Part A: First of all, start by putting the numbers in each set by crescent order.
School A: 6, 6, 7, 9, 14, 15, 15, 17, 17
School B: 5, 8, 8, 11, 12, 13, 15, 16, 19
Five-number summary School A:
1. sample minimum - 6 (the smallest number from the sample)
2. lower quartile - 6.5 (the number in the middle of the minimum and the median)
3. median - 14 (the middle number)
4. upper quartile - 16 (the number in the middle of the median and the maximum)
5. sample maximum - 17 (the biggest number from the sample)
IQR School A = Q3 − Q1 = 16 - 6.5 = 9.5 (The interquartile range is calculated by subtracting the lower quartile from the upper quartile.)
Five-number summary School B:
1. sample minimum - 5 (the smallest number from the sample)
2. lower quartile - 8 (the number in the middle of the minimum and the median)
3. median - 12 (the middle number)
4. upper quartile - 15.5 (the number in the middle of the median and the maximum)
5. sample maximum - 19 (the biggest number from the sample)
IQR School B = Q3 − Q1 = 15.5 - 8 = 7.5 (The interquartile range is calculated by subtracting the lower quartile from the upper quartile.)
Part B:
You can draw the box plots and see if they are symmetric. Below I'll represent it so you can have an idea.
School A - not symmetric
_________________________
|--|___________________|______|-----|
6 7 8 9 10 11 12 13 14 15 16 17
School B - not symmetric (but close)
_____________________
|-------------|__________|__________|-------------------|
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
