of sampling is that the sample should be drawn in such a way that it is a good representative of the population in spite of the fact that it is usually much smaller than the population. Students sampling has so many advantages from the practical point of view. You are able to save a lot of time and money simply because the bulk of work is so much smaller than a complete census. You are able to collect more detailed information about a number of variables. You have the possibility of follow-up. Who do you call follow-up? Students, when you collect data, it is not necessary that all the information you collect is accurate. It is possible that the question that your respondent sent back to you, he answered 9 out of 10 questions but he did not answer 10 questions. Also, you might have the answers but it might be very clear to you that there are some errors in them. In such a situation, you would be following up your query. You contact your respondent again and you try to have him rectify the errors. Obviously, if there is a complete census, there is very little possibility of follow-up because it is such a huge study. You cannot afford to follow-up on your respondent but if it is only a sample, many times it is possible for you to do so. Students, let me now discuss with you two technical concepts. The concept of sampling error and the concept of non-sampling error. Sampling error is defined as the difference between the true value of the population such as the true population mean and the similar value computed from the sample. For example, the sample mean. Yanni, as you can now see on the screen, in case of the mean, sampling error will be defined as x bar minus mu where mu represents the true population mean and x bar represents the sample mean. This difference called sampling error is due to sampling because a sample is only a part of the population. Hence, the value that you compute from the sample cannot be the same as that you would have from the entire population and this error would be there even if your sample has been drawn in a very correct manner. Besides sampling error, there is this other kind of error called non-sampling error because of sampling but which would be there even if you are conducting a complete census. The defect in the sampling frame, faulty reporting of facts due to personal preferences, negligence or indifference of the enumerator and non-response to mail questionnaires are examples of non-sampling error. Students, in the study based on sampling or sampling, note one more point. It is how long should the process of data collection be continued. Obviously, no such study can be done in which the process of data collection can be prolonged to an indefinite period. In fact, the longer your data collection takes, the more possibility there is of having variations in response because of the time lag. Hence, the procedure is that a definite cut-off date is generally established for any database study. Students, I told you a while ago that we can have non-random sampling or random sampling. Of course, my stress in a short while will be very much on random sampling but before this, I would like to discuss with you a little bit what non-random sampling means. Non-random sampling is that in which we would select the elements using our personal judgment. In this, we have different types and one of the most popular types is called quota sampling. Quota sampling is often used in commercial surveys such as consumer market research. For example, suppose that one particular company wants to know the opinion of the people about this new product that they have launched in the market. They may tell their enumerator, this one enumerator, that he should interview ten married women between 30 and 40 years of age living in this particular area whose husbands are professional workers and five unmarried professional women of the same age living in the same town, same area. In other words, this enumerator, he is restricted by quota controls. He has been given a number of men and women but after that, what kind of men and women that is totally up to his own discretion. Islié students, you can see that in this kind of sampling, there is no need for the list of the entire population out of which you would have drawn a sample using the lottery method. As such, it is obvious that this is a very, very convenient form of sampling. There is a lot of cost reduction and also a lot of saving in terms of time. But this is not the one that we have to go for. Islié ke jitna bhi wo samjhe ke jo mai selection karra hoon that is random. It is actually not really random. Students, you will be interested to know that psychological studies have been conducted which have established that the human mind is a poor random selector. Kehne ka maksad ye hai, ke for example, suppose ke mai aapse kahun ke 1 se 20 tak aap randomly number bolte jahi. So, you might say 1, 3, 2, 7, 12, 19 and you think that this is totally random. Lekin aap jab issi data ko aap analize karenge to aap dekhenge ke aap ne bohot zehada number jo bolhe, they were odd numbers and they were very few even numbers. Same is the situation in case of non-random sampling. The numerator may be thinking that he has been able to interview all kinds of men and all kinds of women in this interview regarding this particular product, but it is possible that those people are not really a very, very good representative of the population. Of course, there will be situations when it will be better to resort to non-random sampling. For example, suppose that the rector of your