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Sagot :
Sure, let's solve each part of the given question step-by-step.
### Part A: Calculate the measures of center. (2 points)
The measures of center we need to calculate are the mean, median, and mode for both Bay Side School and Seaside School.
#### Bay Side School:
- Mean (Average):
[tex]\[ \text{Mean} = \frac{\sum \text{(class sizes)}}{\text{number of classes}} = \frac{6 + 8 + 5 + 8 + 6 + 5 + 4 + 2 + 0 + 5 + 3 + 2 + 0 + 0 + 2}{15} = \frac{56}{15} \approx 3.733 \][/tex]
- Median:
To find the median, arrange the data in ascending order:
[tex]\[ 0, 0, 0, 2, 2, 2, 3, 4, 5, 5, 5, 6, 6, 8, 8 \][/tex]
Since there are 15 values, the median is the 8th value: 4
- Mode:
The mode is the value that appears most frequently. Here, the value 0 appears the most frequently (3 times).
#### Seaside School:
- Mean (Average):
[tex]\[ \text{Mean} = \frac{\sum \text{(class sizes)}}{\text{number of classes}} = \frac{5 + 8 + 0 + 1 + 2 + 5 + 6 + 8 + 5 + 5 + 7 + 7 + 8 + 0 + 6 + 3 + 2}{17} = \frac{78}{17} \approx 4.588 \][/tex]
- Median:
To find the median, arrange the data in ascending order:
[tex]\[ 0, 0, 1, 2, 2, 3, 5, 5, 5, 6, 6, 7, 7, 8, 8, 8, 8 \][/tex]
Since there are 17 values, the median is the 9th value: 5
- Mode:
The mode is the value that appears most frequently. Here, the value 5 appears the most frequently (4 times).
### Part B: Calculate the measures of variability. (1 point)
The measures of variability we need to calculate are the standard deviation (std) and range for both Bay Side School and Seaside School.
#### Bay Side School:
- Standard Deviation (STD):
The standard deviation provides a measure of how spread out the values are around the mean. For Bay Side School: 2.619
- Range:
The range is the difference between the maximum and minimum values:
[tex]\[ \text{Range} = 8 - 0 = 8 \][/tex]
#### Seaside School:
- Standard Deviation (STD):
The standard deviation for Seaside School: 2.680
- Range:
The range is the difference between the maximum and minimum values:
[tex]\[ \text{Range} = 8 - 0 = 8 \][/tex]
### Part C: If you are interested in a smaller class size, which school is a better choice for you? Explain your reasoning. (1 point)
Based on the measures of center (mean) calculated, Bay Side School has a mean class size of approximately 3.733, whereas Seaside School has a mean class size of approximately 4.588. Since the mean class size at Bay Side School is smaller than that at Seaside School, Bay Side School would be a better choice if you are interested in smaller class sizes.
Therefore, the better school for smaller class sizes is Bay Side School.
### Part A: Calculate the measures of center. (2 points)
The measures of center we need to calculate are the mean, median, and mode for both Bay Side School and Seaside School.
#### Bay Side School:
- Mean (Average):
[tex]\[ \text{Mean} = \frac{\sum \text{(class sizes)}}{\text{number of classes}} = \frac{6 + 8 + 5 + 8 + 6 + 5 + 4 + 2 + 0 + 5 + 3 + 2 + 0 + 0 + 2}{15} = \frac{56}{15} \approx 3.733 \][/tex]
- Median:
To find the median, arrange the data in ascending order:
[tex]\[ 0, 0, 0, 2, 2, 2, 3, 4, 5, 5, 5, 6, 6, 8, 8 \][/tex]
Since there are 15 values, the median is the 8th value: 4
- Mode:
The mode is the value that appears most frequently. Here, the value 0 appears the most frequently (3 times).
#### Seaside School:
- Mean (Average):
[tex]\[ \text{Mean} = \frac{\sum \text{(class sizes)}}{\text{number of classes}} = \frac{5 + 8 + 0 + 1 + 2 + 5 + 6 + 8 + 5 + 5 + 7 + 7 + 8 + 0 + 6 + 3 + 2}{17} = \frac{78}{17} \approx 4.588 \][/tex]
- Median:
To find the median, arrange the data in ascending order:
[tex]\[ 0, 0, 1, 2, 2, 3, 5, 5, 5, 6, 6, 7, 7, 8, 8, 8, 8 \][/tex]
Since there are 17 values, the median is the 9th value: 5
- Mode:
The mode is the value that appears most frequently. Here, the value 5 appears the most frequently (4 times).
### Part B: Calculate the measures of variability. (1 point)
The measures of variability we need to calculate are the standard deviation (std) and range for both Bay Side School and Seaside School.
#### Bay Side School:
- Standard Deviation (STD):
The standard deviation provides a measure of how spread out the values are around the mean. For Bay Side School: 2.619
- Range:
The range is the difference between the maximum and minimum values:
[tex]\[ \text{Range} = 8 - 0 = 8 \][/tex]
#### Seaside School:
- Standard Deviation (STD):
The standard deviation for Seaside School: 2.680
- Range:
The range is the difference between the maximum and minimum values:
[tex]\[ \text{Range} = 8 - 0 = 8 \][/tex]
### Part C: If you are interested in a smaller class size, which school is a better choice for you? Explain your reasoning. (1 point)
Based on the measures of center (mean) calculated, Bay Side School has a mean class size of approximately 3.733, whereas Seaside School has a mean class size of approximately 4.588. Since the mean class size at Bay Side School is smaller than that at Seaside School, Bay Side School would be a better choice if you are interested in smaller class sizes.
Therefore, the better school for smaller class sizes is Bay Side School.
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