# Lesson 15

Comparing Data Sets

- Let’s compare statistics for data sets.

### Problem 1

Twenty students participated in a psychology experiment which measured their heart rates in two different situations.

- What are the appropriate measures of center and variability to use with the data? Explain your reasoning.
- Which situation shows a greater typical heart rate?
- Which situation shows greater variability?

### Problem 2

- Invent two situations that you think would result in distributions with similar measures of variability. Explain your reasoning.
- Invent two situations that you think would result in distributions with different measures of variability. Explain your reasoning.

### Problem 3

The data set and some summary statistics are listed.

11.5, 12.3, 13.5, 15.6, 16.7, 17.2, 18.4, 19, 19.5, 21.5

- mean: 16.52
- median: 16.95
- standard deviation: 3.11
- IQR: 5.5

- How does adding 5 to each of the values in the data set impact the shape of the distribution?
- How does adding 5 to each of the values in the data set impact the measures of center?
- How does adding 5 to each of the values in the data set impact the measures of variability?

### Problem 4

Here are two box plots:

- Which box plot has a greater median?
- Which box plot has a greater measure of variability?

### Problem 5

The depth of two lakes is measured at multiple spots. For the first lake, the mean depth is about 45 feet with a standard deviation of 8 feet. For the second lake, the mean depth is about 60 feet with a standard deviation of 27 feet.

Noah says the second lake is generally deeper than the first lake. Do you agree with Noah?

### Problem 6

The dot plots display the height, rounded to the nearest foot, of maple trees from two different tree farms.

- Compare the mean and standard deviation of the two data sets.
- What does the standard deviation tell you about the trees at these farms?

### Problem 7

Which box plot has an IQR of 10?

### Problem 8

What effect does eliminating the lowest value, -6, from the data set have on the mean and median?

-6, 3, 3, 3, 3, 5, 6, 6, 8, 10