university wants to send one of the students of this university to some foreign country for this particular conference. Obviously, in this case he should use his best discretion to select a student that who will be able to represent the university in a proper way. And obviously, this student will be one of the most intelligent and good students. But the statistical point of view is that this student will not be a proper representative of the entire population of this university. So, the total population of 2000 to 2500 is present among all the students. Some who are very intelligent, some who are not that intelligent. So, this is the key concept as far as sampling from the statistical point of view is concerned. A sample student is supposed to be a miniature replica of the population. Alright, let us now focus our attention on random sampling. Students, random sampling is the one in which you select your sample by the lottery method. This is the simplest way of saying it. In this category, we have a number of types of sampling such as the simple random sampling, the stratified random sampling, systematic sampling, cluster sampling, multistage sampling and so on and so forth. In this course, I will be focusing on the simplest kind of random sampling and that is simple random sampling. Simple random sampling is the one in which the chance of any one element of the parent population to be included in the sample is the same as for any other element. Now let us see how we actually draw this sample. You know that the traditional method of the lottery is to write the names of the students and fold them and put them in a hat. You would pull out one of those jets of paper. Now as you know very well, better than me, computers are able to conduct the lottery method for you very conveniently by generating random numbers. I will discuss the use of the random number table. A random number table students is a page full of the digits from 0 to 9 which are printed on that page in a totally random manner. Actually these tables are constructed according to certain mathematical principles such that the chance of any one digit to appear on that page is equal to the chance of any other digit to appear. So as you can now see on the screen, these digits is such that they do not have a systematic pattern or order. In order to draw a sample from this kind of a table, I will explain this point with the help of an example. Suppose that we have the frequency distribution of the ages of a population of 1000 college students in any particular country. The ages are as you can see from 13 to 19 and the number of students in the various age groups are 6, 61, 270 and so on. Suppose that we have to draw a sample of size 10 from this population, how do we proceed? The first step is to allot a sampling number to each item in the population and to do that the very first step should be to construct a column of cumulative frequencies. So as you now see on the screen, the cumulative frequencies for this example are 6, 67, 337 and so on. Now that we have all these cumulative frequencies, now we are in a position to allocate the sampling numbers to all these population units. As the cumulative frequency of the first class is 6 students, what we can do and should do in this case is to allocate sampling numbers 0, 0, 0 to 0, 0, 5 to those 6 students who belong to this very first class. Now the cumulative frequency of the second class is 67, whereas the cumulative frequency of the first class was 6. This means that we can allocate sampling numbers 0, 0, 6 to 0, 6, 6 to the 61 students who belong to the second class. Similarly the cumulative frequency of the third class is 337, the cumulative frequency of the second class was 67 and we can therefore allocate to the third class sampling numbers 0, 6, 7 to 3, 3, 6. Proceeding in this manner, you obtain the sampling numbers from 0, 0, 0 to 9, 9, 9 as you now see on the screen. The interpretation of this column of sampling numbers is that the first student whose age is 13, he or she has been allotted the sampling number 0, 0, 0, the sixth student has been allotted the number 0, 0, 5, the seventh student whose age is 14 has been allocated the sampling number 0, 0, 6 and so on such that the last student, the thousandth student whose age is 19 years has been allocated the sampling number 9, 9, 9. I am sure that you are having a question in your mind right now and that is why have we shifted the number backward by 1, i.e. the first student, why have you given 0, 0, 0, 0, 1? The reason is that in all we have 1000 students, if we want to do the exact same numbering which is actual number, then instead of 3 digits, you will have to use 4 digit sampling numbers. The first student would have been allocated the number 0, 0, 0, 1 and the thousandth student would have been allocated the number 1, 0, 0, 0. Now you will have to do all the processes with 4 digit numbers and if I can avoid one number by one of those 4 digits simply by shifting the sampling numbers backward by 1, why shouldn't I do that? Now the next step is to actually select the sample. Sampling number is what we have allocated. Now I have to use the random number table, the one that you just saw in order to select a sample from this population. You may find this very strange, but the process is that you would simply close your eyes and put your finger somewhere on that page and wherever you land, you will get the number. A 3 digit number is exactly where your finger has landed. Suppose that your finger lands on the number 0, 4, 1. This means that the first