Here we continue our lecture on descriptive statistics. Welcome to the lecture. This is just to remind you of what you already saw in the first part of the descriptive statistics lecture. We are looking at measures of location. We did that already. Now we start and we continue. We look at measures of dispersion, measures of shape. And looking at different ways to combine measures together. Some of that is actually going to be done in standardizing data, which will be in another lecture. And working with data from two variables, which is not here, will be in another lecture. This is all a single variable. So we still have a lot to do. Why do we need to look at measures of dispersion? Maybe mean is enough. Well, this example will show you why you want measures of dispersion.  And they've got to have an average life of at least 10 years. You have a choice of two suppliers. We'll call one supplier A, supplier B. If you're smart, you take a random sample of chips. In this case, they took a sample of 10. And look at the data. The data is right there. You can see the mean for supplier B's chips is 94.6 years versus 10.8 years for suppliers A chips. Which one would you use? You only look at the mean.  So that's the one you choose. But if you look very carefully at the data, you'll see A is very consistent. The chips, the 10 in your sample, every one of them lasted 10 or more years. But look at B's chips. Some lasted 170 years. You don't need that or 160 or 150 years. But several of them didn't even get to year three. In fact, four of them, four out of 10, didn't make it to year three. So we need a way to measure this kind of dispersion or variability if you like. And certainly, if you're smart, you don't take chips made by supplier B. And the measures that we're going to use, we're going to look at a whole bunch of measures of dispersion. But now at least you understand why you want measures of dispersion. If you didn't look at measures of dispersion, you would make the mistake of buying chips from supplier B because the higher mean, even a higher median too, in fact, those are measures of location. But we're going to look at other measures that warn us not to buy chips from supplier B with so much variability. What do we mean by dispersion? It's like the spread of the data.  If they're all very, very close to each other or very close to the mean of the data set, obviously it has a very small spread. What about they're very far apart? They're all scattered. They're not near each other. And they're far from the mean of the data set. That has a high dispersion. So we're going to look at five measures of dispersion, the range, the interquartile range. The last three are really almost the same thing. Variation, variance, and coefficient of variation. We often do them together. Those are the five measures of dispersion we're going to examine. The first measure of dispersion we're going to look at is the range. It's the obvious one. We're all born understanding it. You don't need to take this course. You certainly don't need to be a statistician. You can even explain this to your boss. The range is just the range of the data, the largest value minus the smallest value.  The range is the largest value minus the smallest value. 30 minus 1 is 29. Isn't that easy? You don't have to know the center of the data. You don't have to know how many data items you have. Just the largest and the smallest. Easy to explain. You can explain the range to anybody. Anyone can understand it. That's a huge advantage. What's a disadvantage? A disadvantage is if you have any extreme value at the low end or at the high end, it's going to blow up the range, and the range won't really be a very, very good measure of dispersion. Imagine if all the values are close to each other or close to the mean, and then all of a sudden there's one out at the high end. That won't be a very, very good summary measure of your dataset as a whole. The interquartile range is just what it sounds like. If you remember your quartiles, it's the range between Q3 and Q1. Instead of taking largest value minus smallest value, we take the value of the third quartile minus the first quartile. What happened over here? Look at the data. Sample size is 15. The interquartile range is Q3 minus Q1 or 22 minus 3. That's 19 as opposed to the range, which would have been 98. Look at that huge value at the end. 98 is the largest value. 0 is the smallest value. The range is easy to understand, but in this case it doesn't really give you very much information. The interquartile range now is a smaller number. It's a number that's easier to understand. But the way to understand the interquartile range is that it is the range of the central 50% of the data. If you take the central 50% of the data and separate it out, and you can do that easily with quartiles, the range of that is the interquartile range. Any extreme values on the high side or on the low side are basically thrown out, right? They're not thrown out in this case. Looking at them, they don't affect this measure of dispersion. Of course, that's also its greatest flaw. Data is very expensive. It's expensive to purchase. It's expensive to collect. What we're doing here in order to compute this measure is throwing away 50% of the observations and only looking at the central 50%, the range of the central 50%. Let's see if we could do better. Let's look at the standard deviation. This is one of the most famous measures of dispersion. What is the standard deviation? Deviation from what? It's deviations around the mean. It's kind of an average. You're averaging out the deviations. It's a little problem, though, if you just look at the deviations around the mean. The deviation around the mean mathematically would be the sum of xi minus x bar. If you do that, you'll get zero all the time. The average deviation is about the mean, which is zero. The reason for that is you'll have plus deviations. Some of your values are above the mean, some are below the mean. They kind of always work out mathematically to give you zero. That's why we can't just take an average deviation. Here we see the formula for the standard deviation. It's called a definitional formula. We take the average deviations, but we don't want the pluses and minuses to balance each other out, so we square the deviations. We take the sum of the xi minus x bar. That's the mean of the data set. We sum it, and we're summing squares. It's called the sum of squares. We divide by n minus 1. You'll ask why we're going to take an average. Divide by n is the reason. Mathematically, we'll get to it. There's your formula. That's called a definitional formula. It has lots of interesting mathematical properties. One I mentioned, you don't sum up to zero. This is also a minimum, this sum. No other value subtracted from the data set, from the x's. No other value that you look for deviation of the square will give you a smaller value than this. It's called the least squares property. And finally, which I mentioned already, we divide by n minus 1.n. It's called a loss of a degree of freedom. You'll see it's a mathematical adjustment. We're looking at two data sets. We'll call them x and y. Notice, they both sum up to 15. So the average is 15 over 5. So both have the same average of 3. Yet, we'll see, look at the variability. The first one, the x's, are relatively close to the 3. But the second data set, you've got zeros and tens. Obviously, there's a lot more variability. We'll see what that does. Look at the x's. First column is the data. 1, 2, 3, 4, 5. The mean was 3. We're looking at the third column, which is deviations. Minus 2, minus 1, 0, plus 1, plus 1. Notice it adds up to 0. Now we have to square them. So we square each of those deviations. Again, it's called the sum of squares. So we take each of the deviations, square it, sum it, and we get 10. Now, you take 10. Remember, it's n minus 1. You divide it by 4. Take the square root of that, which is basically the square root of 2.5. And you get 1.58. So the standard deviation for x is 1.58. Now, look at the y. You see the deviations are much worse, much higher. You've got 0, 0, 0, 5, 10 in the first column. The mean is still 3. So it's 3, 3, 3. But look at the deviations now. Minus 3, minus 3, minus 3. 