IM 6.8.7 Lesson: Using Histograms to Answer Statistical Questions

Autor:GeoGebra Classroom Activities, IM 6 – 8 Math, Anthony OR 柯志明

Here are four questions about the population of Alaska. Which question does not belong? Explain your reasoning.

In general, at what age do Alaska residents retire?
At what age can Alaskans vote?
What is the age difference between the youngest and oldest Alaska residents with a full-time job?
Which age group is the largest part of the population: 18 years or younger, 19–25 years, 25–34 years, 35–44 years, 45–54 years, 55–64 years, or 65 years or older?

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:

20 millimeters
40 millimeters
60 millimeters
80 millimeters
100 millimeters

Here are the lengths, in millimeters, of the 25 earthworms.

6 11 18 19 20 23 23 25 25 26 27 27 28 29 32 33 41 42 48 52 54 59 60 77 93

Complete the table for the lengths of the 25 earthworms.

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.

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

Write 1–2 sentences to describe the spread of the data. Do most of the worms have a length that is close to your estimate of a typical length, or are they very different in length?

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

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

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?

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?

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.

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

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

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