# 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
1. What is the mean?
2. What is the standard deviation?

### Solution

For access, consult one of our IM Certified Partners.

### Problem 2

Here is a data set:

• 1
• 2
• 3
• 3
• 4
• 4
• 4
• 4
• 5
• 5
• 6
• 7
1. What happens to the mean and standard deviation of the data set when the 7 is changed to a 70?
2. 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

For access, consult one of our IM Certified Partners.

### 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

### Solution

For access, consult one of our IM Certified Partners.

### 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.

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

### Solution

For access, consult one of our IM Certified Partners.

(From Unit 1, Lesson 11.)

### 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:

uniform

### Solution

For access, consult one of our IM Certified Partners.

(From Unit 1, Lesson 10.)

What is the IQR?

A:

5 branches

B:

7 branches

C:

10 branches

D:

12 branches

### Solution

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(From Unit 1, Lesson 11.)

### 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
1. Find the mean.
2. Find the median.
3. Eliminate the greatest value, 42, from the data set. Explain how the measures of center change.

### Solution

For access, consult one of our IM Certified Partners.

(From Unit 1, Lesson 9.)