2 is even 1 of 7. The sum of square deviations, or the sum of squares, notice it's 80. I think 80 divided by n minus 1, 4, and that's the square root of 20, which is 4.47. Notice the standard deviation for the y's, the y dataset, is 4.47. The standard deviation for the x is 1.58. This is what we saw intuitively. The variability of the y dataset is much more than the x dataset. Now we're going to explain why we divide by n minus 1, generally. The reality is if you took a census, you'd have no problem. Then you'd be trying to measure the population standard deviation. Notice the formula is also the sum of the square deviations, but not using mu. It's a population. You have a census. Now you divide by capital N. There's no bias here. You don't have to worry about any kind of bias. So the formula, and again, you have to be careful when using a program like Excel. This standard deviation, you have to divide by n, and I think Excel calls it standard deviations underscore p, to show you that it's a parameter or a population. But normally, in this course, we're going to always assume you've taken a sample. That generally works in the real world. You're taking samples. Now when you're taking samples, s is supposed to be estimating sigma, the population standard deviation. Now mathematicians have shown us that when you do it, you must divide by n minus 1. Otherwise you're going to introduce a bias. S will not be an unbiased estimator of sigma. If you want an unbiased estimator, then you have to divide by n minus 1. Again, those of you who have more advanced mathematical training can look this up in a math book, you'll find out why. That's why we divide by n minus 1. All you have to remember is that when you're getting the standard deviation, if you're working with a census, which is rare, then you'll be dividing by n. If you're working with a sample, you take the deviations and notice you're using x bar, not mu. That causes the bias, actually. So you're taking the sum of the squared deviations around the x bar, you divide by n minus 1, and now s is an unbiased estimator of sigma. So you'll hear the term losing a degree of freedom. Essentially, if your boss says, why are we dividing by n minus 1? I'm sure we'll be averaging it. You tell your boss you're right, but mathematicians show us this introduces a bias. So to get rid of that bias, we must divide by n minus 1. And you'll see this in Excel, too. That this is a standard deviation when you're working with a parameter or population, and it's a standard deviation when you're working with a sample or a statistic. The next measure of dispersion, the variance, is really just exactly the same as the standard deviation. It's a formula that takes the standard deviation and squares it. Or conversely, when you've got the standard deviation, you ended up the process with a square root. Well, everything that was under that square root is called the variance. It's easier to explain standard deviation because you're using the expectation that we want something that's kind of averaging our deviations and it's a form of averaging it. So it's harder to explain the variance. In addition, the standard deviation is in the same units as the original data. The variance is in those units squared. It's harder to explain that. But it's still a valid measure of dispersion and it's used all the time. Where are you going to use the definitional formula? Same as before, same as with the standard deviation. The definitional formula, why do we like it? It helps you to understand what you're doing. You can see the deviations there. You can see the sum of the deviations squared. So you know you're looking at deviations and it helps you to understand that you're looking at the spread of the data about the mean. The computational formula is the one that you need to use if you're doing a computation with a lot of data. If you're using a calculator, you'll use your memory. Most likely you'll be using something like Excel or some kind of statistical package. Or for some people who write those statistical packages, they're going to be using the computational formula. The computational formula is it sounds as you can tell from the name. It's easier for computation. In addition, there's less rounding. In the definitional formula, as you'll see when you do your own problems, X bar is a mean you already have rounding there. Every time you subtract it from a data value and then square it, you're compounding the problem of rounding. So there's a lot of rounding in the end. We don't care because right now all we want is for you to understand it. In the real world, when you do this for real as a user as a statistics or as a statistician or as a business person or as anyone who has to deal with numbers, you're going to be using the computational formula and you're not even going to have to know the formula. It'll just be what's being used in Excel or some other software package. But what I want you to do and what the other Professor Friedman wants you to do is to understand the formula that you're using in order to measure dispersion. Finally, the final measure of dispersion we're looking at is the coefficient of variation. The coefficient of variation is a little bit different from the others is it doesn't only measure dispersion in the data, but it creates a raw number, a perfect number percentage and that means that you can compare data sets because you're not comparing apples and oranges in the classic metaphor. Look at that formula. You can see that what you're doing is answering the question what percent of the mean is the standard deviation? So you're looking at the standard deviation in relation to the mean. You can do that because they're both in the same units and when you cancel the units you get a pure number. You multiply by 100% and you get a percentage. So for example if you find a coefficient of variation that's 100%, it means the sample mean is equal to the sample standard deviation, wow that's a lot of variability. And what if you find the coefficient of variation is 200% certainly that's even worse. So if what we want to do is to look at more than one set of data we probably want to include coefficient of variation in our metrics in our summary statistics, in our descriptive statistics. Why? Because we cancel the effect of the units if we're using coefficient of variation so that if for example, and we have a couple of examples here if for example you're looking at two stocks and you want to compare them and see which is more variable, which is more volatile and one is in dollars and one is in yen or in some other currency. How do you know? Just looking at the numbers. Well, the mean is in the units, let's say dollars, the standard deviation is in the same units, if we divide one by the other we're getting around the effect of the units and looking at just a pure percentage. The same thing is true by the way, even if both data sets are in the same units but are in order of magnitude very, very different. In this case, the example is saying what if you have a stock that sells for around 300 as opposed to one that sells for about 25 cents. Go even further. How about if you're looking at income data and one data set is in the millions and the other data set is around minimum wage. You can't really compare the volatility there's no way to know until you actually get the metric where you're canceling the effect of the units. So the coefficient of variation is not only a better measure of dispersion in these cases it's a very necessary measure to have at our disposal. Those of you interested in finance we have an example here with two stocks. Look at stock A and stock B. Now if somebody asked you, a customer, a client says which one is more risky or volatile, these volatilities are a term in the stock market. If you just look at the standard deviation of variance, look at the standard deviation for stock B it's 11.33 dollars. Look at the standard deviation for stock A it's a dollar 62. You might make the mistake of saying well stock B has a much higher standard deviation it's more volatile. But you'd be wrong. Look at stock B the numbers are really very close to each other your mean is very high your average is 188.8 so when you look at deviations you get big numbers relatively speaking because $210 minus 188 so you're looking at $22 Now look at stock A the average price of the stock is $170 so your biggest deviation is minus $170 just $3.30 so you might again looking simply at the standard deviation or even the variances you'd make the mistake of thinking stock B is more volatile. Notice what happens when you look at the coefficient of variation which is not in dollars the variance would be in dollars squared the standard deviation is in dollars coefficient of variation is a percentage so the coefficient of variation for stock A turns out to be 95.3% showing you that's a lot of volatility that's