Certainly! Let's go through the problem step by step, calculating the necessary statistics for each school.
### Part A: Measures of Center (5 points)
To find the measures of center, we'll calculate the mean and median for the class sizes at each school.
#### Riverside School:
1. Data: [9, 6, 5, 17, 16, 15, 14, 12, 10, 25, 23, 22, 20, 20, 42]
2. Mean:
Mean is calculated by summing all the values and dividing by the number of values.
[tex]\[
\text{Mean} = \frac{9 + 6 + 5 + 17 + 16 + 15 + 14 + 12 + 10 + 25 + 23 + 22 + 20 + 20 + 42}{15}
\][/tex]
[tex]\[
\text{Mean} \approx 17.07
\][/tex]
3. Median:
The median is the middle value in the ordered list. Ordering the data: [5, 6, 9, 10, 12, 14, 15, 16, 17, 20, 20, 22, 23, 25, 42]
The middle value (8th value in the list):
[tex]\[
\text{Median} = 16
\][/tex]
#### South Lake School:
1. Data: [5, 8, 10, 11, 12, 16, 16, 18, 25, 25, 26, 27, 28, 30, 36]
2. Mean:
[tex]\[
\text{Mean} = \frac{5 + 8 + 10 + 11 + 12 + 16 + 16 + 18 + 25 + 25 + 26 + 27 + 28 + 30 + 36}{15}
\][/tex]
[tex]\[
\text{Mean} \approx 19.53
\][/tex]
3. Median:
Ordering the data: [5, 8, 10, 11, 12, 16, 16, 18, 25, 25, 26, 27, 28, 30, 36]
The middle value (8th value in the list):
[tex]\[
\text{Median} = 18
\][/tex]
### Part B: Measures of Variability (5 points)
#### Riverside School:
1. Standard Deviation:
[tex]\[
\text{Standard Deviation} \approx 8.89
\][/tex]
#### South Lake School:
1. Standard Deviation:
[tex]\[
\text{Standard Deviation} \approx 8.95
\][/tex]
### Part C: School Choice Based on Smaller Class Size
To determine which school is better for smaller class sizes, we compare the median and mean values.
- Mean:
- Riverside: 17.07
- South Lake: 19.53
- Median:
- Riverside: 16
- South Lake: 18
Both the mean and median class sizes are smaller at Riverside School (17.07 mean vs 19.53 mean and 16 median vs 18 median).
Therefore, if you are interested in a smaller class size, Riverside School is a better choice.
