Answers to Comparing Data Distributions Quick Check

Use the image to answer the question.

An illustration shows two sets of dot plots. One is titled Weight in Pounds, Cats and the other is Weight in Pounds, Small Dogs. The plots are shown as an abacus-like representation with dots in a vertical row over each number on a number line. For Cats, a number line with arrows on both ends ranges from 9 to 13 in increments of 1. There is 1 dot above 9, 2 dots above 10, 4 dots above 11, 2 dots above 12, and one dot above 13. For Small Dogs, a number line with arrows on both ends ranges from 8 to 15 in increments of 1. There is 1 dot above 8, 2 dots above 9, 4 dots above 10, 2 dots above 11, 2 dots above 12, 2 dots above 13, 1 dot above 14, and 1 dot above 15.

The dot plots show the weights of randomly selected cats and small dogs in different households. Based on an informal assessment of the visual overlap of these distributions, which animal has the least variability in their weights? Why?

A: Cats, because the range of their weights is less than that of small dogs.

Use the image to answer the question.

An illustration shows two sets of dot plots. One is titled Weight in Pounds, Cats and the other is Weight in Pounds, Small Dogs. The plots are shown as an abacus-like representation with dots in a vertical row over each number on a number line. For Cats, a number line with arrows on both ends ranges from 9 to 13 in increments of 1. There is 1 dot above 9, 2 dots above 10, 4 dots above 11, 2 dots above 12, and one dot above 13. For Small Dogs, a number line with arrows on both ends ranges from 8 to 15 in increments of 1. There is 1 dot above 8, 2 dots above 9, 4 dots above 10, 2 dots above 11, 2 dots above 12, 2 dots above 13, 1 dot above 14, and 1 dot above 15.

The dot plots show the weights of randomly selected cats and small dogs in different households. What is the difference between the modal weights of cats and small dogs?

A: 1 pound

The data shows the number of miles run per week by randomly selected students from two different classes. Find the difference between the medians. Which class has a higher median? By how much?

Class 1: 6, 8, 10, 11, 14, 4, 5, 8, 2, 7, 7, 5, 10, 12, 11
Class 2: 6, 4, 5, 6, 7, 8, 12, 9, 10, 11, 5, 8, 7, 4, 10

A: Class 1 has a higher median than Class 2 by 1 mile.

Two fertilizers are applied to randomly selected potato plants. After several weeks, the potatoes are weighed. The weights in kilograms are as follows. Which fertilizer is generally more effective?

Fertilizer A: 27, 20, 16, 18, 22, 19, 23, 21, 17, 19
Fertilizer B: 28, 19, 18, 21, 24, 20, 25, 27, 29, 21

A: Fertilizer B is generally more effective, because the mean and median weights of the potatoes that were treated with it are higher.

Use the image to answer the question.

Two number lines extend from 1 to 10 in increments of 1 and are labeled as Number of States Visited, Hiking Club, and Number of States Visited, Swimming Club. The number lines show an abacus-like representation with columns of open circles over the numbers. Above the number line labeled as Number of States Visited, Hiking Club, there are no circles over 1, two circles over 2, three circles over 3, five circles over 4, six circles over 5, five circles over 6, four circles over 7, three circles over 8, two circles over 9, and one circle over 10. Above the number line labeled as Number of States Visited, Swimming Club, there is one circle over 1, two circles over 2, one circle over 3, two circles over 4, two circles over 5, three circles over 6, four circles over 7, five circles over 8, six circles over 9, and six circles over 10.

For a geography project, you have surveyed the people in your hiking club and swimming club to find the number of states they have visited. You make a table and dot plots to show the results. Use the dot plots to compare the shapes and spreads of the dot plots. What conclusions can you draw about the shapes and the spreads?

A: The swimming club has a greater spread than the hiking club. The hiking club is symmetrical, and the swimming club is skewed left. The hiking club has a peak at 5. The swimming club has peaks at 9 and 10.

Nppp!