if mean is greater than standard deviation
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Can standard deviation be greater than the average? Best Answer: It is possible for the standard deviation to be greater than the mean, even if all data points are positive numbers. However, the only way for this to happen is for most, if not all, data points to be at the extremes (with one extreme much greater in magnitude than the other) and nothing near the average.
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- Problem 21. If a random sample of size 100 is obtained from a population with a mean of 40 and a standard deviation of 14, find the value of c so that the probability is 0.40 that the mean of the sample is greater than c.Problem 23.he times required for workers to complete a certain task are normally distributed with a mean of 30 minutes and a standard deviation of 9 minutes. If a random sample of 25 workers is drawn from the work force, find the probability that the mean completion time for the sample of workers is between 28 and 33 minutes.
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What Is the Difference Between Mean Scores & Standard Deviation? Standard deviation is a statistical measurement of the variation in a set of data. Standard deviation indicates how much the values of a certain data set differ from the mean on average.
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- Jul 24, 2015. Outliers increase the standard deviation. Mean is most affected by outliers, since all values in a sample are given the same weight when calculating mean. A value that is far removed from the mean is going to likely skew your results and increase the standard deviation. Say you have five values: 2, 1, 2, 1.5, and 2.1.
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How do you interpret standard deviation? Standard deviation is most usually measured in the same units as the mean. I suppose if you had a situation where spread was very small compared to mean you might use g for mean and mg for s.d. Standard deviation does not directly give you the maximum and minimum values although for many distributions these are each about three s.d. above and below the mean.
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Coefficient of variation (Redirected from Standard deviation/mean). Not to be confused with Coefficient of determination. In probability theory and statistics, the coefficient of variation (CV), also known as relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution.t is often expressed as a percentage, and is defined as the ratio of the standard deviation to the mean (or its absolute value,). The CV or RSD is widely used in analytical chemistry to express the precision and repeatability of an assay.
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This site is no longer maintained and has been left for archival purposes So, if we had a sample of 4 values (120, 135, 160, 150) and the mean with standard deviation (s) was 138.8 19.31 mm, then the mean with standard error (s n) would be 138.8 9.65 mm, because we divide s by Ö n (which is 2) to obtain the standard error. Note 1.
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- best way is to determine each score’s standard deviation (or “average difference”) above or. below the mean of the total group of scores. This placement in standard deviation units above or. below the mean is called a Z-score, or standard score.
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What is a standard deviation and how do I compute it? As shown below, the larger the standard deviation, the more. dispersion there is in the process data. All three processes above have a mean (average) of 10, but the standard. deviations vary. A smaller standard deviation means greater consistency, predictability and quality.
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Standard deviation larger than mean A standard deviation much larger than the mean is certainly possible. It could be, for example, that your data are highly skewed. E.g. take. the simple dataset 42, 50, 55, 999. The outlier makes it very skewed. and the dataset has a mean of 287 but a st.dev of 475.
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- The standard deviation of the mean is calculated by dividing the standard deviation of the sample by the square root of the number of things in the sample. What this essentially tells you is how certain are that your sample accurately describes the entire group.
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Measures of variability: the range, inter-quartile range and standard deviation Figure 3 shows this concept in diagrammatical form. If the mean of a dataset is 25 and its standard deviation is 1.6, then. 1  68% of the values in the dataset will lie between MEAN-1SD (25-1.6=23.4) and MEAN+1SD (25+1.6=26.6). 2  99% of the values will lie between MEAN-3SD (25-4.8=20.2) and MEAN+3SD (25+4.8=29.8).igure 3 shows this concept in diagrammatical form. If the mean of a dataset is 25 and its standard deviation is 1.6, then. 1  68% of the values in the dataset will lie between MEAN-1SD (25-1.6=23.4) and MEAN+1SD (25+1.6=26.6). 2  99% of the values will lie between MEAN-3SD (25-4.8=20.2) and MEAN+3SD (25+4.8=29.8).
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- Then say you have five values: 2, 1, 2, 1.5, and 10. Your mean would be 3.3 and your standard deviation would be 3.77. That one outlier (10) makes your standard deviation much greater when compared to the earlier set of numbers. The effect would be less though if our sample size was larger and we only had one outlier.
