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4 measures of variability

This document discusses measures of variability, or dispersion, which describe how spread out values are in a distribution. The five most commonly used measures are the range, interquartile range, variance, standard deviation, and coefficient of variation. The standard deviation is the most widely used measure for interval or ratio data, as it indicates the average deviation of values from the mean and describes whether a sample is heterogeneous or homogeneous. The standard deviation is calculated by computing the sum of squared deviations from the mean, dividing by the sample size minus one, and taking the square root.

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MEASURES OF VARIABILITY (DISPERSION) 1 College of Nursing 3rd stage Biostatistics Dr. Nazar A. Mahmood
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3 Measure of variability (dispersion):- • Measures of variability describe how spread out the values are in a distribution of values. • When describing a variable, it is important to describe both its measure of central tendency and its measure of dispersion. • The five most commonly used measures of dispersion are the range, interquartile range, variance, standard deviation, and coefficient of variation. • Measure of dispersion depends on the measurement scale of the variable.
4 Range: • The range is the difference between the maximum value and minimum value of a variable. • The range is used when you have ordinal data or you are presenting your results to people with little or no knowledge of statistics. • The range is rarely used in scientific work as it is fairly insensitive. • For example, in a sample there might be five subjects ages: 10, 14, 20, 55, and 95. The age range of the sample = 95 - 10 = 85 years
5 Standard deviation: • The standard deviation is a measure that indicates the average deviation or variability of all the values from the mean of a set of values. • The standard deviation is the most widely used measure of variability when interval or ratio data are described. • When the standard deviation is large, the spread among the values in the data set is large, indicating a heterogeneous sample. • When the deviation is small, most of the scores are very close to the average score, indicating a more homogeneous sample.
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8 Standard deviation formula
9 Computing the variance and standard deviation Step 1: Compute the sum of the squared deviations about the mean = 10543.6 Step 2: Divide by the sample size n - 1. 10543.6 / (10-1) = 10543.6 /9 = 1171.511 Since:
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