Measures of Variability

Application: Measures of Variability

Measures of central tendency are some of the most widely used statistics for describing data. Recall that measures of central tendency capture what a typical case or score looks like. An equally important characteristic of data, however, is how the cases or scores are distributed and how much they vary from one another. Measures of variability—including the range, interquartile range, variance, and standard deviation—describe the distribution and variability of data.

Consider again the arrest records of inmates. It is possible that some inmates have committed many offenses, whereas others are one-time offenders. To describe how the number of offenses of inmates is distributed, you could calculate the range and the interquartile range. The range would show the difference between the highest and the lowest number of offenses. The interquartile range would show the middle 50 percent of the number of offenses. To describe how much the offenses vary from each other, you could calculate the variance and the standard deviation. The variance is typically not part of data interpretation; rather, it is a statistic that is calculated when determining the standard deviation. The standard deviation would show, on average, how far each inmate’s number of arrests deviates from the mean number of arrests of all inmates.

To prepare for this assignment:

Review the assigned pages of Chapter 13 of your course text, The Practice of Research in Criminology and Criminal Justice (5th ed.). Pay attention to the explanations of the range, interquartile range, variance, and standard deviation. Also, consider how to calculate each.
Review the article, “Measures of Variability.” Focus on how and when measures of variability are used.
Review the 10 cases in the sample listed below. Calculate the range, interquartile range, variance, and standard deviation.
Consider how your calculations might be used to explain the distribution and variance of the data in this sample.

Person

Number of Arrests

Bob

0

Johnny

1

Sarah

3

Julie

5

Barbara

0

Ken

2

Keith

8

Nicole

2

Sam

1

Stuart

3

The assignment (1–2 pages):

Using the sample provided, respond to the following questions:

What is the range of the sample?
What is the interquartile range of the sample?
What is the variance of the sample?
What is the standard deviation of the sample?
Based on your calculations, explain the distribution and variance of data.