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Measures of Dispersion in Statistics

Measures of dispersion quantify how strongly individual data points are distributed around a central value (usually the mean). They provide information about the heterogeneity or variance in a data collection. Important measures of dispersion include variance (average of squared deviations), standard deviation (square root of variance), and range (difference between maximum and minimum values).

Examples of Measures of Dispersion

• Variance: Average of squared deviations from the mean
• Standard deviation: Square root of the variance
• Range: Difference between maximum and minimum values
• Interquartile range: Difference between 75th and 25th percentile
• Mean absolute deviation: Average of absolute deviations from the mean

Example Calculation

For the data collection [2, 4, 4, 4, 5, 5, 7, 9]:

• Mean: 5
• Range: 9 - 2 = 7
• Variance: 4
• Standard deviation: 2