Lesson 8: Practice Problems

Problem 1

Alexandria recorded the number of times she saw an animal in her backyard each day for a week. She recorded 5, 11, 3, 8, 12, 9, 7. Alexandria made a mistake: The 3 in the data should have been 13.

How would changing the 3 to 13 affect the mean and median of the data set?

  1. The mean would decrease and the median would not change.

  2. The mean would increase and the median would not change.

  3. The mean would decrease and the median would increase.

  4. The mean would increase and the median would increase.

Problem 2

Here is a dot plot that shows the ages of players on a soccer team.

A dot plot of age in years ranging from 16 to 40.

Which of these statements is true of the data set shown in the dot plot?

  1. The mean is less than the median.

  2. The mean is approximately equal to the median.

  3. The mean is greater than the median.

  4. The mean cannot be determined.

Problem 3

Use the dot plot from the previous problem and create a box plot.

  1. What is the median score?

  2. What is the first quartile (Q1)?

  3. What is the third quartile (Q3)?

  4. What is the interquartile range (IQR)?

Problem 4

Create two dot plots or two box plots for which the mean is approximately equal to the median. Label your dot plots or box plots.

Problem 5

Cora and Lincoln each played 10 games of a card game and recorded the scores. Cora’s median score was 120, and her IQR was 5. Lincoln’s median score was 118, and his IQR was 15. Whose scores probably had less variability? Explain how you know.

Problem 6

Solve each equation. Show your work, or explain your reasoning.