Chapter 2 How it Works

2.1 CREATING A FREQUENCY TABLE

Imagine that we ask everyone in a class of 20 first-year college students how many nights they went out to socialize in the previous week. In this case, we might specify that to socialize means to leave your place of residence for at least 3 hours after 6:00 p.m. for any purpose unrelated to academic work. This observation allows only a very specific set of possible responses: 0, 1, 2, 3, 4, 5, 6, or 7 nights. If we asked each of the 20 students how many nights a week they typically go out to socialize, we might get a data set that looks like this:

How can we use these data to create a frequency table? First, we reorder the “nights socializing” data into a table with two columns, one for the range of possible responses (the values) and one for the frequencies of each of the responses (the scores). The frequency table for these data follows.

2.2 CREATING A HISTOGRAM

How can we use these same data to create a histogram? First, we put the number of nights socializing on the x-axis and the frequency for each number on the y-axis. The bar for each frequency is centered at the appropriate number of nights out. The figure below shows the histogram for these data.

2.3 CREATING A FREQUENCY POLYGON

How can we use these same data to create a frequency polygon? As with the histogram, we put the number of nights socializing on the x-axis and the frequency for each number on the y-axis. Instead of bars, we now place a dot for each frequency above the appropriate number of nights out. We add additional values at the next whole numbers below and above this range, −1 and 8, and put dots indicating a frequency of 0 at each of these values. The figure below shows the frequency polygon for these data.