Question

In Exercises 1–6, refer to the data below, which are total home game playing times (hours) for all Major League Baseball teams in a recent year (based on data from Baseball Prospectus).

236 237 238 239 241 241 242 245 245 245 246 247 247 248 248 249 250 250 250 251 252 252 253 253 258 258 258 260 262 264

Histogram Construct the histogram corresponding to the frequency distribution from Exercise 1. For the values on the horizontal axis, use the class midpoint values. Which of the following comes closest to describing the distribution: uniform, normal, skewed left, skewed right?

Short answer

The following histogram is constructed:

Among the given distributions, it appears that the normal distribution comes closest to describing the data.

Step-by-step solution

Given information

A frequency distribution is constructed for the number of playing hours.

Refer to Exercise 1CRE; the following frequency distribution is given:

Playing Times (in hours)	Frequency
235-239	4
240-244	3
245-249	9
250-254	8
255-259	3
260-264	3

Define histogram

A histogram is a plot that depicts the frequencies of each class interval using adjacent vertical bars.

The length of the bars shows the frequency of the corresponding interval.

Construct the midpoints of the classes

The midpoint of any class is obtained by taking the average of the lower and upper limits of the class.

The midpoints of the class intervals are computed below:

$$\begin{gathered} {\text{Midpoint}}_1=\frac{235+239}{2} \\ =237 \\ {\text{Midpoint}}_2=\frac{240+244}{2} \\ =242 \\ {\text{Midpoint}}_3=\frac{245+249}{2} \\ =247 \\ {\text{Midpoint}}_4=\frac{250+254}{2} \\ =252 \\ {\text{Midpoint}}_5=\frac{255+259}{2} \\ =257 \\ {\text{Midpoint}}_6=\frac{260+264}{2} \\ =262 \end{gathered}$$

Construct the histogram

Use the given steps to construct the histogram:

• Mark the values from 0 up to 9with a gap of 1 unit on the vertical axis.
• Mark the values from 237 to 262 with a gap of 5 units on the horizontal axis.
• Draw vertical bars with a length equal to the given frequency corresponding to each midpoint of equal width.
• Label the horizontal axis as “Total Number of Played Hours” and the vertical axis as “Frequency.”

The histogram is constructed as follows:

Describe the shape of the histogram

The following shapes of the histogram depict the corresponding distribution:

• If a histogram is symmetric and bell-shaped, the corresponding distribution is normal.
• If a histogram has flat and even-sized bars, the corresponding distribution is uniform.
• If a histogram has a tail towards the right, the corresponding distribution is skewed to the right.
• If a histogram has a tail towards the left,the corresponding distribution is skewed to the left.

Here, the given histogram appears to be approximately bell-shaped and symmetric.

Thus, it can be said that the distribution is normal.