Standard Deviation

ID: sutok-fanuf
Created by Illustrative MathIllustrative Math
Subject: Algebra, Algebra 2
Grade: 8-9

Standard Deviation

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Problem 1

The shoe size for all the pairs of shoes in a person's closet are recorded.

7, 7, 7, 7, 7, 7, 7, 7, 7, 7

1) What is the mean?

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2) What is the standard deviation?

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Problem 2

Here is a data set:

1, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 7

3) What happens to the mean and standard deviation of the data set when the 7 is changed to a 70?

4) For the data set with the value of 70, why would the median be a better choice for the measure of center than the mean?

Problem 3

5) Which of these best estimates the standard deviation of points in a card game?

A template for answering this question. Ask your instructor for an alternative.
a) 5 points\text{5 points}b) 20 points\text{20 points}c) 50 points\text{50 points}d) 500 points\text{500 points}
Problem 4

The mean of data set A is 43.5 and the MAD is 3.7. The mean of data set B is 12.8 and the MAD is 4.1.

6) Which data set shows greater variability?

a) Data set A\text{Data set A}b) Data set B\text{Data set B}c) They both show the same amount of variability\text{They both show the same amount of variability}d) Not enough information has been provided\text{Not enough information has been provided}

7) Explain your reasoning.

8) What differences would you expect to see when comparing the dot plots of the two data sets?

Problem 5

9) Select all the distribution shapes for which the mean and median must be about the same. Write each corresponding letter in the answer box and separate letters with commas.

a) bell-shaped b) bimodal c) skewed d) symmetric e) uniform

Problem 6

10) What is the IQR?

A template for answering this question. Ask your instructor for an alternative.
a) 5 branches\text{5 branches}b) 7 branches\text{7 branches}c) 10 branches\text{10 branches}d) 12 branches\text{12 branches}
Problem 7

The data represent the number of cans collected by different classes for a service project.

12, 14, 22, 14, 18, 23, 42, 13, 9, 19, 22, 14

11) Find the mean.

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12) Find the median.

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13) Eliminate the greatest value, 42, from the data set. Explain how the measures of center change.