Certainly! Let's tackle each part of this question step by step.
Part A: Calculate the measures of center.
To determine the measures of center, we calculate the mean and the median for the class sizes of both schools.
Mountain View School:
- Class Sizes: 9, 8, 2, 0, 8, 7, 6, 5, 5, 4, 4, 3, 1, 0, 3
- Mean:
To find the mean, sum all class sizes and divide by the number of classes.
[tex]\[
\text{Mean} = \frac{9 + 8 + 2 + 0 + 8 + 7 + 6 + 5 + 5 + 4 + 4 + 3 + 1 + 0 + 3}{15} = \frac{65}{15} \approx 4.33
\][/tex]
- Median:
To find the median, list the class sizes in ascending order and find the middle value.
Sorted list: 0, 0, 1, 2, 3, 3, 4, 4, 5, 5, 6, 7, 8, 8, 9
Since there are 15 values, the middle value (8th value) is the median.
[tex]\[
\text{Median} = 4
\][/tex]
Bay Side School:
- Class Sizes: 5, 6, 8, 0, 2, 4, 5, 6, 8, 2, 3, 5, 4, 2
- Mean:
To find the mean, sum all class sizes and divide by the number of classes.
[tex]\[
\text{Mean} = \frac{5 + 6 + 8 + 0 + 2 + 4 + 5 + 6 + 8 + 2 + 3 + 5 + 4 + 2}{14} = \frac{60}{14} \approx 4.29
\][/tex]
- Median:
To find the median, list the class sizes in ascending order and find the middle value.
Sorted list: 0, 2, 2, 2, 3, 4, 4, 5, 5, 5, 6, 6, 8, 8
Since there are 14 values, the median is the average of the 7th and 8th values.
[tex]\[
\text{Median} = \frac{4 + 5}{2} = 4.5
\][/tex]
Measures of Center:
- Mountain View School: Mean ≈ 4.33, Median = 4
- Bay Side School: Mean ≈ 4.29, Median = 4.5
Part B: Calculate the measures of variability.
To determine the measures of variability, we calculate the standard deviation for the class sizes of both schools.
Mountain View School:
- Class Sizes: 9, 8, 2, 0, 8, 7, 6, 5, 5, 4, 4, 3, 1, 0, 3
- Standard Deviation:
[tex]\[
\text{Standard Deviation} \approx 2.895
\][/tex]
Bay Side School:
- Class Sizes: 5, 6, 8, 0, 2, 4, 5, 6, 8, 2, 3, 5, 4, 2
- Standard Deviation:
[tex]\[
\text{Standard Deviation} \approx 2.335
\][/tex]
Measures of Variability:
- Mountain View School: Standard Deviation ≈ 2.895
- Bay Side School: Standard Deviation ≈ 2.335
Part C: If you are interested in a larger class size, which school is a better choice for you? Explain your reasoning.
To determine which school has a larger average class size, we compare the means:
- Mountain View School: Mean ≈ 4.33
- Bay Side School: Mean ≈ 4.29
Since the mean class size is slightly higher at Mountain View School (approximately 4.33) compared to Bay Side School (approximately 4.29), Mountain View School would be a better choice if you are interested in larger class sizes. This does indicate that, on average, classes are slightly larger at Mountain View.
