At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
Sure! Let's go through each part step by step.
### Part A: Calculate the measures of center
We need to calculate the mean and median for each school.
1. Siry View School:
- Data from the stem-and-leaf plot: [tex]\(0, 9, 7, 2, 0, 18, 17, 16, 15, 15, 15, 14, 13, 11, 10, 20\)[/tex]
- Mean:
[tex]\[ \text{Mean} = \frac{\sum \text{data}}{\text{number of data points}} = \frac{182}{16} = 11.375 \][/tex]
- Median:
- Sorting the data: [tex]\(0, 0, 2, 7, 9, 10, 11, 13, 14, 15, 15, 15, 16, 17, 18, 20\)[/tex]
- The median is the average of the 8th and 9th values:
[tex]\[ \text{Median} = \frac{13 + 14}{2} = 13.5 \][/tex]
2. South Lake School:
- Data from the stem-and-leaf plot: [tex]\(5, 8, 10, 11, 12, 16, 16, 13, 25, 25, 26, 27, 28, 30, 36\)[/tex]
- Mean:
[tex]\[ \text{Mean} = \frac{\sum \text{data}}{\text{number of data points}} = \frac{288}{15} = 19.2 \][/tex]
- Median:
- Sorting the data: [tex]\(5, 8, 10, 11, 12, 13, 16, 16, 25, 25, 26, 27, 28, 30, 36\)[/tex]
- The median is the 8th value:
[tex]\[ \text{Median} = 16.0 \][/tex]
### Part B: Calculate the measures of variability
We need to calculate the variance and standard deviation.
1. Siry View School:
- Data: [tex]\(0, 9, 7, 2, 0, 18, 17, 16, 15, 15, 15, 14, 13, 11, 10, 20\)[/tex]
- Variance ([tex]\(s^2\)[/tex]):
[tex]\[ \text{Variance} = \frac{\sum (x_i - \bar{x})^2}{n-1} = 39.583 \][/tex]
- Standard Deviation ([tex]\(s\)[/tex]):
[tex]\[ \text{Standard Deviation} = \sqrt{\text{Variance}} = \sqrt{39.583} \approx 6.292 \][/tex]
2. South Lake School:
- Data: [tex]\(5, 8, 10, 11, 12, 16, 16, 13, 25, 25, 26, 27, 28, 30, 36\)[/tex]
- Variance ([tex]\(s^2\)[/tex]):
[tex]\[ \text{Variance} = \frac{\sum (x_i - \bar{x})^2}{n-1} = 88.6 \][/tex]
- Standard Deviation ([tex]\(s\)[/tex]):
[tex]\[ \text{Standard Deviation} = \sqrt{\text{Variance}} = \sqrt{88.6} \approx 9.413 \][/tex]
### Part C: Determine the better school for smaller class size
To determine the better school based on smaller class sizes, we compare the means of the two schools.
- Siry View School has a mean class size of [tex]\(11.375\)[/tex]
- South Lake School has a mean class size of [tex]\(19.2\)[/tex]
Since [tex]\(11.375\)[/tex] (Siry View) is less than [tex]\(19.2\)[/tex] (South Lake), Siry View has smaller class sizes on average.
### Conclusion
Hence, if you are interested in a smaller class size, Siry View is the better choice. This conclusion is based on the lower mean class size observed at Siry View compared to South Lake.
### Part A: Calculate the measures of center
We need to calculate the mean and median for each school.
1. Siry View School:
- Data from the stem-and-leaf plot: [tex]\(0, 9, 7, 2, 0, 18, 17, 16, 15, 15, 15, 14, 13, 11, 10, 20\)[/tex]
- Mean:
[tex]\[ \text{Mean} = \frac{\sum \text{data}}{\text{number of data points}} = \frac{182}{16} = 11.375 \][/tex]
- Median:
- Sorting the data: [tex]\(0, 0, 2, 7, 9, 10, 11, 13, 14, 15, 15, 15, 16, 17, 18, 20\)[/tex]
- The median is the average of the 8th and 9th values:
[tex]\[ \text{Median} = \frac{13 + 14}{2} = 13.5 \][/tex]
2. South Lake School:
- Data from the stem-and-leaf plot: [tex]\(5, 8, 10, 11, 12, 16, 16, 13, 25, 25, 26, 27, 28, 30, 36\)[/tex]
- Mean:
[tex]\[ \text{Mean} = \frac{\sum \text{data}}{\text{number of data points}} = \frac{288}{15} = 19.2 \][/tex]
- Median:
- Sorting the data: [tex]\(5, 8, 10, 11, 12, 13, 16, 16, 25, 25, 26, 27, 28, 30, 36\)[/tex]
- The median is the 8th value:
[tex]\[ \text{Median} = 16.0 \][/tex]
### Part B: Calculate the measures of variability
We need to calculate the variance and standard deviation.
1. Siry View School:
- Data: [tex]\(0, 9, 7, 2, 0, 18, 17, 16, 15, 15, 15, 14, 13, 11, 10, 20\)[/tex]
- Variance ([tex]\(s^2\)[/tex]):
[tex]\[ \text{Variance} = \frac{\sum (x_i - \bar{x})^2}{n-1} = 39.583 \][/tex]
- Standard Deviation ([tex]\(s\)[/tex]):
[tex]\[ \text{Standard Deviation} = \sqrt{\text{Variance}} = \sqrt{39.583} \approx 6.292 \][/tex]
2. South Lake School:
- Data: [tex]\(5, 8, 10, 11, 12, 16, 16, 13, 25, 25, 26, 27, 28, 30, 36\)[/tex]
- Variance ([tex]\(s^2\)[/tex]):
[tex]\[ \text{Variance} = \frac{\sum (x_i - \bar{x})^2}{n-1} = 88.6 \][/tex]
- Standard Deviation ([tex]\(s\)[/tex]):
[tex]\[ \text{Standard Deviation} = \sqrt{\text{Variance}} = \sqrt{88.6} \approx 9.413 \][/tex]
### Part C: Determine the better school for smaller class size
To determine the better school based on smaller class sizes, we compare the means of the two schools.
- Siry View School has a mean class size of [tex]\(11.375\)[/tex]
- South Lake School has a mean class size of [tex]\(19.2\)[/tex]
Since [tex]\(11.375\)[/tex] (Siry View) is less than [tex]\(19.2\)[/tex] (South Lake), Siry View has smaller class sizes on average.
### Conclusion
Hence, if you are interested in a smaller class size, Siry View is the better choice. This conclusion is based on the lower mean class size observed at Siry View compared to South Lake.
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.
