# Chapter Main Points and Learning Objectives

Chapter main points

• Measures of variability are numbers that describe how much variation or diversity there is in a distribution.
• The index of qualitative variation is used to measure variation in nominal variables. It is based on the ratio of the total number of differences in the distribution to the maximum number of possible differences within the same distribution. The index of qualitative variation can vary from 0.00 to 1.00. The range measures variation in interval-ratio and ordinal variables and is the difference between the highest (maximum)and the lowest (minimum) scores in the distribution. To find the range, subtract the lowest from the highest score in a distribution. For an ordinal variable, report the lowest and the highest values without subtracting.
• The interquartile range measures the width of the middle 50% of the distribution for interval-ratio and ordinal variables. It is defined as the difference between the lower and upper quartiles (Q1 and Q3). In some instances, reporting the full range (the values of Q1 and Q3) may provide more information than the single interquartile range value.
• The box plot is a graphical device that visually presents the range, the interquartile range, the median, the lowest (minimum) score, and the highest (maximum) score. The box plot provides us with a way to visually examine the center, the variation, and the shape of a distribution.
• The variance and the standard deviation are two closely related measures of variation for interval-ratio and ordinal variables that increase or decrease based on how closely the scores cluster around the mean. The variance is the average of the squared deviations from the center (mean) of the distribution; the standard deviation is the square root of the variance.

Learning objectives

1. Explain the importance of measuring variability
2. Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation
3. Identify the relative strengths and weaknesses of the measures