# ﻿Mean

Warmup

Use the digits 0–9 to write an expression with a value as close as possible to 4. Each digit can be used only one time in the expression.

Activity #1

Investigating the Mean.

• Read the story below and complete the activity described.

Five security officers were scheduled to work the number of hours shown below. They decided to share the workload, so each one would work equal hours.

• Officer A: 3
• Officer B: 6
• Officer C: 11
• Officer D: 7
• Officer E: 4
• Think about how you would rearrange the hours so that each officer gets a fair share. Then, draw a new graph to represent the rearranged hours.

• On the grid, drag 5 bars whose heights represent the hours worked by officers A, B, C, D, and E.

(1.) Based on your second drawing, what is the average or mean number of hours that the servers will work?

(2.) Explain why we can also find the mean by finding the value of 31 ÷ 5.

(3.) Which Officer will see the biggest change to work hours? Which Officer will see the least change?

(4.) Officer F, working 7 hours, offers to join the group of five officers, sharing their workload. If Officer F joins, will the mean number of hours worked increase or decrease? Explain or show how you know.

Activity #2

`Where is the Mean?`

• For each box-and-whisker plot below, drag the red point to where you think the mean of the data set is located. ​
• Click on the button to confirm. ​
• Click on the button to create two new box-and-whisker plots.

Activity #3

`Interpret the Mean.`

• Study the data and data sets before and answer the questions that follow.

(A.) For the past 12 school days, Mai has recorded how long her bus rides to school take in minutes. The times she recorded are shown in the table.

Find the mean for Mai’s data. Show your reasoning.

(B.) For 5 days, Tyler has recorded how long his walks to school take in minutes. The mean for his data is 11 minutes.

• data set A: 11, 8, 7, 9, 8
• data set B: 12, 7, 13, 9, 14
• data set C: 11, 20, 6, 9, 10
• data set D: 8, 10, 9, 11, 11

(1.) Without calculating, predict if each of the data sets shown could be Tyler’s. Explain your reasoning.

(2.) In this situation, what does the mean tell us about Mai’s trip to school?

(3.) Determine which data set is Tyler’s. Explain how you know.

Challenge #1

Calculate the mean in the 3 different sets of numbers in the applet below. Use the slider for a new set on numbers.

Challenge #2

A preschool teacher is rearranging four boxes of playing blocks so that each box contains an equal number of blocks. Currently Box 1 has 32 blocks, Box 2 has 18, Box 3 has 41, and Box 4 has 9.

Challenge #3

An earthworm farmer examined two containers of a certain species of earthworms so that he could learn about their lengths. He measured 25 earthworms in each container and recorded their lengths in millimeters.

Here below are histograms of the lengths for each container.

Quiz Time