student who has to be selected in your sample is the 42nd student. Remember 42nd student was given the sampling number 0, 4, 1. So the sample size is 10 and your first element has been selected. What do you do after that? You don't have to keep your finger again because all the tables are totally random digits. Now you can simply go down and you will get the next number and then the next number and then the next number and you will get your sample. So as you now see on the screen, suppose that in this example the numbers that you obtain are 0, 4, 1, 1, 0, 3, 3, 7, 4 and so on. And accordingly the ages of the students that have been selected are 14, 15, 16 and so on. In this example, we are dealing with the ages of the students. And suppose that our first objective is to find the mean age of these students. Now the sample that we have selected, if we remove the mean of those ages, then that will be denoted by X bar and if we compute the mean age of the entire population, then that is equal to that is denoted by mu. The population mean age comes out to be 15.785 years whereas the sample mean age comes out to be 15.6 years. Students, these values I have computed in some way, we will talk about these details in a few lectures. So, you see that in this example, our sampling error means the difference between the sample mean and the population mean that comes out to be minus 0.185, it is quite small. And this sampling error came out to be so small because of the fact that it was a proper random sample. Whenever you do random sampling, the probability will be high that your sample is a miniature replica of the population. Students as stated earlier, there are various other types of random sampling such as stratified sampling, systematic sampling, cluster sampling and so on. As I mentioned, we will not have the opportunity to discuss all these different designs in detail in this particular course, but I would like to present to you a brief description of the concept of stratified sampling. The first and foremost point to be noted in this regard is that the procedure of simple random sampling the one that I just described is appropriate in that situation when the units contained in our population are similar to each other with respect to the object of our study. In other words, simple random sampling is appropriate when our population is homogeneous. In contrast, there are numerous situations where the units of the population under study are not all similar to each other. In other words, the population is not homogeneous but may be regarded as a heterogeneous population. Stratified random sampling is a type of probability sampling which is suitable in this kind of a situation and in this situation the population is divided into relatively homogeneous groups technically called strata. Students, let me explain this point with the help of an example. Suppose that a study is to be conducted regarding the advertising expenditures of the 352 largest companies in a particular country. Suppose that the objective of the study is to determine whether firms with high returns on equity that is high profitability spend more on advertising than firms with a low return or a deficit. Now since there is a considerable amount of variation between the 352 firms with respect to profitability therefore in this situation we cannot say that the population is homogeneous and we would rather divide the firms into various groups in accordance with their profitability level. The grouping being done in such a way that the companies that fall within a group are relatively homogeneous. Suppose that it was decided that the 352 firms should be divided into five strata as shown in the table that you now see on the screen. Stratum one consisting of those companies whose return on equity is 30 percent or higher. Stratum two the companies having return between 20 percent and 30 percent. Stratum three companies having return between 10 percent and 20 percent. Stratum four companies having return between 0 percent and 10 percent and Stratum five companies who have to suffer a deficit. Suppose you can see on the slide out of the 352 firms eight fell in the first group 35 in the second 189 in the third 115 in the fourth and only five in the fifth and last strata. The concept of stratified sampling is that once the population has been divided into various strata a simple random sample should be drawn from each stratum. In this regard the first question that arises is how large a sample should be drawn from the i-th stratum? The answer to this question is that stratified sampling can be done either by the method of proportional allocation or by the method of non-proportional allocation. Now the allocation is said to be proportional when the total sample size small n is distributed among the different strata in proportion to the number of units in those strata. In other words the allocation is said to be proportional if small n i is equal to capital n i multiplied by small n over capital n and students in this formula small n i is the i-th stratum sample size capital n i is the population size of the i-th stratum small n is the overall size of the sample and capital n is the total size of the population. In this particular example capital n 1 is 8, capital n 2 is 35 and so on and of course capital n the overall population size is 352 therefore applying the formula that I just presented small n i is equal to 0.142 times capital n i. Applying this formula on each one of the five strata that we have in this example we obtain small n 1 is equal to 0.142 times 