Descriptive Statistics Involves computing summary measures and constructing

Measures of Location • • Arithmetic Mean or Average; Median; Mode; and Weighted Average

Measures of Variability or Spread • • Range; Variance; Standard Deviation, and Coefficient of

Measures of Location Measures of location describe data by providing a central tendency (location)

Arithmetic Mean or Average Population: x = (Xi) / N where: x = population

Median The median is the middle observation in data that have been arranged in

Mode The mode is the value in a set of data that appears most

Weighted Average A weighted average is an arithmetic mean for which each value (X)

Measures of Variability or Spread Measures of variability or spread describe data by indicating

Range The range of the data set is the difference between the largest and

Variance The variance provides a numerical measure of how the data tend to vary

Standard Deviation The standard deviation may be thought of as a measure of distance

Coefficient of Variation The coefficient of variation is a measure of relative variation Population:

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Descriptive Statistics Involves computing summary measures and constructing graphs, tables and charts to illustrate those measures

Measures of Location • • Arithmetic Mean or Average; Median; Mode; and Weighted Average

Measures of Variability or Spread • • Range; Variance; Standard Deviation, and Coefficient of Variation

Measures of Location Measures of location describe data by providing a central tendency (location) value for the data

Arithmetic Mean or Average Population: x = (Xi) / N where: x = population mean; Xi = the ith value in the data set; = summation symbol; and N = population size Sample: X = (Xi) / n where: X = sample mean; Xi = the ith value in the data set; = summation symbol; and n = sample size

Median The median is the middle observation in data that have been arranged in ascending or descending numerical sequence Median = (n + 1) / 2 ranked observation where n = number of observations

Mode The mode is the value in a set of data that appears most frequently

Weighted Average A weighted average is an arithmetic mean for which each value (X) is weighted (W) according to some welldefined criterion Xw = (XW) / W

Measures of Variability or Spread Measures of variability or spread describe data by indicating the extent of the differences between the values of a data set

Range The range of the data set is the difference between the largest and smallest values in the set Range = Largest Value - Smallest Value

Variance The variance provides a numerical measure of how the data tend to vary around the arithmetic mean x 2 = ( Xi - s 2 = x ) 2 / N for populations ( Xi - X )2 / (n - 1) for samples

Standard Deviation The standard deviation may be thought of as a measure of distance from the mean STD = SQRT of Variance Population: = SQRT OF Sample: 2 S = SQRT of S 2

Coefficient of Variation The coefficient of variation is a measure of relative variation Population: Sample: V = ( / x ) * 100 V = ( S / X ) * 100 where: V = Coefficient of Variation