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.

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

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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.