# Lesson 13

More Standard Deviation

### Problem 1

Three drivers competed in the same fifteen drag races. The mean and standard deviation for the race times of each of the drivers are given.

Driver A had a mean race time of 4.01 seconds and a standard deviation of 0.05 seconds.

Driver B had a mean race time of 3.96 seconds and a standard deviation of 0.12 seconds.

Driver C had a mean race time of 3.99 seconds and a standard deviation of 0.19 seconds.

- Which driver had the fastest typical race time?
- Which driver’s race times were the most variable?
- Which driver do you predict will win the next drag race? Support your prediction using the mean and standard deviation.

### Solution

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### Problem 2

The widths, in millimeters, of fabric produced at a ribbon factory are collected. The mean is approximately 23 millimeters and the standard deviation is approximately 0.06 millimeters.

Interpret the mean and standard deviation in the context of the problem.

### Solution

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### Problem 3

Select **all** the statements that are true about standard deviation.

It is a measure of center.

It is a measure of variability.

It is the same as the MAD.

It is calculated using the mean.

It is calculated using the median.

### Solution

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### Problem 4

The number of different species of plants in some gardens is recorded.

- 1
- 2
- 3
- 4
- 4
- 5
- 5
- 6
- 7
- 8

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

### Solution

### Problem 5

A set of data has ten numbers. The mean of the data is 12 and the standard deviation is 0. What values could make up a data set with these statistics?

### Solution

### Problem 6

Which box plot has the largest interquartile range?

### Solution

### Problem 7

- What is the five-number summary for 1, 3, 3, 3, 4, 8, 9, 10, 10, 17?
- When the maximum, 17, is removed from the data set, what is the five-number summary?