Question

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

Bay Side School Seaside School
8, 6, 5 0 5, 8
8, 6, 5, 4, 2, 0 1 0, 1, 2, 5, 6, 8
5, 3, 2, 0, 0 2 5, 5, 7, 7, 8
3 0, 6
2 4
Key: 2 | 1 | 0 means 12 for Bay Side 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 of each set of data.

For Bay Side School:

Mean = (2 x 12 + 1 x 10 + 1 x 8 + 3 x 6 + 1 x 5 + 1 x 4 + 1 x 3 + 1 x 2) ÷ 15 = 6.4

Median = (5 + 5) ÷ 2 = 5

For Seaside School:

Mean = (2 x 10 + 1 x 8 + 2 x 7 + 2 x 6 + 1 x 5 + 1 x 2) ÷ 9 ≈ 7.11

Median = (5 + 6) ÷ 2 = 5.5

Part B:

To calculate the measures of variability, we need to find the range and interquartile range (IQR) of each set of data.

For Bay Side School:

Range = Largest value - Smallest value = 8 - 2 = 6

IQR = Q3 - Q1 = (6 + (8 ÷ 2)) - (3 + (5 ÷ 2)) = (6 +4) - (3+2.5) =4.5

For Seaside School:

Range = Largest value - Smallest value =8 -2=6

IQR=Q3-Q1=(7+(8÷2))−(5+(0÷2))=(7+4)−(5+0)=6

Part C:

If you are interested in a smaller class size, Seaside School is a better choice for you because it has a smaller mean and median than Bay Side School. The mean and median are both measures of center, so they give us an idea of what the typical class size is like at each school. Since Seaside School has smaller values for both measures of center, it is likely that the classes are smaller on average at Seaside School.