Interpreting the Standard Deviation

New York State Common Core Math Algebra I, Module 2, Lesson 6

Worksheets for Algebra 1

Lesson 6 Summary

The mean and the standard deviation of a data set can be found directly using the statistical features of a calculator.

The size of the standard deviation is related to the sizes of the deviations from the mean. Therefore, the standard deviation is minimized when all the numbers in the data set are the same and is maximized when the deviations from the mean are made as large as possible.

Example 1

A set of eight men had heights (in inches) as shown below.
67.0 70.9 67.6 68.9 68.7 70.9 68.7 67.2

Indicate the mean and standard deviation you obtained from your calculator to the nearest hundredth.

Exercise 2

Ten people attended a talk at a conference. At the end of the talk, the attendees were given a questionnaire that consisted of four questions. The questions were optional, so it was possible that some attendees might answer none of the questions while others might answer 1, 2, 3, or all 4 of the questions (so the possible numbers of questions answered are 0, 1, 2, 3, and 4).

Suppose that the numbers of questions answered by each of the ten people were as shown in the dot plot below.

Use the statistical features of your calculator to find the mean and the standard deviation of the data set.

Exercise 4

Suppose that every person answers all four questions on the questionnaire.

a. What would the dot plot look like?

b. What is the mean number of questions answered? (You should be able to answer without doing any calculations!)

c. What is the standard deviation? (Again, don’t do any calculations!)

Exit Ticket

1. Use the statistical features of your calculator to find the standard deviation to the nearest tenth of a data set of the miles per gallon from a sample of five cars.

24.9 24.7 24.7 23.4 27.9

2. Suppose that a teacher plans to give four students a quiz. The minimum possible score on the quiz is 0, and the maximum possible score is 10.

a. What is the smallest possible standard deviation of the students’ scores? Give an example of a possible set of four student scores that would have this standard deviation.

b. What is the set of four student scores that would make the standard deviation as large as it could possibly be? Use your calculator to find this largest possible standard deviation.

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