## Assignment: 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 variabilityâ€”including the range, interquartile range, variance, and standard deviationâ€”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. In this Assignment, you calculate the range, interquartile range, variance, and standard deviation of a hypothetical set of data.

**To prepare:**

- 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.
- In 500 words, using the sample provided, respond to the following below.

- 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.
- Explain how the ability to analyze the data in these ways can affect your criminal justice practice.
- Explain how the ability to understand data presented in these ways can affect citizen understanding of crime.