# Summarizing Deviations from the Mean

Examples, solutions, and videos to help Algebra I students learn how to calculate the deviations from the mean for two symmetrical data sets that have the same means.

Learning Objective:
Students interpret deviations that are generally larger as identifying distributions that have a greater spread or variability than a distribution in which the deviations are generally smaller.

### New York State Common Core Math Algebra I, Module 2, Lesson 4

Lesson 4 Summary

For any given value in a data set, the deviation from the mean is the value minus the mean.

The greater the variability (spread) of the distribution, the greater the deviations from the mean (ignoring the signs of the deviations).

Exercise

1. A consumers’ organization is planning a study of the various brands of batteries that are available. As part of its planning, it measures lifetime ( how long a battery can be used before it must be replaced) for each of six batteries of Brand A and eight batteries of Brand B. Dot plots showing the battery lives for each brand are shown below.
a. Does one brand of battery tend to last longer, or are they roughly the same? What calculations could you do in order to compare the battery lives of the two brands?
b. Do the battery lives tend to differ more from battery to battery for Brand A or for Brand B?

c. Would you prefer a battery brand that has battery lives that do not vary much from battery to battery? Why or why not?

2. The lives of 100 batteries of Brand D and 100 batteries of Brand E were determined. The results are summarized in the histograms below.

3. Estimate the mean battery life for Brand D. (Do not do any calculations!)

4. Estimate the mean battery life for Brand E. (Again, no calculations!)

5. Which of Brands D and E shows the greater variability in battery lives? Or do you think the two brands are roughly the same in this regard?

6. Estimate the largest deviation from the mean for Brand D.

7. What would you consider a typical deviation from the mean for Brand D?

Exit Ticket

Five people were asked approximately how many hours of TV they watched per week. Their responses were as follows.

6 4 6 7 8

1. Find the mean number hours of TV watched for these five people.
2. Find the deviations from the mean for these five data values.
3. Write a new set of five values that has roughly the same mean as the data set above but that has, generally speaking, greater deviations from the mean.

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