Measures of central tendency 1 1 1 2 2 3 4 4 4 4 5 Mean: =AVERAGEA Mode: the most frequent value =MODE.SNGL Median: middle value =MEDIAN Measures of variability Sample variance =VAR.S Sample Standard deviation =STDEV.S Range R=max xi - min xi Variation coefficient Variance represents one of the most important characteristics of variability. It takes into account all the values from the statistical set and is based on the distance of the values from the arithmetic mean. The standard deviation tells us how much the typical cases in the set of numbers under study differ from each other. "If it is small, the elements of the set are mostly similar to each other, and on the contrary, a large standard deviation signals great mutual differences. " "Using the 1σ and 2σ rules, one can approximately determine how far the numbers in the set are from the average, or how far the values of the random variable are from the mean. " The standard deviation is the most widely used measure of variability. "Kurtosis: The measure of the ""tailedness"" of the data." "Kurtosis is a statistical measure that describes the shape of a data distribution, specifically how the tails (extreme values) of the distribution compare to a normal distribution. " "When we say kurtosis is a measure of the ""tailedness"" of the data, we are referring to how heavy or light the tails are in comparison to a normal distribution." Skewness: The measure of asymmetry in the data distribution. ##### Sheet/List 2 ##### Revenues in the department store (in thousands) Task: Divide the data into an appropriate number of classes and construct a frequency histogram. 33.7 56.32 10.97 45.09 57.05 39.89 50.12 59.49 class the upper limit of the class frequency 9.97 62.54 20.15 42.16 (5;20> 75.93 21.47 9.96 34.42 (20;35> 48.67 36.05 63.75 18.56 (35;50> 35.26 17.76 32.76 68.1 (50;65> 11.49 82.7 53.91 39.73 (65;80> 5.97 30.06 15 79.01 (80;95> 21.25 50.1 41.72 27.18 94.86 19.92 25.01 51.45 calculations n: number of class max: min: variation range the width of the class ##### Sheet/List 3 ##### Amount of barrels of oil taken by individual companies (in thousands) Task: Divide the data into an appropriate number of classes and construct a frequency histogram. 11 15 17 13 8 16 18 14 18 10 7 2 10 12 17 20 16 9 9 11 15 22 15 6 21 14 14 13 19 6 3 21 16 21 17 10 13 17 17 13 19 6 23 11 18 12 12 20 8 15 13 1 11 16 9 22 9 18 19 16 9 15 5 6 7 11 15 8 25 14 17 10 15 10 12 11 7 20 15 5 10 18 14 4 19 5 13 7 20 9 12 8 10 13 15 4 12 1 15 14 calculations n: number of class max: min: variation range the width of the class ##### Sheet/List 4 ##### Measures of central tendency Mode: =MODE.SNGL Median: =MEDIAN Population mean: =AVERAGEA Sample mean: =AVERAGEA Geometric mean =GEOMEAN Measures of variability Range: R=max xi - min xi Population variance =VAR.P Sample variance =VAR.S Population standard deviation =STDEV.P Sample standard deviation =STDEV.S Data → Data Analysis → Descriptive Statistics Frequency histogram Sturgers rule Data → Data Analysis → Histogram