8 and that is approximately equal to 1. Similarly, small n 2 comes out to be equal to 5, small n 3 is 27, small n 4 is 16 and small n 5 is equal to 1. This leads to the table that you now have on the screen and as you can see this table shows that if a total of 50 firms are to be selected for intensive study then one firm with a level of profitability of 30 percent or more will be included in our sample, five firms in the 20 to 30 percent stratum would be selected in our sample at random and so on. So, students this is the procedure of stratified sampling by proportional allocation. Yani jo proportion overall sample size ka overall population size ke saath banta hai, wohi proportion har stratum ke andar maintain hota hai. Students regardless of whether the stratified sampling has been done by proportional allocation or non-proportional allocation the important question is what is the advantage of this particular type of sampling. The answer to this question is that stratified sampling ensures that every group present within the heterogeneous population is represented in the sample. In the example that we just discussed it is worth noting that only two percent of the firms fell in stratum one and only one percent in stratum five. Agar hum simple random sampling karthe poori population me se ekhi martabha simple random sample draw kar lete to aan mumkin tha ke in doh strata me se koi bhi company hamare sample me shamil na hoti. But a stratified random sample ensures that at least one firm from stratum one and one from stratum five are represented in the sample. In other words in such a situation stratified sampling has the advantage of being able to reflect the characteristics of the population more accurately than simple random sampling. So, this was a brief introduction to the concept of stratified sampling. But students in this particular course all the techniques of inferential statistics that we will be discussing in the forthcoming lectures they will be with reference to simple random sampling the one that is applicable in the case of a homogeneous population. Students this brings us to the end of today's lecture and I would like to encourage you very much to study in some detail the concept of sampling. Best of luck and Allah Hafiz.


We all know that we should be adding chapters to our YouTube videos, don't we? But I don't know if you're like me, but sometimes it's something that I don't always get around to. And part of the reason is just the process of going around, watching the video back, figuring out where those markers need to be, jotting them down, copying and pasting them into the description. I'm making excuses here, but there's always a little bit of friction for me to do this. Well, fortunately, there is a really easy way to do this now with TubeBuddy. So let's have a little look at the TubeBuddy chapter feature that was recently added. So I'm over here now in a video that I've just made, and I haven't got any chapter markers in here. There are two places where we can access this function. First of all, is if I just bring this up a little bit and scroll down, you'll see that not here through the description, but rather down here, you'll see we've now got this button here that says Add Chapters. You can also access it, though, when you go into any video from this little TubeBuddy icon just here, underneath the thumbnail at the top left. And then you've got, in here, there it is, miscellaneous. You've got the chapter editor just there. So clicking on either one of those things is going to bring up a view like this. It will start the video playing.  This is part of the reason why I don't like adding in chapter markers, because it means I have to go and listen to myself back.  And so as to half the agony, I actually just increase the speed here to playback speed is double so that it gets over and done with as quick as possible. And now the way that this works is I'll just turn the volume down on here just so that you are not going to actually hear it on my roadcaster. But now what you'll notice is over here on this side, you'll see that it has actually already put in that first introduction checkmark. It gives you some of the rules that you need to be aware of in adding in chapters in YouTube. This is not a TubeBuddy. This is just a general thing on YouTube, but it does actually explicitly state them here. So chapters must include a minimum of three chapters. So within the video, you have to have a minimum of three if you are going to use chapters. All chapters must be at least 10 seconds long. So you can't just have a load of chapters really close together for SEO spamming or something like that. And then the next one is all chapters must have titles.  And this is now playing back. I can't hear it at the moment. But if I was doing this properly, I would do. And what you can notice is that as well as having the timeline moving along here, we've also got this timeline moving along just down here. And if we've come to a key area where we want to add in a chapter, all we do is we just click on the little plus and you'll notice that it's paused the video. And then it's come over here and it's created this chapter and it's already put in the time. So let's just say this is whatever I was talking about there. Let's call that software update. This was about the Stream Deck software update. So I can't talk and type. So there we go. I assume I've just typed in a really relevant title there. And then what we do is we come back over to here and we hit the play button again and the play heads moving and