# Study

**Chapter Summary**

If a variable is measured on a scale, it has a continuous probability distribution. These distributions can take on many different shapes, but the most common shape is a normal curve. Like all bell- shaped curves, the normal curve is symmetrical and unimodal. As a result, the mean, median, and mode are identical, and half the cases lie above and half below the average. The normal curve differs from other bell curves in precisely how the probability is distributed along the curve. We can find that probability by using a z table, which standardizes the position on the distribution into a distance, measured in units the size of a standard deviation for the variable. By knowing the mean and standard deviation of a variable, we can calculate the z-score for a particular value of the variable. We can then look up the z-score on a z table to find the probability of a case falling between the mean and that z-score.

**Learning Objectives**

After reading this chapter, you should:

- Know the definition of a z-score
- Be able to calculate a z-score
- Be able to read a Z Table
- Be able to find the probability of being in a particular range of a normal curve
- Be able to find the range which contains a particular proportion of cases
- Know how to find a z-score using SPSS
- Be able to select a subset of cases using SPSS
- Be able to identify select cases in SPSS