Estimating Population Measures of Center

Warmup

Activity #1

Practice Exercise Questions on Measures of Center.

• Use the data samples below to answer the questions that follow.

Here are the ages (in years) of a random sample of 10 viewers for 3 different television shows. The shows are titled, “Science Experiments YOU Can Do,” “Learning to Read,” and “Trivia the Game Show.”

(2.) Which show do you think each sample represents? Explain your reasoning.

Here are three more samples of viewer ages collected for these same 3 television shows.

(4.) Which show do you think each of these samples represents? Explain your reasoning.

(5.) For each show, estimate the mean age for all the show’s viewers.

Activity #2

Practice Exercise Questions on Measures of Center.

• Read the story below and use the dot plot to answer the questions that follow.

A movie rating website has many people rate a new movie on a scale of 0 to 100. Here is a dot plot showing a random sample of 20 of these reviews.

(2.) Use the sample to estimate the measure of center that you chose for all the reviews.

(3.) For this sample, the mean absolute deviation is 19.6, and the interquartile range is 15. Which of these values is associated with the measure of center that you chose?

(4.) Movies must have an average rating of 75 or more from all the reviews on the website to be considered for an award. Do you think this movie will be considered for the award? Use the measure of center and measure of variability that you chose to justify your answer.

Challenge #1

(1.) Would you use the median or mean to describe the center of each data set? Explain your reasoning.

(2.) Would you use the median or mean to describe the center of each data set? Explain your reasoning.

Challenge #2

Clare and Priya each took a random sample of 25 students at their school.

• Clare asked each student in her sample how much time they spend doing homework each night. The sample mean was 1.2 hours and the MAD was 0.6 hours.
• Priya asked each student in her sample how much time they spend watching TV each night. The sample mean was 2 hours and the MAD was 1.3 hours.

(1.) At their school, do you think there is more variability in how much time students spend doing homework or watching TV? Explain your reasoning.

(2.) Clare estimates the students at her school spend an average of 1.2 hours each night doing homework. Priya estimates the students at her school spend an average of 2 hours each night watching TV. Which of these two estimates is likely to be closer to the actual mean value for all the students at their school? Explain your reasoning.

Quiz Time

https://www.ixl.com/math/grade-7/compare-populations-using-measures-of-center-and-spread