Question

the table shows the test scores of students who studied for a test as a group (group a) and students who studied individually (group b). which would be the best measures of center and variation to use to compare the data? student test scores (out of 100) group a 84 80 77 96 92 88 88 84 92 100 group b 92 86 85 87 83 85 83 78 80 88 the scores of group b are skewed right, so the mean and range are the best measures for comparison. both distributions are nearly symmetric, so the mean and the standard deviation are the best measures for comparison. both distributions are nearly symmetric, so the median and the interquartile range are the best measures for comparison. the scores of both groups are skewed, so the median and standard deviation are the best measures for comparison.

Explanation:

Step1: Recall measure - selection rules

For symmetric distributions, the mean is the best measure of center as it takes into account all data - points, and the standard deviation is the best measure of variation as it measures the average distance of data points from the mean. For skewed distributions, the median is a better measure of center as it is not affected by extreme values, and the inter - quartile range is a better measure of variation as it is also resistant to outliers.

Step2: Analyze the distributions

By looking at the data of Group A: 84, 80, 77, 96, 92, 88, 88, 84, 92, 100 and Group B: 92, 86, 85, 87, 83, 85, 83, 78, 80, 88, we can see that both distributions are nearly symmetric. There are no extreme outliers that would skew the data significantly.

Answer:

Both distributions are nearly symmetric, so the mean and the standard deviation are the best measures for comparison.