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Summary of Descriptive Statistics - Handout


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A summary of all fundamental concepts in descriptive statistics on a single page, with Excel functions: measures of central tendency, measures of variation, percentiles, five-number summary, etc.

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Summary of Descriptive Statistics - Handout

  1. 1. Handout: Descriptive Statistics - Numerical Methods → Fundamental concepts: Population parameter; Point estimate; Sample statistic; Sampling error Concept Definition Symbol Excel equivalent or formula Number of observations Population size / sample size / number of entries in a data set n COUNT() Data set A data set / population / sample of observations or measurements x1, x2, …, xn A range of cells, e.g. (A2:A52) Minimum Smallest measurement MIN() Maximum Largest measurement MAX() Summation/ Aggregate All measurements added up ∑ 𝒙𝒊 𝒏 𝒊=𝟏 SUM() Population mean The sum (aggregate) divided by the number of measurements; the average μ (‘mew’) AVERAGE() Sample mean The sum (aggregate) divided by the number of measurements; the average x̄ (x-bar) AVERAGE() Median The middlemost measurement Md MEDIAN() Mode The measurement that occurs most frequently Mo MODE() Range Difference between Maximum and Minimum MAX()-MIN() Population Variance Average of the squared deviations from the mean σ2 (sigma square) (also VAR) VAR.P() Sample Variance Sum of squared deviations from the mean, divided by (n-1) s2 (also VAR) VAR.S() Population Standard Deviation Square root of the population variance σ (sigma) (also SD) STDEV.P() Sample Standard Deviation Square root of the sample variance s (also SD) STDEV.S() Coefficient of Variation A measure of the variation of a sample or population relative to its mean SD/mean z-score Deviation of a data value from the mean, measured in standard deviations z=(x-mean)/SD Tolerance Interval An interval of several SDs around the population mean that contains a specified percentage of a population (according to the Empirical Rule) Standard Error of the Sample Mean A measure of the accuracy with which the sample mean estimates the population mean. SE=SD/√n Confidence Interval An interval of about 2 standard errors around the sample mean, which with a high confidence contains the population mean Percentile The pth percentile is a value such that p percent of measurements fall at or below that value. PERCENTILE.EXC() Quartiles The 25 th , 50 th (i. e. median) and 75 th percentile of a data set; the three points that divide the data set into four equal groups Q1, Q2=Md, Q3 Interquartile range Difference between the third and first quartile IQR Q3- Q1 5-number summary Summary of a dataset as: Minimum, First quartile, Median, Third quartile, Maximum Quartile, Quintile, Decile A data set ordered from smallest to largest can be thought of as divided into 4, 5 or 10 equal- sized subsets. The terms quartile, quintile or decile may refer either to these subsets (sociology, economics) or to the values that divide them (descriptive statistics, cf. Quartiles).