Algebra 1 | Unit 1 | Lesson 15: Comparing Data Sets | Practice Problems

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.

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• Only mean is appropriate.

• Only median is appropriate.

Which situation shows a greater typical heart rate?

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• Both situations show the same heart rate.

Which situation shows greater variability?

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• Both situations show the same variability.

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.

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?

• The shape becomes skewed to the right.

• The shape remains symmetric.

• The shape becomes skewed to the left.

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

• Both mean and median increase by 5.

• Only mean increases by 5.

• Mean increases, median remains the same.

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

• Standard deviation increases by 5.

• IQR remains the same.

• Both standard deviation and IQR remain the same.

Here are two box plots: Which box plot has a greater median?

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• Both have the same median.

Which box plot has a greater measure of variability?

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• Both have the same variability.