incredibly volatile stock A you can see looking at the numbers this stock at one time was 20 cents in August and then it jumped up to $5 in July and then you see it's been jumping around all over the place you can lose a lot of money investing in a stock like that stock B look at the coefficient of variation it's 6% because it doesn't vary that much it was $210 in August and it was $175 in February but that's not as huge a jump as you see with stock A so the conclusion here is that do not use the standard deviation to compare two stocks use the coefficient of variation that has no units it's a percentage and essentially gives you the idea of the standard deviation what percentage is it of the mean let's look at a problem we're going to get all the basic descriptive statistics okay the data has been ordered for you starting with 0 there's 10 observations 0, 0, 40, 50 all the way to 100 okay now you're asking the descriptive statistics well the mean you add them all up the sum of the x which is 560 divided by 10 so the mean is 56 the median remember what you got to do when n is even you look at the two middle values the median q2 is 55 okay the mode well which one came up most frequently well it seems like you have three modes 0, 50 and 100 okay the approximate q1 and the approximate q3 remember the numbers below the median you have five numbers so q1 is 40 taking the median of 0, 0, 40, 50, 50 do the same for the above the median 60, 70, 90, 100 so the median of those five numbers is 90 so q1 is 40 q3 is 90 the range okay now are measures of dispersion the range highest minus lowest 100 minus 0 the range is 100 then to quartile range q3 minus q1 and you got 90 minus 40 which is 50 the variance take each number minus the mean and square it so you are going to do 0 minus 56 squared 0 minus 56 squared 40 minus 56 squared until you get to 100 minus 56 squared okay those are the sum of squared deviations the sum of squares that's 11,840 remember you divide by n minus 1 10 minus 1 is 9 and there is your variance 1,315.5 the standard deviation just the square root of that which is 36.27 and the coefficient of variation is a percentage 36.27 which is the standard deviation divided by the mean of 56 times 100% and you have a very variable data set it's the coefficient of variation of 64.8% that's quite variable we have looked at measures of location in our data in other words where this data sits on the scale of real numbers and especially the central location measures of central location the center of gravity of the data then we looked at measures of dispersion how far apart are the data from each other how far apart or how dispersed is the data around the mean how large is that the amount of data and now we are looking at the shape of the data is the data symmetric about the mean or about the median or is it a skewed by extreme values either on the right or the left if our data is skewed it could be positive skewed or negative skewed if it's positive skewed it means that there are extreme values on the high side and so the mean is greater than the median if it's negative skewed it's the other way around it means that there are extreme values on the low side and so the mean is less than the median and of course this is nothing new to us because we already know that the mean is affected by extreme values while the median is always going to be the center point of the data here is the same explanation only with pictures graphical explanation you can see that if something is left skewed it's pulled to the left by an extreme value or more than one if a distribution is right skewed it's pulled to the right kind of imagine an elastic band being pulled by some large data value if it's symmetric you don't see either one of those than the data set is symmetric around the central location the measure of central location let's examine a data set we're looking at 12 employees and determining how long it took each of the 12 to complete a certain task note the fastest employee did it in 2 hours 8 hours and then the maximum value was 63 hours somebody took a long long time any case you look at the mean of this data set and the mean is 180 over 12 which is 15 hours the median is 10 hours when you see a huge discrepancy between the mean and the median that tells you something it usually indicates what we call skewness notice the mean is much higher than the median again the mean is 15 versus a median of 10 a 5 hour difference now what caused that why are the mean and the median so far apart and obviously you look at the data you'll see there's one value you might call it an outlier that 63 seems to be very different from the rest that 63 throws everything off now what happens when you have one very high value it makes the mean higher but the median which is really location stays where it is so the median is 10 but that 63 now throws the mean so it's much higher than the median and the same way what would happen on the left side if we had a very very low value okay but this is called a positive skew and you see the mean is so much more than the median you have what's called a positive skew now try to imagine your mind that 63 would be 163 let's say it's the boss's son and he's the total klutz took him 163 hours to do something that should take about 10 hours or so well then now the mean is even higher than 15 it jumps okay so you can't fire the boss's son but you're certainly going to have very skew data and this is called a positive skew because you have a very high number an outlier that throws the mean and makes it much higher than the median and just to complete the data set alright let's look at the variance turns out to be 2868 over 11 which is 260.73 square again don't ask what a square hour is that's what happens when you use variances you get a square it's a square hour the standard deviation which is a square root is 16.15 hours and the coefficient of variation is 107.7% just as a statistician you should look at this data and say that's interesting that the standard deviation is higher than the mean that shows incredible variability in a data set if you're in quality control you want that coefficient of variation to be a lot lower than a 107.7% but that's again something for another course but anyway now you've seen how data gets skewed one way of presenting data is with a 5 number summary that gives you some information about the shape basically you need the smallest value which in this case was 2 the largest value which is 63 the q1 and the q3 and q1 is 8 and q3 is the average of 15 and 18 one thing we could see from this data set just looking at it but we have the median too just looking at this data set we could see the distance between q3 and the largest value is a lot more than q1 to the smallest value that's going to indicate that it's skewed to the right so we're going to see that this is skewed data again look at the bottom you can see the distance from q3 to the largest value is 16.5 to 63 and that's a lot more than the distance from the smallest value to to the q1 which is 8 so that's an indication of a right skew this is another way to present the data it's called a box plot or a box and whisker plot sometimes they use the word whisker you show the data from the smallest to the highest you see the line starts at roughly 2 and goes all the way to 63 and just looking at this you could see in the box in the center which gives you q1 you see the 8 and then you see the median there which is 10 and then you see q3, 16.5 now notice it's the box which has q1, the median and q3 is all the way to the left it's not in the middle when data is symmetric it will be right in the middle everything will be, you'll see what it looks like common sense tells you what it's supposed to look like here we see that whisker to the right which starts at 16.5 it goes all the way to 63 that's a long, long whisker the whisker on the left which starts at 2 and goes to 8, this is a tiny whisker it's the same logic we had before by the way with a 5 number summary but you can get this kind of print out you ask for a box plot or a box and whisker plot and some computer programs will print it out for you and right away you'll see if the data is skewed to the right skewed to the left if it's symmetric, if everything's in the center and it's centered then you've got symmetric data this is not symmetric we're still in the middle of the descriptive statistics part of the course there's going to be another descriptive statistics lecture following this one but for now you have enough material to start doing problems and remember do your homework, do whatever problems you can find problems everywhere because the more you practice the better you're going to be you'll remember the material and you'll also do well on your exams practice, practice and as always practice


