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 analyze the appropriate summary statistics for comparing the two data sets, let's go through each statement provided:

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
     • Explanation: Both data sets contain extreme outliers (20 in Classroom A and 22 in Classroom B), which can skew the mean and increase the standard deviation. Therefore, using the mean and standard deviation may not be appropriate.

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

   • Answer: No
     • Explanation: Neither data set appears to be normally distributed. Both have outliers and visible skewness which suggests that they are not symmetrical and thus not normally distributed.

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
     • Explanation: The interquartile range (IQR) and median are robust statistics that are not affected by outliers or skewed distributions. Since both data sets contain outliers and are skewed, it is appropriate to use the IQR and median for comparison.

In summary:

1. No
2. No
3. Yes