then it's still moving down here as well. So we'll let that play out a little bit. You could also just jump around if you know that you've jumped around, you don't have to actually watch the whole thing back. So if I say, okay, well, there that was definite transition, I could just click into here and you can see that this timeline has moved along as well. So this is where I'm going to start talking about the next section. So click on the plus once again, it's paused it, it's come over here, inserted the new chapter. And this is the next chapter. So that is the way that this works. As you can see, pretty simple. I can move forward to another step, add another chapter in there. And so let's call this the final chapter. And there we go. So then once you've done that, all you do is you can copy to clipboard and it will copy all of that text to clipboard. Maybe you want to use this somewhere else as well. But you can also just click in here, add to video. When you click add to video, as you can see, it says your chapters have been added to the description, please review and click on save. So just click on okay, it hasn't been added until you click on the save, because what's happened is if you come down to the very bottom of your description, it's basically just added these chapter markers just there to the very end in the format that they need to be for YouTube. So chapters need to start with this 00,00, and then introduction or whatever you want to call it. And it's just added in all of those chapters there. If you do want to then make sure that you save those, all you would do then is just click on the save button up there. This makes it really streamlined. It saves the whole sort of starting and stopping or maybe looking at it in your editor or whatever. And then adding them into a text editor or typing them directly in here, just a really slick, seamless way to do it. TubeBuddy is being a real lifeline in terms of starting my YouTube channel and with the continued growth of it and these sort of analytics and things like that. I highly recommend it. You can get a free trial at takeonetech.io slash TubeBuddy. And to really get the most out of it, what I really recommend is that you check out my TubeBuddy playlist, which is coming up, which will teach you about all of the different features of it. So I'll see you in those videos.


The Linux show starring Nick Carter, master detective presented by the three great Linux home Brighton This is the story of a man known the world over as one of the most daring and resourceful characters in the history of detective fiction a Man whose name has become a symbol of the triumph of right and justice over the sinister forces of crime and lawlessness Nick Carter master detective Today's exciting case the talking tree another exciting chapter dramatized from the life story of Nick Carter In just a moment We'll hear how Nick Carter Investigated the murder of a beggar with a fortune in his pocket and found the solution to the strange case of a talking tree And now for today's exciting case from the life of Nick Carter Today is file index day at the old Brownstone mansion at the corner of fifth and fourth The giant study is filled with piles of neatly typed cards as Nick and Patsy keep regular tabs on the thousands of criminals The famous detective has encountered in his long career Charlie buzz burns tried and convicted for forgery July 1941 sentence August 1941 to seven-year term and eating penitentiary check Well, that finishes the deal that the fees Okay, but it feels like it's gonna be a long hard day Albert cabal tried and convicted the first degree assault April 1931 hold it Bell's on a parole for his card in the active file with a note last seen in st. Louis July of this year, right? Johnny Kevin tried and convicted. Oh goody the door. That means a five-minute vacation wherever it is Send him away. We've got to finish this job. I will but my heart won't be in it Johnny Kevin tried and convicted the second degree murder life time at east and state I remember Johnny He was the one who swore no private detective was ever there to take him wrong The no friend of mine this Mr. Peter Simpson. He takes me writing twice a day. Thanks for writing twice See street garden up there. That's a Mr. Carter Miss Bond takes my car every morning every night at the cross-town passes right behind his house Mr. Simpson's got a problem. One of his customers won't get off the trolley. How's that? Well, she ended my run behind your house, so I left the trolley there and run up to see you I remembered miss Bowen talking about how you help folks out when I get in a jam I'm in a bad one sir. What's the trouble?  Carter? He's been murdered This is my trolley car here, mr. Carter. I closed the doors and left everything wait a minute. I'll open a door for you Come up sir He's in the back of the car. You can see him. He was the last one and I said to him last stop wall out He don't move. I thought he was asleep. I understand. Yeah, fine. I thought you would. Oh, Nicky He's been stabbed. There's a nice sticking in his side. Yes wait Well, not dead yet, but it will be in a minute bleeding for half an hour mostly internal can't be moved or say Oh wait trying to talk Where with you can you tell us who did this on? Valley what that's don't valley talking Free what was that? talking tree killed by talking mean Oh He's dead. Oh, this is awful. Mr. Carter.  