Next we have Dave Brown talking about the DIY electric car, so enjoy. All righty, thanks for coming out. I'll try and go through this first part pretty quick since we're a little behind. My name is Dave Brown. I go under the name regedit on the DC forums or Volkswagen at live.com if you have any questions after the con. Be sure to download the latest copy of the presentation from the website after it's up. A little background about me. I have 8 years experience in IT, 3 years in IT security, and I've been doing electronics and other stuff for 12 years. A few projects I've done. My first big thing was first robotics. I was the programming and electronics guy. And I like to build all kinds of stuff. Usually I'm working in the garage when I have spare time. So I'm just going to cover real quick over the history of EVs, some acronyms, pros and cons, what you can use them for, the parts you need, the layout, some open source hardware stuff and tools and the steps to actually do it. So EVs have been around for a long time. They're not something new. They've been around for about 150 years. They're just now starting to make a comeback. Originally electricity was really expensive. People didn't have it in their homes. And once oil was struck, it was a lot cheaper to drive gas cars. So there have been a few events in history that have caused EVs to have surges. There was an OPEC oil embargo that made all the manufacturers start making cars. And then also in California whenever they pass car mandates, that gets people interested also. And then recently we have the Tesla and Nissan Leaf and IMEAV and a few others that are hitting the market now. Primarily this is because of advances in smartphone batteries. They've really driven the battery technology so that it really makes an electric car feasible. So some acronyms you need to know. I'm sure you know amps, volts, amp hours is how you measure a battery capacity. Lots of watt hours is how much power you're getting out of that battery. Your watt hour per mile is how much power you need to go somewhere. Miles per gallon equivalent. That's how you can compare it to a gas car. A BEV, battery electric vehicle. Usually we just call it an EV. NEV, neighborhood EV. Those are short range vehicles or low speed vehicles. And there's plug-in hybrids. That means it runs on gas but you can also plug it in so you don't have to use gas. Then extended range EV and range extended EV are just weird things that GM made up because they didn't want to call it a hybrid. Okay so EV pros. The best things about it is they're less complex, less maintenance. They're more efficient. They last longer. It's more sustainable because you're using electricity that can be generated in dozens of different ways. So this leads to energy independence. A lot of people that drive electric cars also have solar panels on their house so they're completely self-sustained there. Also national security. If everyone was driving electric cars we wouldn't need any oil from the Middle East. We could just do everything right here at home. And of course there are environmental reasons too. This is a picture of an electric motor, the heart of an electric car. You can see there's only a few moving parts. The only things that wear at all are the bearings and the brushes. The bearings are usually good for about 250,000 miles which is about the life of most cars. And the brushes are usually good for 1 to 200,000 miles. And they can be replaced in about 5 minutes. So it's really easy maintenance and low cost for long sustainability. So the cons of course are the batteries. They're very expensive to purchase up front. Newer batteries that are coming out now will last up to 10 years. So if you build it into the price of the EV then it's not really a big deal because you don't have to replace them. But compared to gas it is low energy density and so because of that your range is also lower. Charging stations are an issue. Obviously there aren't charging stations all over the place and availability of them can be a problem too. If you have a couple EV charging spaces in a parking lot and someone with a gas vehicle is parked there you can't charge. Also political issues sometimes cause problems. One of the places where I work occasionally they went and installed some low level chargers and then people complained that the two EV drivers were getting 20 cents of free electricity a day so they turned them off. Charge time. Batteries really aren't the limitation for charge time. You can fill a battery as fast as you can fill a car with gasoline. But unless you have a front row seat at a nuclear power plant you can't get that much power. So that's kind of an issue. So some things people don't really understand about electric cars. Lots of people think the grid can't handle it. They think we're going to need to double the amount of coal-fired power plants we need to do this. But since you charge electrics at night it really doesn't even take hardly anything. Obviously it will be many many years before a significant portion of us are driving electric cars. So it's no impact for now. But most people like in Texas they're giving away electricity at night because they have to run their base loads anyway and nobody's using it. So it really has a very low impact on the grid. Also my car uses about 10% of my electric bill per the month. Electricity has been going down over the last five years running. A couple months this year I had a $30 electric bill. So that's including the car. It really doesn't use hardly anything. Some people think it takes a lot more resources and causes more pollution. I'm not sure where this comes from but some people call the Prius the most polluting car on the planet because the dirty batteries which are 99% recycled anyway and it uses such low amount of carbon emissions anyway that it really completely offsets it and then some in the first few months of use. Also many people think lithium is very scarce. The reality is there's tons and tons of it stockpiled around the world. To make a battery you only use a few ounces of it anyway. In the U.S. we're just reopening a lithium mine that's the second biggest in the world. So there's really plenty of capacity there to make it.  We needed a downhill and a good breeze to get up to 30 miles an hour. But really there isn't much limitation on the speed that you can use and the first car to ever hit 60 miles an hour was an electric car so they can certainly do it. And here's a little clip I just wanted to show. This is a car turning right. It'll play. I guess not. Oh well. Anyway it's just a funny clip because the dude just does a U.E. right in the intersection and takes off. So EV uses. There's lots of different things people use them for. One popular is neighborhood electric vehicles. There's business that's starting to use them a lot. They're used in racing and my favorite commuting. Neighborhood electrics everyone's familiar with golf carts. Also they're very popular for security and maintenance vehicles because they're quieter and there's no emissions. Things like that. People use them for grocery getters just running errands around town. This is because to have a low speed car it's very cheap to build and there's often cheaper maintenance. You sometimes don't have to do registration. You don't have to have your safety and emissions inspections. Lots of things like that because it depends on the state but they can be a lot cheaper to operate. Businesses like them because if you're putting a lot of miles on a vehicle it'll pay for itself really quick. Also the best way to make an EV pay for itself is to maximize everything you have. If you buy a Tesla Roadster and you drive it 10 miles a day obviously it's not going to pay for itself. But if you're using the full range constantly then it will make a big difference quick. Also because the electric motors take pretty much no maintenance it's really great for fleet vehicles. I'm racing. People love them there too. You have peak torque from zero RPM and a wide power band so you don't have to shift much. With my car it's a manual transmission but I never shift it. I just leave it in second and I can do zero to 45 no problem in second. And if I want to shift into third or fourth then I can do up to 70. So my favorite use is commuting. 