# Using Histograms to Answer Statistical Questions

Warmup

Select the data set you think is represented by the histogram and check your answer.

Activity #1

`Read and Interpret Histograms.`

An earthworm farmer set up several containers of a certain species of earthworms so that he could learn about their lengths. The lengths of the earthworms provide information about their ages. The farmer measured the lengths of 25 earthworms in one of the containers. Each length was measured in millimeters.

• In the applet below, draw a line segment for each length: (Use and to hide points and labels.
• Use to measure the line segments.) Make sure to label the length of each line segment.
• 20 millimeters
• 40 millimeters
• 60 millimeters
• 80 millimeters
• 100 millimeters

(1.) Complete the table for the lengths of the 25 earthworms.

(2.) Use the grid and the information in the table to draw a histogram for the worm length data. Be sure to label the axes of your histogram. The red dots are the bar handles.

(3.) Based on the histogram, what is a typical length for these 25 earthworms? Explain how you know.

Here is another histogram for the earthworm measurement data. In this histogram, the measurements are in different groupings.

(1.) Based on this histogram, what is your estimate of a typical length for the 25 earthworms?

(2.) Compare this histogram with the one you drew. How are the distributions of data summarized in the two histograms the same? How are they different?

(3.) Compare your estimates of a typical earthworm length for the two histograms. Did you reach different conclusions about a typical earthworm length from the two histograms?

Activity #2

`Interpret Histograms.`

• Study the histogram below and answer the questions that follow.

Professional basketball players tend to be taller than professional baseball players. Here are two histograms that show height distributions of 50 male professional baseball players and 50 male professional basketball players.

(1.) Decide which histogram shows the heights of baseball players and which shows the heights of basketball players. Explain your reasoning.

(2.) Write 2–3 sentences that describe the distribution of the heights of the basketball players. Comment on the center and spread of the data.

(3.) Write 2–3 sentences that describe the distribution of the heights of the baseball players. Comment on the center and spread of the data.

Challenge #1

Forty sixth-grade students ran 1 mile. Here is a histogram that summarizes their times, in minutes. The center of the distribution is approximately 10 minutes.

On the blank axes below, draw a second histogram that has:

(a.) a distribution for a different group of 40 six-grade students,

(b.) a center of 10 minutes,

(c.) less variability than the distribution shown above. The red dots are handles of the bars.

Challenge #2

These two histograms show the number of text messages sent in one week by two groups of 100 students. The first histogram summarizes data from sixth-grade students. The second histogram summarizes data from seventh-grade students.

(1.) Do the two data sets have approximately the same center? If so, explain where the center is located. If not, which one has the greater center?