All right I was got to work that day Emptiest pocket Collie Nick, what do you mean killed by a talking tree and Been saddling about a million dollars. I don't know Dying men usually speak the truth I'd like to know what the truth is about that talking tree Nothing worthwhile in any of his pockets badly A torn and empty no handkerchief no wallet 27 cents in chains total asset. Oh So where do we stand exactly nowhere? What do you mean? No identification of any kind in this man badly nothing to tell us who he is or why he was killed What about the murder weapon that knife that's an ordinary kitchen knife no prints on the handle Golly Killer probably sat beside him drove a knife into his side got up and left the trolley.  I don't know yet That wait a minute. Oh here's something I overlook Seems to be a hard lump in the front corner of the jacket probably slipped down from the torn pocket here. Wait a minute What is it Nick? Answer to your question Look It looks like a big lump of crystals happens to be an opal opal You mean that rough piece of material looking stone is a dual opal uncut and unpolished That's way about 30 terits with quite a bit of money That's he that's maybe the answer to why our victim was killed No, it doesn't answer the question of how it came into his possession Or explain his dying speech about talking trees. What do we do now? Leave the body for sergeant mathison and our friends at the homicide department We're hustling down to the dual center where there's opal tampering with evidence again, Nick Or maybe that's what the police would call it that I call it solving a murder I see I'm going to give you a lesson in the art of jewels Every person doesn't realize that jewelers keep track of gems as closely as the police watch x convict Every stone of any real value cut or uncut can be checked and traced Here's that place international appraising company. Well, there are dozens of appraising officers down here as anyone will do Come on, right? Customers I'm just going out to lunch But I'd go to world appraising across the street. I won't keep you a minute. Come on out. I'm nick Carter Listen, I got bad suggestion. That's good for me to miss my lunch hour What's in your mind? Mr. Carter trouble plenty case of murder. It's happened to be one of the clues, mr. Bowman, let's see That piece of opal, huh, right? I'd like to trace it now Which doctors come from general source and so on who sells this variety I can do better than that I put a price on this stone an hour ago. You what you heard me lady This stone was brought into me an hour ago for appraisal. I gave him the price me left. Hey, how many? Two men Little guy looked like a tramp and the other Nice looking Kind of professional looking doctor, maybe Looked like the tramp was trying to sell this down to the other called in professor Professor steven. Professor steven. Good enough for me. Thanks a lot bowman. What's your fee? I've been paid one for appraising this down. That's enough Now go away. I got my digestion to worry about. Thanks. Come on patty. Let's find a university catalog Maybe we can locate this professor stevens and find out about the talking tree Okay, patty. You're going uptown rock make Any luck all the luck in the world professor. WA stevens chair of mineralogy at the university office 227 geology hall Mineralogy well that you could tie in with opal, can't it? It also tie in with a million dollars in the murder Wish our dead friend had been with a botanist that would have explained the talking tree Well, maybe we'll find a stevens doubles in botany or ever bet you've been cut off. Watch out Let me handle it. That wasn't an accident. Say right where you are carter You tell lady I got a rod and a license to carry it Well, hello carpent patty meet double the carpent when we get back to our file cards You'll meet him in the sea can the double torque retain carter Now look, I don't want no trouble from you Keep the opal if you want Just give me the math what math this is a friendly talk.  So okay You want to catch the killer good luck? But being family with my pal.  We didn't hold it, but it How much is the map worth to your dub z?   I speak mine I'll be seeing you again carter And I'll let something else talk you into handing over the math That's car passing So long dub z Remember what I tell you To the university passing Maybe professor Stevens can tell us what's going on This is it Nick. Let's go Garly I'm often mixed up in this case Nick. Well, it isn't simple The man we found in the trolley was Sammy the bum. That's what dub z coffin indicated right in here Well from the way coffin talk it didn't sound as though he saved him Could simply be talk Suppose it could But he mentioned the map. Do you think Sammy was killed for that? Very possible I think there's Evidently there's a map tied up with the opal Sammy was carrying Yes, but it's my belief the opal's just a side issue Carpenter didn't seem to care about that and Sammy tried to send it to professor Stevens. Then what what? Professor Stevens office Maybe he's got a class could be Let's go in and wait To wait a long time to speak to professor Stevens that he's been murdered Two murders for an opal a missing map and a mysterious talking tree How can nick tie these strange events together? We'll see in just a moment I believe that this nation should commit itself to achieving the goal Before this decade is out Of landing a man on the moon and returning him safely to the earth And now back to our story The dying words of a murdered tramp mentioned a talking tree to nick Carter Investigation of the murder and the odd statement led the master detective to the office of professor Stevens at the university When nick and patty