80% of the US commutes are under 40 miles. So really for the vast majority of people a pretty cheap EV can take care of things. You're not using any power when you're sitting in a light or if you're waiting for a train or whatever stop and go traffic you're not using anything. Compared to gas it costs less than two cents per mile compared to your 10 to 30 cents for a gas vehicle. Also you have very high mileage which is measured in MPGE. So for your MPGE there's two ways to calculate that. Two proper ways. There's some others that the OEMs come up with. The first way is the empirical way which is just using the energy equivalency and based on that my car gets 120 MPGE. The other way to do it is to compare it with the price of gas and the price of electricity. So based on the average in my state right now I get 150 on that. A month ago it was over 200 compared to gas. So this is my car. It's a 74 Volkswagen Beetle range originally 16 to 26 miles. 70 miles per hour. The conversion cost 6000 bucks and took about 100 hours to get it on the road. I've probably spent at least 100 on it since then just working on other stuff. Here's a list of parts. I don't expect you to be able to read all of them from here but it's on the slides just so you can refer to it if you're interested.  We'll talk about the big ones here. Here's the EV layout. You've got your traction battery pack is what you call the battery that really moves the vehicle. You also have a 12 volt accessory battery. Then you've got your motor.  That's a charger. So with many projects you have a time to money trade off so conversion kits are one way to cut down on the time if you have extra money.  There's also the option to have a vehicle converted for you.  Most of them are real low volume but there are few that have done several hundred vehicles. Conversion kits in general can make things easier for you but I prefer to just use them as a checklist. You can usually get the parts cheaper by shopping around so if you take a list and at least all the big ticket items shop around and see what the best pricing can get is, that's the way to go. So your motor, adapter plate and shaft coupler. You have to connect your motor to your transmission somehow. So for something like a Volkswagen Beetle it's really easy if there's only four bolts that connect your transmission to your engine.  This is what my original shaft coupler looked like. It's basically part of an old clutch disc that gets welded onto a coupler that goes onto the electric motor. After a couple thousand miles the teeth on mine got worn off so I had to replace it with one of these springy types. They're supposed to be a lot better and last better. My motor is pretty small. It's about the smallest you can use for a road going vehicle but it's good enough for a bug. It's 12 horse power. It's the rating on it but EVs are rated very differently from combustion cars. With your regular car they rate it at the red line power so what it's going to explode at whereas an EV is rated at what it can run at forever. So my car could run it on 12 horsepower. My car could run it 60 miles an hour forever. It peaks at about 60 horsepower running at 120 volts and you can bump the voltage up if you want and you can run more amps through it if you want. Also if you blow some extra air through it to cool it off better. That's really the limit on the power that an electric motor has is just the heating. You have to keep that under control. So some common motor options. There's warp motors in the U.S. The people who make that also have an impulse motor that's a bit shorter and can fit better in some cars like VW bugs. For people in Europe the co-stops are very popular. Obviously a motor is pretty heavy so they're usually around 60 to 150 pounds. So shipping costs can be pretty high. So Europeans like to go that route. Also a popular option is forklift motors. People take a 30 year old motor, recondition it and up the voltage on it and they have a road going motor for that's it's already been around for 30 years and they'll put another 30 years on it and total cost can be under 200 bucks. So that's a good low cost option. So AC versus DC. Most of the OEMs are using alternating current motors. They like these because they have regenerative braking. Regenerative braking is very popular but it's not really all it's cracked up to be. It only gives you about 10 to 30 percent of your energy back. But AC costs a lot more. So your typical motor with AC, your motor controller combo will be about 5,000 whereas for a DC it'll be around 2 or 3,000. And most of what you get for regen you could get anyway if you just drove smarter. If you drive like a jackrabbit then regen will help you out a lot. But if you drive like a say a typical Prius driver then you're not going to get anything out of the regen anyway. So it's not really helping you. Also AC motors are brushless. So remember the picture I showed you where you have the bearings and the brushes that wear out on an AC motor. You don't have those brushes to wear out.  Motor controller. This is what tells your motor how fast to go. It takes your full pack voltage and converts it into PWM for the motor to handle. I'm running a Curtis 1221C and pretty much I'll at least DC motor controllers need some extra cooling on them. So that's why it has a heat sink on it. If you need extra cooling beyond that you can throw a fan on the heat sink as well but I didn't need that at all. Here's some different motor control options. The solitons are considered the top of the line. They have several different options. They've got a junior. This one's a soliton one. They have a new thing called the Shiva destroyer that's pretty much designed for racing vehicles and can push over a megawatt of power. The zillas are also pretty high power. I'm running a Curtis. This is a picture of an AC Curtis and one thing that's very popular now is the open revolt which is a open source controller. I'm chargers. There's tons of chargers all over the place. I'm using a quick charger. It's not really that quick but it works great for overnight. My battery pack. To begin with I started out with 10 Marine deep cycle batteries. These are not recommended for EV use but I wanted to use them because I only needed 10 as opposed to 15 using golf cart batteries and that way it keeps my weight down also. So with this pack it was 600 pounds instead of the 900 that would be with full golf carts. So I started out with these plus they had a great warranty so when I drove them into the ground I could replace them for pretty cheap. It was 15 kilowatt hour pack total running at 120 volts. To figure out how much battery power you need here's the calculations basically you take the range that you need times it by your watt hours per mile. Now to figure out your water hours per mile you can look and see what other people are using how much power they're getting or you can take an estimate where basically you take the weight of the car divided by 10 and that's about what your watt hours per mile will be. You divide it by 50% in depth of discharge for a lead acid battery. Even deep cycle batteries don't like to be cycled that deeply so you don't really want to go beyond 50% on a regular basis if you want the batteries to last long. And there's something called a pukeert effect. Every battery has a sticker rating and that sticker rating is if you take 20 hours to drain that battery that's how much power you get out of it.  You're draining about one hour maybe half an hour so you can't get nearly as much. Usually it's somewhere between 70 or 60% so we throw that in there. So for mine it works out gives me a 15 mile range that's my nominal range. You can use 80% for the depth of discharge for an occasional thing if you need more than that so that's why mine has a range of 15 to 26 depending on how far I take the batteries. So for lithium batteries you don't have that pukeert effect so you can use a lot more of the batteries. Also you can discharge them down to 70 or 80% without hurting the batteries so you can get a lot more out of them. So battery options. Lead acid has historically been the go-to option. Even 100 years ago the presidential limo got 80 miles off lead acid batteries. The vehicles that were made back in the 70s and again in the 90s mostly ran on lead acid batteries and many of these batteries were still good today but the OEMs usually patent squat or buyout companies make them disappear so you're not allowed to use most of those. So everyone just uses golf cart batteries for the most part because they're designed for traction uses they last lots longer than the marine deep cycles that I used. They last about 500 to 700 cycles which is 200 to 300 years. Depending on your usage some people manage to get 5 to 7 years out of them but lithium batteries have gotten so much better in recent years that there's really no reason to be using lead unless you're just really the option is lead or no EV that's the only case you'd want to use lead.  