Sure, let's go through this step-by-step:
### Part A: Calculate the measures of center
1. Mean
- Bay Side School: To find the mean, you sum all the class sizes and divide by the number of classes.
- Bay Side School class sizes: 8, 6, 5, 18, 16, 15, 14, 12, 10, 25, 23, 22, 20, 20, 42
- Sum of Bay Side School class sizes: [tex]\( 8 + 6 + 5 + 18 + 16 + 15 + 14 + 12 + 10 + 25 + 23 + 22 + 20 + 20 + 42 = 256 \)[/tex]
- Number of classes: 15
- Mean [tex]\( \frac{256}{15} \approx 17.07 \)[/tex]
- Seaside School: Similarly, calculate the mean for Seaside School.
- Seaside School class sizes: 5, 8, 10, 11, 12, 15, 16, 18, 25, 25, 27, 27, 28, 30, 36
- Sum of Seaside School class sizes: [tex]\( 5 + 8 + 10 + 11 + 12 + 15 + 16 + 18 + 25 + 25 + 27 + 27 + 28 + 30 + 36 = 293 \)[/tex]
- Number of classes: 15
- Mean [tex]\( \frac{293}{15} \approx 19.53 \)[/tex]
2. Median
- The median is the middle value of the ordered data set.
- Bay Side School:
- Ordered class sizes: 5, 6, 8, 10, 12, 14, 15, 16, 18, 20, 20, 22, 23, 25, 42
- The median is the 8th number: 16.0 (since there are 15 numbers, the median is the middle one, which is the 8th here)
- Seaside School:
- Ordered class sizes: 5, 8, 10, 11, 12, 15, 16, 18, 25, 25, 27, 27, 28, 30, 36
- The median is the 8th number: 18.0
Hence, the measures of center are:
- Bay Side School: Mean ≈ 17.07, Median = 16.0
- Seaside School: Mean ≈ 19.53, Median = 18.0
### Part B: Calculate the measures of variability
1. Standard Deviation
- Bay Side School: Standard deviation is a measure of how spread out the numbers are.
- Standard Deviation ≈ 8.96
- Seaside School: Similarly,
- Standard Deviation ≈ 9.03
2. Range
- The range is the difference between the highest and lowest values.
- Bay Side School:
- Highest value: 42
- Lowest value: 5
- Range = 42 - 5 = 37
- Seaside School:
- Highest value: 36
- Lowest value: 5
- Range = 36 - 5 = 31
Hence, the measures of variability are:
- Bay Side School: Standard Deviation ≈ 8.96, Range = 37
- Seaside School: Standard Deviation ≈ 9.03, Range = 31
### Part C: If you are interested in a smaller class size, which school is a better choice for you? Explain your reasoning.
If you are interested in a smaller class size, you should consider:
- Mean Class Size: The mean class size at Bay Side School (≈ 17.07) is smaller than that at Seaside School (≈ 19.53).
- Median Class Size: The median class size at Bay Side School (16.0) is also smaller than that at Seaside School (18.0).
Therefore, Bay Side School is a better choice if you are looking for smaller class sizes because both the mean and median class sizes at Bay Side School are smaller compared to those at Seaside School.
