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)

PLEASE HELP ASAP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 1

person up top did a great job

Answer 2

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

For Bay Side School, the median class size is the average of the 8th and 9th values when the data is sorted in ascending order. The 8th and 9th values are both 25, so the median class size is 25.

To find the mean class size for Bay Side School, we can add up all the class sizes and divide by the total number of classes. The sum of the class sizes is 12 + 12 + 12 + 14 + 15 + 15 + 16 + 16 + 18 + 18 + 20 + 20 + 23 + 25 + 25 = 243. There are 15 classes, so the mean class size is 243/15 ≈ 16.2.

For Seaside School, the median class size is the average of the 8th and 9th values when the data is sorted in ascending order. The 8th and 9th values are both 15, so the median class size is 15.

To find the mean class size for Seaside School, we can add up all the class sizes and divide by the total number of classes. The sum of the class sizes is 10 + 10 + 10 + 11 + 12 + 15 + 15 + 16 + 17 + 17Part A (continued):

18 + 18 + 20 + 20 + 25 = 222. There are 14 classes, so the mean class size is 222/14 ≈ 15.9.

Therefore, the measures of center for Bay Side School are: median = 25, mean ≈ 16.2.

The measures of center for Seaside School are: median = 15, mean ≈ 15.9.

Part B: To calculate the measures of variability, we can find the range and the interquartile range (IQR) for each school.

For Bay Side School, the range is the difference between the largest and smallest class sizes. The largest class size is 25, and the smallest class size is 12, so the range is 25 - 12 = 13.

To find the IQR for Bay Side School, we need to find the first quartile (Q1) and the third quartile (Q3) of the data. From the stem-and-leaf plot, we can see that Q1 is 15 and Q3 is 20. Therefore, the IQR is 20 - 15 = 5.

For Seaside School, the range is the difference between the largest and smallest class sizes. The largest class size is 25, and the smallest class size is 10, so the range is 25 - 10 = 15.

To find the IQRPart B (continued): for Seaside School, we need to find the first quartile (Q1) and the third quartile (Q3) of the data. From the stem-and-leaf plot, we can see that Q1 is 12 and Q3 is 18. Therefore, the IQR is 18 - 12 = 6.

Therefore, the measures of variability for Bay Side School are: range = 13, IQR = 5.

The measures of variability for Seaside School are: range = 15, IQR = 6.

Part C: If you are interested in a smaller class size, Seaside School is a better choice because its measures of center are lower than those of Bay Side School, indicating that its class sizes tend to be smaller on average. Additionally, Seaside School has a smaller range and IQR, indicating less variability in class size. Therefore, there is less chance of encountering very large classes at Seaside School compared to Bay Side School.