There's lots of great options out there. Unfortunately none of them are in the U.S. right now. Pretty much everything comes from China or Korea. Here's some different types of batteries. These square ones are called prismatics and the big companies that make those are Calb, Sinopoli and Winston. Calb has a distributor in California so they're one of the better options right now. There's also cylindrical batteries. The most popular ones are headways right now. Those ones are great because they have little screw on terminals so even though you need they're smaller and you need a lot more of them they're easier to combine. Previously people used cylindricals from A123 but they were they're the ones that come in DeWalt battery packs and A123 doesn't sell to people so the only way you could make a battery pack out of those was to buy tons of DeWalt battery packs for tools and rip them apart and steal all the cells out of them so obviously it's a pain to do that. A123 also has these new pouch cells. When their their production for the Fisker Karma dropped off these cells went crazy in China being sold on the gray market so lots of VV-ers were snapping them up pretty cheap. They're getting sold for about 12 bucks each whereas A123 through their distributor sells them for about 60 so it was a great option for lots of people but they're a lot more work to put together into a pack because they don't have any terminals on them they just have these little tabs and so lots of people are working on creative ways to combine them into packs. So these these cells you need four of them to match a regular car battery a 12 volt battery they're at 3.2 volts nominal each and they'll last for anywhere from 2,000 to 5,000 cycles depending on the manufacturer and how you drive them. So most people are expecting these to last for 8 or 10 years. Obviously they haven't been around long enough for us to really know that but that's what people are expecting. Some of them could last as long as 15 or 20 we don't really know when the calendar life will start to have a significant impact on it. They can test the cycle life but there's no telling with the calendar life. So your lead versus lithium obviously lead is cheaper up front they're less sensitive because a flooded lead battery you can't overcharge all it does is turn into a fuel cell once it's full. So it just gasses and all you have to do is add water to it and it's okay whereas a lithium battery if you overcharge it you'll vent it which destroys the battery. There's no balancing necessary with lead because it itself balances at the top whereas with lithium you have to make sure all your batteries are at the exact same capacity otherwise one of them will go over before others get fully charged. Lead also has a much greater slope on the discharge curve so you can tell how much juice you have based on your packed voltage but lithium has a very flat curve so you can't really tell you have to use special tools to tell you how much power you've used but they last tons longer so they're really the way to go they can put out more power and there's less maintenance lead lead acid batteries because they gas at the end of the charging cycle you have to put water in them every few months to not kill them also cold weather performance lithium's a lot better at this lead battery will lose half its capacity when it's too cold out and lithium will only lose about 10 or 15 percent and if you heat them properly then it's not really an issue. So BMS this is one of the holy wars of EV conversions lots of people insist that you absolutely have to have a battery management or monitoring system other people say it's a waste of time and money also most electrical fires or most house fires that have involved electrical vehicles it's really hard to know the truth behind all of those because there's always an OEM involved in the investigation and supposedly the electric vehicle and the charger is never implicated in it but no one really believes this and one of the culprits is suspected to be the BMS so the thing that's supposed to protect your batteries the way it protects it is when a battery gets full it starts passing the extra power through a resistor and obviously if you're doing that for a while the resistor will get hot and so if it gets too hot things will burn so for that reason many people myself included think you don't need a BMS here's a couple pictures of different kinds of BMS's there's distributed like this one here or centralized so distributed you have a little circuit between each battery cell and distributed you just have tons of wires running all over the place and a few circuit boards that control everything so in order to not use a BMS you have to balance your batteries no two cells are identical so they're not going to reach full at the exact same time so you want to try to get them as close as you possibly can so that's what the balancing process is for right now people are expecting to only have to do it once for the lifetime of your batteries will wait and see if they ever drift but for now most people are experiencing that they can run them for years and they don't drift at all after they've properly balanced because the charge curve is so flat you have to do it at either the top or the bottom and by matching them all the same you can make it so you can really charge your pack to near capacity without damaging anything one really easy way to stay safe is to just stay away from the ends if you don't charge it up to 100% and don't discharge it down to 100% then you're pretty safe if you're trying to push the limits and get the max you can out of it then you're in the danger zone and you might hurt yourselves so this shows that the discharge curve you can see it's really flat your voltage is at about 3.2 volts for almost the entire time but at the very end of your charge cycle it'll shoot up quickly if you get much over 4 volts your cell is destroyed also once it gets down to 3 volts it's just about empty if you take it down to 0 volts or below it's destroyed so you have to keep it there in the middle one popular and inexpensive way of doing that is with what's called a half-pack bridge which is basically just a system of comparing two halves of the pack so if one of your cells gets weak and reaches the end of that curve where it stops dropping quickly you can see that very easily by comparing the two voltages of the packs because they should be basically identical and so if one starts dropping then you know you need to do something so some people make a circuit that can either disable their battery pack or turn on a warning light or something to let them know and that way they can take action or you can just have a couple meters monitoring that for you and just pay attention to it obviously if you're only using say 70% of your capacity on a regular basis anyway you don't really have to worry about anything because you won't be you won't be getting close to those ends important thing to know about this is a common question that newbies have is what's a pre-charge so your contactor is a really big relay that's designed to handle the hundreds of volts that you're pushing through your electric vehicle so your motor controller is full of lots of large capacitors and when they're empty and you turn on your relay and push the volts through it your voltage differential is large so the current goes to infinity obviously infinity is a bad current to have in your motor controller so what you do is you stick a resistor in the circuit and that way you can control how much resistance is there how much current goes in so you give it five or five or ten seconds to charge up the capacitors before you turn on your full contactor and that way you protect your controller and also it protects the contactor because if you're pushing infinity amps you basically have a spot welder so that can ruin things there's also a coil suppression diode sometimes you need this sometimes you don't it depends on the controller and the contactor that you're using but it can prevent a voltage spike when you first there's lots of large inductors in an electric motor so when you turn off the switch there will be a large voltage spike to try and