entered the office they discovered Stevens murdered Stevens a shot at close range with a thought of shotguns at the typical gangster's weapon Head practically torn to pieces. Oh, it's awful nick Nothing in his pocket to help us either Nothing So where's that leave us about one jump ahead of the homicide squad They won't be pleased with the way I've handled this case sergeant Madison would call it miss him and he won't be far from wrong I'm not happy myself Well Let's get on the ball patty. Let's do some thinking. It's your department nick. I'm just the audience Sammy got hold of an opal and a map We know he showed the opal to Stevens. Mm-hmm. We don't know about the map Stevens and sammy were killed The map disappeared Now what's so valuable about that map it showed the mind where the opal came from The patty opals don't come from mine they could What is it nick? Suddenly my brain started to work Suddenly I'm getting a glimmer Patty. I think I know what this talking tree business is what nick look here on Stevens desk There's an atlas open to this state. Mm-hmm. I look across the page where the light hits it. Yeah You can only see what I want to show you by reflected light Are you seeing anything unusual? Oh, wait a minute. My eyes aren't as sharp as yours Yes I see a faint pencil mark as though a pencil point that taps the map lightly in a small town The town of dead tree Remember that that's a dead tree But that isn't talking tree true enough and I think that at dead tree we might find a talking tree And that's the it's going to speak a language that'll astonish you who don't be so mysterious nick. All right. Here's another clue Opals don't grow in mind. They grow on trees Oh, you're crazy.  Come on Golly, I'm getting inferiority complex. It's going to light three laps behind you the way I do The only trouble in this case is that I happen to be three steps behind a killer. Well, that puts me out of the running Back to the three round walk to the corner. Oh, nick That's my luck. I haven't got a gun on me down the hall run. It's a killer. This is a well-wisher Oh, this hole is the dead end we're trying Here through this door Patty quick Oh That was close. That's too close. Not that for us that door wasn't locked. Did you see who was going to shooting? No, and the trouble is he saw where we went. What are we going to do? He was looking fine to repel the attack Now it's a small lab at some sort. If I can only find... Oh, yeah, Nick, I can hear steps Oh, got it, Patty. Get up the matches quick. Matches? You heard me. Oh, what are you going to do with matches in that bottle? You're going to light a whole pack of matches and throw it out into the hall. This bottle is easier I'll break it near the burning matches I'd like the matches quick They're burning, Nick. All right. Now throw them out as soon as I open the door and I'll throw out the bottle right now All right, Patty. All clear now. You can come out. Is he still here? Yes. Knocked out and burned by the explosion. He'll live and regret it. Who is it, Nick? One of Dudley Coffin's gunmen. Hophead kid named Vern. Oh, I guess Coffin wasn't kidding about letting something else talk to him But he forgot that some people talked back. Now listen, Patty. In about 20 seconds this place is going to be like a beehive I can hear people coming now. It wasn't Saturday afternoon. The place will be crowded already. Now we've got to get out of here. Well, then let's go. Not together. When we're picked up, they see us running. We'll separate and meet at the car. Okay. Try to stop at a drugstore and pick up some sandwiches. We've got a long drive ahead of us. Where to? Dead tree? Right. We're going to Dead Tree to find the talking tree. You've got a sandwich, Nick? No, thanks. You can finish them. I've eaten too many already and I'm supposed to be on a diet. They weren't the best sandwiches I ever had either. I feel as if I were getting bowmans into Jesse How much further is it, Nick? It's getting dark. It should be in Dead Tree any minute. We've passed six signs in the last six miles. Each one said Dead Tree half a mile. Well, at least we're holding our own. It should have added a prox. I think we're a prox there now. Looks like a town. What do we have of it? Well, give me a second to get used to it. Yeah, it's a town all right.  The sheriff's office? Right. Come on. Oh, we're not going to get in trouble again, are we? I've got visions of Sergeant Madison waiting for us back in town. He'll greet us with comparatively open arms if we bring him home a solution. All right, let's go in. Okay. Yes. Is this the sheriff, uh... Jason. Yes. Well, my name is Nick Carter. Yes. Chef, Denson, I'd like to ask you a few questions. Yes. I assume that means go ahead and ask. Yes. Do you keep any kind of a check on vagrants passing through Dead Tree? Yes. Do you recall whether a tramp answering to the name of Sammy the Bum passed through here last week? Yes. How long was he in this section? Don't know. Maybe a couple of days. Golly! He can say something else, can't he? Please, Patty. I can talk, young lady, when there's something worth wasting breath over. Why is this town called Dead Tree? On account of a section of sandy waste up in the hills. You mean desert? Yes. Kind of like the desert up in Maine. Wind swept section, about 10 miles square, nothing but sand and rocks. All eroded. I thought so. Probably petrified trees up there too, huh? Well, that's what gives you town's name. How'd you know, Nick? Couldn't be any other answer, Patty. Two more questions, Sheriff. That desert area is