Sure, let's go through the problem step by step.
### Part A: Calculate the measures of center (mean and median)
#### Bay Side School
Bay Side class sizes: [tex]\(8, 6, 5, 18, 16, 15, 14, 12, 10, 25, 23, 22, 20, 20, 42\)[/tex].
Mean:
[tex]\[ \text{Mean} = \frac{\sum \text{data points}}{\text{number of data points}} = \frac{8 + 6 + 5 + 18 + 16 + 15 + 14 + 12 + 10 + 25 + 23 + 22 + 20 + 20 + 42}{15} = 17.07 \][/tex]
Median:
Arrange the data in ascending order: [tex]\(5, 6, 8, 10, 12, 14, 15, 16, 18, 20, 20, 22, 23, 25, 42\)[/tex]. As there are 15 data points, the median will be the 8th data point:
[tex]\[ \text{Median} = 16.0 \][/tex]
#### Seaside School
Seaside class sizes: [tex]\(5, 8, 10, 11, 12, 15, 16, 18, 25, 25, 27, 27, 28, 30, 36\)[/tex].
Mean:
[tex]\[ \text{Mean} = \frac{\sum \text{data points}}{\text{number of data points}} = \frac{5 + 8 + 10 + 11 + 12 + 15 + 16 + 18 + 25 + 25 + 27 + 27 + 28 + 30 + 36}{15} = 19.53 \][/tex]
Median:
Arrange the data in ascending order: [tex]\(5, 8, 10, 11, 12, 15, 16, 18, 25, 25, 27, 27, 28, 30, 36\)[/tex]. As there are 15 data points, the median will be the 8th data point:
[tex]\[ \text{Median} = 18.0 \][/tex]
### Part B: Calculate the measures of variability (standard deviation and range)
#### Bay Side School
Standard Deviation:
[tex]\[ \text{Standard Deviation} = 8.96 \][/tex]
Range:
[tex]\[ \text{Range} = \text{Maximum} - \text{Minimum} = 42 - 5 = 37 \][/tex]
#### Seaside School
Standard Deviation:
[tex]\[ \text{Standard Deviation} = 9.03 \][/tex]
Range:
[tex]\[ \text{Range} = \text{Maximum} - \text{Minimum} = 36 - 5 = 31 \][/tex]
### Part C: School choice for smaller class size
If you are interested in smaller class sizes, you should consider the mean class size of each school. A lower mean value indicates smaller average class sizes.
Bay Side School:
Mean = 17.07
Seaside School:
Mean = 19.53
Better choice:
Since [tex]\( 17.07 < 19.53 \)[/tex], the better choice for smaller class sizes is Bay Side School.