get that current back up and so this suppression diode will reduce that and protect things. Accessories one of the great things about a VW bug is you don't need squat there's hardly anything extra on it everything's manual obviously with more modern vehicles and for people with more discriminating tastes you need things like air conditioning power steering power brakes myself I don't get this air conditioning thing I've lived in Houston for 20 years everyone says it's essential but I don't really care so if you need accessories there's two ways to do it one is to drive it off an auxiliary shaft so you have a motor where the shaft goes all the way through the motor and you can hook up a flywheel and whatever you need to on the other side of it so this is an example where they have air conditioner power steering and power brakes all hooked up to to a little belt on the end of the motor or the alternative is you have each one connected to a separate electric motor that will run everything so this is the part that I most wish I'd known about before building my car the open source options that are out there it's really a great way to save money there's some great plans out there for motor controllers for chargers for different instrumentation and for lots of the other little miscellaneous things that that electric car needs things like those BMS circuits your pre-charge circuits all kinds of other things there's lots of stuff lots of work people have done and shared here's just a picture of a kit that you can get to build a charger so open revolt is one of the most popular projects it's not really one specific thing anymore it started out as a motor controller do-it-yourself project but now it also includes chargers it's a whole family of controllers there's all kinds of other things they're working on to just a large community is working on this stuff and developing things some of them are so well-developed that you can go to digikey or mouser with a little parts list and just hit a button and it adds it to your shopping cart and then you can just check out instantly and you have everything you need excuse me so they started out with DC motor controllers they're also working on AC options so there's all kinds of great stuff you can do there plus it's just really cool to mess with all that electronics and the best thing about having a do-it-yourself controller is everything's customizable so with my car I have a hundred and twenty volt charger I have a hundred and twenty volt controller if I want to upgrade to a hundred and forty four volts I have to replace both of those and what they do it yourself you can just change a couple lines of code and you're running at something different as long as your components can handle it so it's really easy to upgrade it within a certain range and even if you want to upgrade it outside of that range usually all you have to do is replace the capacitors or something like that so this is a open source charger that some guys are working on the bunch of people have built these but it's a continuing developing process these are for this specific one is for a very high power cars they're running at like five hundred volts and thousands of amps so this is basically a three thousand dollar controller that you can build for around eight hundred bucks and then some of the other options out there obviously you can be cheaper for less performance EV dashboard there's a number of different different projects out there to do this stuff that's really cool it puts the OEMs to shame with what you can do there's Android apps out there there's stuff in the Apple the App Store and they have cool things where you can pick every gauge you want you can move them around you can resize them you can do anything you want to some of the some of the motor controllers will connect to ethernet so you can hook it up to a wireless router and just send everything directly to you know an iPad or any Android tablet or other small device and they can pick up your signal straight off there or some of them run off a Bluetooth so you don't even have to route any wires anywhere you just run everything wireless and have it control everything for you so this big list of EV convergent tools that you need obviously don't expect you to read everything there one of the important things that I wish I'd done differently was get a high clearance trolley jack I spent a lot of time moving my jack back and forth to get the car high enough to get the engine out and also working on things because it's an old car I'm always having to work on the mechanicals so if you have a good jack that helps also all your tools you should put some insulation around the handles you don't want to be using a tool and have it smack against a battery and short things out because then you've created a welder that you're holding so I of course didn't bother to do that until I had my first high voltage event and then I went and did it so conversion steps first of all you want to build your requirements explore the possibilities find a donor car get out all your old internal combustion engine stuff and eliminate waste and install your all your EV stuff we'll talk about those so requirements first thing you figure out why you want to do this if you're wanting to build a car for say the environment you probably don't need a high performance race car you're probably interested in efficiency and conservation things like that you want to maximize your utility in order to get the most out of it just like with the example you don't want a car that does 250 miles if you're only going to use 20 how far do you really need to go how fast you need to go what's your budget what are your skills and then you need to do a reality check there's lots of people that say okay I want electric car I need a hundred mile range it needs to do 70 miles an hour for that entire hundred miles and I have $10,000 not going to happen your batteries are going to cost more than that so you have to make sure you manage your expectations and really build to what you need lots of people say that they only need a 10 mile range but they want a car that does 100 like well why why are you going to spend 20,000 bucks to do that if all you need is 10 miles keep it legal make sure you know the rules in your country and your state before you get started especially in Europe they have really strict requirements they have ridiculous things like your car is not allowed to have more power than it did originally so lots of people don't like that also in the US different states will have some strange requirements many states make it very difficult for an electric car to pass an emissions test even though it's zero emissions because the car CPU isn't telling them there's zero emissions they don't believe it some states require you have to have a tailpipe to verify that there's zero emissions so I've heard stories of people having to either use a clamp or some duct tape to stick a tailpipe on their bumper and say here hook your machine up and that's how they get it legal in Texas they don't even know what the heck an electric car is they don't believe you can possibly convert it their systems can't handle that so on your title in your registration the motor type even though it's a field there it's read only so you can't change it sometimes that might be a good thing though because there are lots of congressmen think they need to track electric vehicles there have been a number of states that have tried to pass bills requiring GPS for all EV conversions so they can tax you properly they're very concerned that the you know a couple thousand electric vehicles on the roads aren't paying their fair share right now so that they're they want to set up these million dollar red tape systems so they can collect a couple hundred bucks of taxes so make sure you know what the rules are in your area so that you can not run into issues when you get done so explore the possibilities EV album is a really great place to look around and see what people are doing with cars if you have a type of car in mind you can search for that if you have a type of component in mind say there's a motor you like or a controller you like you can look and see what people are doing with that stuff also lots of people have their contact info here obviously most of us that drive electric cars we don't mind talking about them so we'll post our contact information and you can ask us questions we'll be happy to answer so you can search the album and find the car that you want and find out what what a reasonable reasonable expectations