The distribution of test scores for two random samples of students is shown in the stem-and-leaf plots.
Group A
5 5 8
6 1 3 7
7 0 1 1 2 5 6 7 8 8 8
8 1 2 3 3 3 4 4 5 6 8
9 0 2 7
10 0 0
Key: 5|5 represents 55
Group B
5 7
6 4 8
7 1 2 2 5 6
8 0 2 4 5 5 5 7 7
9 1 3 4 5 6 7 7 8 8 9 9
10 0 0 0
Key: 5|7 represents 57
Part A: Calculate the mean, median, range, and interquartile range for each data set. (2 points)
Part B: Using the appropriate measures, compare the center and variability of the two groups of students. Explain your reasoning based on the shapes of the distributions. (2 points)

To find the median, we need to arrange the values in ascending order and find the middle value. If the number of values is odd, the median is the middle value. If the number of values is even, the median is the average of the two middle values.

Range:

To find the range, we subtract the smallest value from the largest value.

Range = Largest value - Smallest value

Interquartile Range:

To find the interquartile range, we need to find the difference between the first quartile (Q1) and the third quartile (Q3). The first quartile is the median of the lower half of the data, and the third quartile is the median of the upper half of the data.

For Group B:

Mean, median, range, and interquartile range are calculated in the same way as for Group A.

Part B:

To compare the center and variability of the two groups, we can look at the mean, median, range, and interquartile range.

For the center:

Compare the mean and median of both groups. If the mean and median are close in value, the data is symmetrically distributed. If the mean is larger than the median, the data is positively skewed, and if the mean is smaller than the median, the data is negatively skewed.

For the variability:

Compare the range and interquartile range of both groups. If the range and interquartile range are similar, the data has similar variability. If the range is larger than the interquartile range, the data has outliers and higher variability.

Based on the shapes of the distributions, we can make observations about the center and variability of the two groups. For example, if Group A has a higher mean and larger range than Group B, we can conclude that Group A has a higher average score and more variation in scores compared to Group B.

Remember, these are just examples, and you should provide your own analysis based on the actual values from the stem-and-leaf plots.