# Lesson 12

Standard Deviation

- Let’s learn about standard deviation, another measure of variability.

### 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?

### 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?

### Problem 3

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

A:

5 points

B:

20 points

C:

50 points

D:

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.

- 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?

### Problem 5

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

A:

bell-shaped

B:

bimodal

C:

skewed

D:

symmetric

E:

(From Unit 1, Lesson 10.)
uniform

### Problem 6

What is the IQR?

A:

5 branches

B:

7 branches

C:

10 branches

D:

(From Unit 1, Lesson 11.)
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

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