for that car what kind of power does it use what does it require how hard was it were there any snags in the build process all great stuff that you can find from people who've already done it so first you need to find a donor the most important thing is your car has to be fun to drive you're going to put a ton of time and money into this so it needs to be something that you really like a lot of people just want to take some car that someone gave them for free where they find something for a couple hundred bucks on craigslist and they say hey I want to do this well you're going to be sinking thousands of dollars into this so why is the most important part thing that you want to cheap out on so make sure it's in good working order you don't want some rust bucket that's going to fall apart in a few years your EV components should last decades so you want to make sure that the car is pretty good to aerodynamic depending on what you're doing if you're doing long distance high mileage you're going to want an aerodynamic car for short range low speed something like a VW bug is fine because it doesn't matter if you're a brick it doesn't even matter until you get over 30 miles an hour and it's still not even much 45 light weight if it's a short distance car your weight is a big factor it doesn't matter so much if you're on the highway because once you get moving you don't have to do it again stop and go driving though takes a lot of power if you're really heavy also cargo space if you need long range you're going to need space and weight capacity for all those batteries so first step deice important thing you want to pull out the the engine before you do that see if you can find a buyer for it sometimes they'll even help you get the engine out and it's a lot easier to sell it if they can see it running so you'll pull the pull the motor out drain and remove your gas tank your radiator all that other junk you don't need eliminate waste something like a VW bug with no power steering no brakes all that stuff is really easy not very complex doesn't take extra power so there are many cars that don't need power brakes you can do just fine with manual same singles for steering so if you can convert those you use less power also something like a spare tire with an electric vehicle you're not going terribly far from home so if you need help you're not that far off also lots of people have you know triple A or something like that so it's a good way to lose some weight by ditching your spare and just carry a fix of flat or something I just barely replace my 12 year old tires a few months ago so that shows how often you really expect to get a flat so and then you install your EV components once you have everything it's pretty straightforward with the bug it's just four bolts to put the motor on once you get it lined up properly install your motor and controller you need to build and install your battery boxes that's probably the hardest part is built building battery boxes you need some good insulation if you're in cold weather area you want to do your batteries last because the technology is changing so quick you don't want to buy something if you're going to be building for two years it depends a lot on the amount of free time you have mine took about six months to do some people if you're really good at it and you've done it a bunch of times you can do it in as little as four hours if you have the right prep work done but some people spend a year or two on the project so you don't want to buy your batteries and have them sitting around in a garage for a couple years and then you install your instruments your wiring all that other extra stuff where to charge this is something you need to plan for for me I pretty much only charge at home so I just use a standard home outlet just running out of my garage the max you can charge from is eight miles per hour with one of these you can also use drier sockets or oven sockets to give you four times as much power so that'll let you charge a lot quicker if you want to do public charging you're going to need an adapter so that no one's decided on an official standard the U.S. uses the J 1776 but there's still some some arguments over how to do that obviously you can get a lot more power out of these up to 76 miles of charge per hour the the standard used by Japan is Chadimo they've got a lot of these going in in the U.S. these are called level three chargers and they can give you up to 250 miles of charge in an hour and like I said before the real limitation here is the power supply it's not the batteries batteries can take power four or five times this fast so like if there were a charger available that could give the max power that some good lithium batteries can put out I could charge my car in a minute but those probably won't ever exist because it's just too much power you're not going to have nuclear power plant in your neighborhood to plug into but with these level three chargers that's an immense amount of power anyway so obviously if you can do 250 miles of charge in an hour you're certainly not driving that fast so it's filling you up pretty quick so then hit the road this was a video of my car in action but of course it's not going to work so okay so a lot of people get some weird ideas when they first want to build a car so I just want to give you some information about that first of all perpetual motion no you cannot hook alternators to your wheels and charge your batteries while you're driving not going to work you cannot hook fans to your car to run wind turbines and charge your batteries using your vehicle speed not going to work these things create extra resistance and use more power than they give you back also hydrogen fuel cells they're not very efficient supercapacitors they're really heavy and really expensive just by more lithium hub motors do you really want all your expensive electronics spending hundreds of rpms and hitting potholes probably not do it yourself hybrid the volt has three clutches in it and six different drive configurations so it's guaranteed to require more maintenance than any other car on the road probably not something you want to mess with also solar you're not going to get a lot of power you're really never done with electric vehicle conversion it's fun to keep doing stuff I converted mine to do all my 12 volt charging off a solar panel and I'm doing some hybrid battery experiments so it's really fun here's a bunch of EV resources for you guys just so you can look at the slides and see where you can get stuff and here's my obligatory mastercard slide so if you want to drive an electric car because you you're sick of buying gas or for whatever other reason you can wait around for the the OEMs to build something that meets your needs and that you really like or you can just do it yourself thank you


Hello all and welcome to the session. Today the question is, construct a triangle ABC in which BC is equal to 5 cm, angle B is equal to 45 degrees and angle C is equal to 60 degrees. Draw the circle of the triangle ABC. And now we will start with the solution. Now first of all we will draw a rough figure that is a rough diagram of a triangle ABC where angle B is equal to 45 degrees and angle C is equal to 60 degrees and BC is equal to 5 cm. Now we will start with the steps of construction. First of all we will draw a line segment BC is equal to 5 cm. Now here you can see we have drawn a line segment BC which is 5 cm. And now in the second step we will construct an angle CBX is equal to 45 degrees. As you can see here we have constructed an angle CBX is equal to 45 degrees. And now in the third step we will construct an angle BCY is equal to 60 degrees. As you can see here we have constructed an angle BCY which is equal to 60 degrees. Now let the A, BX and CY intersect at A. BX and CY let this point be A and hence ABC is the required triangle. Now in the fourth step draw BQ and RS perpendicular bisectors of CY, A, B and BC respectively leading each other at all. Now you can see here BQ is the perpendicular bisector of the CY AB and RS is the perpendicular bisector of CY BC and both of them are intersecting at point O. Now in the last step with all of the CY and OA as radius draw a circle such that it passes through the points A, B and C. Now you can see here with all as the center and OA as the radius we have drawn the circle which is passing through the point A, B and C and this is called the circle circle of the triangle ABC. So this is the required construction and that's all for this session. Hope you all have enjoyed the session.