Unit 8, Lesson 9
Mean
Grade 6
9.1
Warm-up
Close to Four
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.
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The preschool teacher wants the kittens distributed equally among the boxes. How might that be done? How many kittens will end up in each box?
Another preschool room has 6 boxes. No 2 boxes have the same number of kittens, and there is an average of 3 kittens per box. Draw or describe at least 2 different arrangements of kittens that match this description.
Five servers are scheduled to work the number of hours shown. They decide to share the workload, so each one would work equal hours.
Server A: 3
Server B: 6
Server C: 11
Server D: 7
Server E: 4
On the first grid, draw 5 bars whose heights represent the hours worked by Servers A, B, C, D, and E.
Then, think about how you would rearrange the hours so that each server gets a fair share. On the second grid, draw a new graph to represent the rearranged hours. Be prepared to explain your reasoning.
Explain why we can also find the mean by finding the value of the expression
Sometimes a general description of a distribution does not give enough information, and a more precise way to talk about center or spread would be more useful. The mean, or average, is a number we can use for the center to summarize a distribution.
We can think about the mean in terms of “fair share” or “leveling out.” That is, a mean can be thought of as a number that each member of a group would have if all the data values were combined and distributed equally among the members.
For example, suppose there are 5 containers, each of which has a different amount of water: 1 liter, 4 liters, 2 liters, 3 liters, and 0 liters.
There are 5 identical tape diagrams that are each partitioned into 4 equal parts. The first diagram has 1 part shaded. The second diagram has 4 parts shaded. The third diagram has 2 parts shaded. The fourth diagram has 3 parts shaded. The fifth diagram has no parts shaded.
To find the mean, first we add up all of the values. We can think of this as putting all of the water together:
To find the “fair share,” we divide the 10 liters equally into the 5 containers:
The mean is useful when each unit of measurement has equal importance. For example, it may make sense to find the mean score of assignments of the same importance, such as all quizzes. If some grades are more important, it may not make sense to find the mean. For example, it may not make sense to find the mean score when there are 6 short homework assignments and one major essay.
Suppose the quiz scores of a student are 70, 90, 86, and 94. We can find the mean (or average) score by finding the sum of the scores
In general, to find the mean of a data set with
The average is another name for the mean of a data set. To find the average, add all the numbers in the data set. Then divide by how many numbers there are.
The average is 7.5.
The mean is one way to measure the center of a data set. It can be thought of as a balance point. To find the mean, add all the numbers in the data set. Then divide by how many numbers there are.
The mean is 11. So, the typical travel time is 11 minutes.
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