Question

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

Riverside School South Lake School
9, 6, 5 0 5, 8
7, 6, 5, 4, 2, 0 1 0, 1, 2, 6, 6, 8
5, 3, 2, 0, 0 2 5, 5, 6, 7, 8
3 0, 6
2 4
Key: 2 | 1 | 0 means 12 for Riverside and 10 for South Lake


Part A: Calculate the measures of center. Show all work. (5 points)

Part B: Calculate the measures of variability. Show all work. (5 points)

Part C: If you are interested in a smaller class size, which school is a better choice for you? Explain your reasoning. (2 points)

Answer 1

A. (look at explanations)

B. (look at explanations)

C. (look at explanations)

Explanation:

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

For Riverside School, the data is:

5, 6, 7, 9, 10, 12, 15, 16, 20, 20, 22, 23, 24, 25, 26

The mean is the sum of the data divided by the number of data points. The mean is:

(5 + 6 + 7 + … + 25 + 26) / 15 = 16.8

The median is the middle value of the data when it is arranged in order. The median is:

15

The mode is the most frequent value of the data. The mode is:

20

For South Lake School, the data is:

5, 8, 10, 11, 12, 16, 16, 18, 20, 20, 25, 25, 26, 27, 28

The mean is:

(5 + 8 + 10 + … + 27 + 28) / 15 = 18.4

The median is:

18

The mode is:

20 and 25

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

For Riverside School, the range is the difference between the maximum and minimum values of the data. The range is:

26 - 5 = 21

The standard deviation is a measure of how much the data varies from the mean. To find it, we need to calculate the variance first. The variance is the average of the squared differences from the mean. The variance is:

[(5 - 16.8)^2 + (6 - 16.8)^2 + … + (25 - 16.8)^2 + (26 - 16.8)^2] / 15 = 46.96

The standard deviation is the square root of the variance. The standard deviation is:

sqrt(46.96) = 6.85

For South Lake School, the range is:

28 - 5 = 23

The variance is:

[(5 - 18.4)^2 + (8 - 18.4)^2 + … + (27 - 18.4)^2 + (28 - 18.4)^2] / 15 = 49.44

The standard deviation is:

sqrt(49.44) = 7.03

Part C: If you are interested in a smaller class size, Riverside School is a better choice for you. This is because Riverside School has a lower mean and median class size than South Lake School (16.8 vs. 18.4 and 15 vs. 18). This means that on average and in general, Riverside School has smaller classes than South Lake School.

Additionally, Riverside School has a lower standard deviation than South Lake School (6.85 vs. 7.03). This means that Riverside School has less variation in class size than South Lake School. This means that you are more likely to find a class size close to the average at Riverside School than at South Lake School.

Therefore, based on these measures of center and variability, Riverside School has smaller and more consistent class sizes than South Lake School.