# Lesson 12

Standard Deviation

### 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

- What is the mean?
- What is the standard deviation?

### Solution

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### Problem 2

Here is a data set:

- 1
- 2
- 3
- 3
- 4
- 4
- 4
- 4
- 5
- 5
- 6
- 7

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

### Solution

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### Problem 3

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

5 points

20 points

50 points

500 points

### Solution

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### 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.

- Which data set shows greater variability? Explain your reasoning.
- What differences would you expect to see when comparing the dot plots of the two data sets?

### Solution

### Problem 5

Select **all** the distribution shapes for which the mean and median *must be* about the same.

bell-shaped

bimodal

skewed

symmetric

uniform

### Solution

### Problem 6

What is the IQR?

5 branches

7 branches

10 branches

12 branches

### Solution

### 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

- Find the mean.
- Find the median.
- Eliminate the greatest value, 42, from the data set. Explain how the measures of center change.