constantly enlarging and changing as the wind sweeps it, huh? Yes. Will you show us how to drive there close as possible? Yes. Sheriff, are you 170 years old? No. Patty, for the love of Pete. I'm sorry. I just wanted to hear him say no, and I did. Great. We can't drive any further, Patty. We'll have to hook it through the desert. Golly. It looks just like the real thing, doesn't it? Sand and rocks? And petrified trees. Come on. We'll have to keep pretty quiet now. This sand was dead in our footsteps, fortunately, because of the strong chance the killer may be up here ahead of us. Oh. Do you know where to look for him, Nick? I do. We'll find him under the talking tree. Oh, Nick. I'm not fooling you. Oh, all right if you say so. But where we find the talking tree? I'm not sure. We'll have to listen for it. Listen for 10 square miles? We won't have to cover that much. See, if Simon located it, it couldn't be very far off the road.  So the tree can't be far from here. Oh, I'm listening for it like mad. I don't hear anything yet. Keep trying. It's awfully dark, Nick. Can't we use a light? Hey, for not to. Keep your ears open. Okay. Golly. Those twisty black tree stumps. They look so spooky. They're petrified trees, Betsy. Dead thousands of years. They can't hurt you. Well, I wish they'd talk to me and get this over. Maybe they will. Keep listening. Yes. I think I hear a funny noise. Like water running. Not here in this desert. No, not water. It sounds like... like music. Hmm? Listen. I hear it, Betsy. That's what we've been searching for. The talking tree? That's the way those trees talk. Coming from around that small hammock. Oh, come on. Let's go interview it. Careful now. Very careful now. I think I hear someone digging or something. The killer. Here? Told you we'd find him under the talking tree. Quiet. And watch. What did he not petrified tree for? Let's go down and ask him. Oh, Nick, be careful. You haven't got a gun. I've got something he'll take it, please. Good evening. Have I held you? Call her. What? It's an Anthony appraise. Bowman. Don't mind me calling her. Don't move. You're calling. I am I. That's rough talk. Must be difficult for a man of your culture, Mr. Bowman.  Professor Steven. Me? All right. Call her. You're asking for this. Oh, my God, Nick. Here you are. What's going on? Oh. Oh. Professor is a rank amateur when it comes to handling a gun. Oh, nice going, Nick. How'd you do it? Barely through a handful of sand in his eyes. And when he was blinded, hit him. That's all. That's all. Well, that's enough. Now you have his gun, and he's out cool. And he's also on his way to the electric chair. Nick, do you mean to tell me Professor Steven's murdered Sammy the bum? Yes, Patsy. And that pretend he was killed himself. And he did all that for the sake of a dead tree? Well, take my flashlight, Patsy, and look at that dead tree. It's all crystal and glittery, and... Oh, it's like a tree of jewels. Pure opal, Patsy. An opal tree, worth a fortune. Too bad we don't hang killers in this state. To be an excellent place to hang Professor Steven. We'll return to Nick Carter in just a moment to hear the final details of the Talking Tree. The happy birthday, W-O-R, from Pointy Towsky Brothers of Flemington, New Jersey. Pointy Towsky Brothers. And now let's hear from Nick Carter himself. Nick, you'd better start at the beginning and explain everything. I'm entirely at sea now. All right, Patsy. The story started millions of years ago when the trees of dead tree valley died. It started petrifying. Uh-huh. After untold centuries, deep under the ground, they turned to stone, and then began to crystallize into opal. Today, as the winds slowly ate away the sand and earth covering them, they were brought to the surface. And when Sammy went out to sleep in the desert, he slept under this opal tree that had been uncovered by the wind. Right. The talking part was the tinkle of the crystalline branches swaying in the wind. Sammy broke off a piece of the tree and took it into town. Went to Steven's for advice, since he didn't know the value of that opal. Well, then what? Steven saw the maps Sammy had made, and, of course, the jewel. He went with Sammy to have it appraised, just to make sure it was valuable enough to pay him to commit murder. When he found it was, he killed Sammy for the map. But he staged his own murder, too. Why? Sammy talked too much. Stevens didn't know Sammy had told his old pal, Dudzie Coffin, but he did know Sammy told the real bowman, the appraiser. So, to protect the secret, he killed Bowman probably only a few minutes before we entered the store. You remember he stalled before coming out to talk to us? Oh, that's right. I remember he talked about his indigestion. He pretended to be Bowman, then rushed the body to his own office at the university, perhaps in a laundry basket or a bag. And there, staged his own death. He didn't know it, Nick, but that was just a preview of what's really going to happen to him. It doesn't pay to play act with Nick Carter. Well, that was an unusual tale, Nick. Now how about a preview of next week's story? What's it going to be? Well, next week, Ken, I'm going to tell you about the case of an 80-year-old man, feeble, sick, harmless, who suddenly began driving down the highways like a savage, injuring people, wrecking cars, and generally behaving like a maniac. Oh, I remember. It was all because of a beautiful Egyptian queen who died 3,000 years ago. Breaking traffic laws because of a dead queen. Sounds good. What do you call the case? The case of the queen's eyebrows.