The majority of variables that social scientists study are not normally distributed. This doesn't typically cause problems in analysis when the goal of a study is to calculate means and standard deviations-as long as sample sizes are greater than about 50. (This will be discussed in later chapters.) However, when characterizing the distribution of scores in one sample, or in a complete population (if this information is available), a non-normal distribution can cause complications. We can illustrate this point by examining the distribution of age in the GSS data file.
a. Create a histogram for AGE (click on Graphs, Legacy Dialogs, Histogram; insert the variable age) with a superimposed normal curve (click on the option Display Normal Curve). How does the distribution of AGE deviate from the theoretical normal curve?
b. Calculate the mean and standard deviation for AGE in this sample, using either the Frequencies or Descriptives procedure.
c. Assuming the distribution of AGE is normal, calculate the number of people who should be 25 years of age or less.
d. Use the Frequencies procedure to construct a table of the percentage of cases at each value of AGE. Compare the theoretical calculation in (c) with the actual distribution of age in the sample. What percentage of people in the sample are 25 years old or less? Is this value close to what you calculated? Why might there be a discrepancy?