Question

The stem-and-leaf plot displays data collected on the size of 15 classes at two different schools.

Mountain View School Seaside School
0 5, 8
9, 8, 2, 0 1 0, 1, 2, 5, 6, 8
8, 7, 6, 5, 5, 4, 4, 3, 1, 0 2 5, 5, 7, 7, 8
0 3 0, 6
Key: 2 | 1 | 0 means 12 for Mountain View and 10 for Seaside


Part A: Calculate the measures of center. Show all work. (2 points)

Part B: Calculate the measures of variability. Show all work. (1 point)

Part C: If you are interested in a smaller class size, which school is a better choice for you? Explain your reasoning. (1 point)

Answer 1

Part A: To calculate the measures of center, we need to find the mean and median for each school.

For Mountain View School:
Mean: We add up all the values and divide by the total number of values.
Mean = (0 + 5 + 8 + 9 + 8 + 2 + 0 + 1 + 0 + 1 + 2 + 5 + 6 + 8 + 8 + 7 + 6 + 5 + 5 + 4 + 4 + 3 + 1 + 0 + 2 + 5 + 5 + 7 + 7 + 8) / 30
Mean = 139 / 30
Mean ≈ 4.633

Median: We arrange the values in ascending order and find the middle value.
Median = (0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 8, 8, 8, 8, 9)
Median = (5 + 5) / 2
Median = 5

For Seaside School:
Mean: We add up all the values and divide by the total number of values.
Mean = (5 + 8 + 10 + 10 + 12 + 12 + 15 + 17 + 17 + 18) / 10
Mean = 134 / 10
Mean = 13.4

Median: We arrange the values in ascending order and find the middle value.
Median = (5, 8, 10, 10, 12, 12, 15, 17, 17, 18)
Median = 12

Part B: To calculate the measures of variability, we need to find the range for each school.

For Mountain View School:
Range = Maximum value - Minimum value
Range = 9 - 0
Range = 9

For Seaside School:
Range = Maximum value - Minimum value
Range = 18 - 5
Range = 13

Part C: If you are interested in a smaller class size, the better choice would be Mountain View School. This is because the mean class size at Mountain View School (4.633) is smaller than the mean class size at Seaside School (13.4). Additionally, the median class size at Mountain View School (5) is also smaller than the median class size at Seaside School (12). Both the measures of center indicate that the class sizes at Mountain View School tend to be smaller compared to Seaside School.