The number of hours each student spent studying for a test in Classroom A and Classroom B are shown below.

Question

Classroom A: 1, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 8, 9, 11, 20

Classroom B: 1, 4, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 8, 10, 22

Determine whether each description of the summary statistic applies to the two data sets shown above. Select Yes or No for each summary statistic.
Summary Statistic
Yes
No
The standard deviation and mean should be used to compare the data sets because the data sets do not contain any extreme outliers.
The standard deviation and mean should be used to compare the data sets because the data sets are normally distributed.
The interquartile range and median should be used to compare the data sets because both data sets contain extreme outliers and are skewed.

Answer 1

To determine whether each summary statistic is appropriate for comparing the data sets from Classroom A and Classroom B, we need to analyze the characteristics of the data, including the presence of outliers and the distribution shape.

1. The standard deviation and mean should be used to compare the data sets because the data sets do not contain any extreme outliers.

   Answer: No

   • Both data sets contain extreme outliers: Classroom A has a value of 20, and Classroom B has a value of 22. This presence of outliers affects the mean and standard deviation. Thus, it would not be advisable to use these statistics for comparison.

2. The standard deviation and mean should be used to compare the data sets because the data sets are normally distributed.

   Answer: No

   • The data does not appear to be normally distributed, especially given the presence of outliers. The distribution of hours studied in both classrooms is skewed due to the extreme values at the higher end. Therefore, the use of mean and standard deviation is not appropriate.

3. The interquartile range and median should be used to compare the data sets because both data sets contain extreme outliers and are skewed.

   Answer: Yes

   • Since both data sets contain extreme outliers and are skewed, the interquartile range (IQR) and median are more appropriate summary statistics for comparison. IQR is resistant to outliers and provides a better measure of spread in skewed distributions.

In summary:

• Question 1: No
• Question 2: No
• Question 3: Yes