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- 1) A manufacturer representing the spread of the lifetimes of bulbs from his production line. The standard deviation is 15.9 hours and the interquartile range is 27.7 hours. 2) Whether a businessman should use the median and IQR or the mean and standard deviation to compare the daily sales for this year with last year's. I really need to understand WHY so please give a reason for your choice. Thanks :)
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- Note: 1  The standard deviation is like a distance: by definition, it is positive. 2  The standard deviation can be zero if all the data points are the same. 3  The standard deviation can be larger than the mean. The range of numbers has to be large for this to occur. One such sample is {0, 0, 1, 15, 20}, where = 7.2 and s 8.6. If 5 were added to each number in a set of data, the mean would increase by 5 and the standard deviation would remain the same.
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2. Mean and standard deviation The data are plotted in Figure 2.2, which shows that the outlier does not appear so extreme in the logged data. The mean and median are 10.29 and 2, respectively, for the original data, with a standard deviation of 20.22. Where the mean is bigger than the median, the distribution is positively skewed.
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Statistics Chapter 3 The standard deviation is the square root of the variance, which in this case is or 1.73. Comparison to mean absolute deviation. The mean absolute deviation is when the negative sign is ignored so that all deviations are converted to positive numbers, summed, and then averaged.he standard deviation is the measure that is most often used to describe variability in data distributions. It can be thought of as a rough measure of the average amount by which observations deviate on either side of the mean.
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What is 'Standard Deviation' The greater the standard deviation of a security, the greater the variance between each price and the mean, indicating a larger price range. For example, a volatile stock has a high standard deviation, while the deviation of a stable blue-chip stock is usually rather low. BREAKING DOWN 'Standard Deviation'
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What does it mean when the standard deviation is higher than the mean? What does that tell you about the data? A smaller standard deviation indicates that more of the data is clustered about the mean. A larger one indicates the data are more spread out. Comparing the standard deviation to the mean will tell you different things depending on the data you are working with.
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Standard deviation Thus, the standard deviation is equal to the square root of (the average of the squares less the square of the average). See computational formula for the variance for a proof of this fact, and for an analogous result for the sample standard deviation.n the case where X takes random values from a finite data set, with each value having the same probability, the standard deviation is. or, using summation notation, The standard deviation of a (univariate) probability distribution is the same as that of a random variable having that distribution.
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Standard deviation Thus, the standard deviation is equal to the square root of (the average of the squares less the square of the average). See computational formula for the variance for a proof of this fact, and for an analogous result for the sample standard deviation.
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Hypothesis Test of Mean for Student T-Test - One Small Sample Solution: The population mean is greater than 100 means the alternate hypothesis is H1: m m a, reject the null hypothesis; otherwise, do not reject the null hypothesis. Press STAT and the right arrow twice to select TESTS.To select the highlighted 2:T-Test Press ENTER.Use right arrow to select Stats (summary values rather than raw data) and Press ENTER. Use the down arrow to Enter the hypothesized mean, sample mean, standard deviation, and sample size. Select alternate hypothesis. Press down arrow to select Calculate and press ENTER.nter sample mean, standard deviation, and sample size for samples 1 and 2. Select alternate hypothesis. Select pooled: Yes. Press down arrow to select Calculate and press ENTER. Results: Since the p-value is 0.384, do not reject the null hypothesis with an alpha value of 0.02 (because 0.384 is not less than 0.02).
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Standard score In statistics, the standard score is the (signed) number of standard deviations an observation or datum is above the mean. Thus, a positive standard score indicates a datum above the mean, while a negative standard score indicates a datum below the mean.hus, a positive standard score indicates a datum above the mean, while a negative standard score indicates a datum below the mean.
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- Standard Deviation Part II. Standard deviation is a mathematical tool to help us assess how far the values are spread above and below the mean. A high standard deviation shows that the data is widely spread (less reliable) and a low standard deviation shows that the data are clustered closely around the mean (more reliable).
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What is the relationship between the mean and standard deviation in statistics? If you have a set of values with low standard deviation, it means that in general, most of the values are close to the mean. A high standard deviation means that the values in general, differ a lot from the mean. The variance is the standard deviation squared. That is to say, the standard deviation is the square root of the variance.