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Calculate the variance for the following data: 5, 7, 9, 11. (2022)
Calculate the variance for the following data: 5, 7, 9, 11. (2022)
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Calculate the variance for the following data: 5, 7, 9, 11. (2022)
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Mean = (5 + 7 + 9 + 11) / 4 = 8. Variance = [(5-8)² + (7-8)² + (9-8)² + (11-8)²] / 4 = 3.5.
Questions & Step-by-step Solutions
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Q: Calculate the variance for the following data: 5, 7, 9, 11. (2022)
Solution:
Mean = (5 + 7 + 9 + 11) / 4 = 8. Variance = [(5-8)² + (7-8)² + (9-8)² + (11-8)²] / 4 = 3.5.
Steps: 8
Show Steps
Step 1: Add all the numbers together: 5 + 7 + 9 + 11.
Step 2: Calculate the total: 5 + 7 = 12, 12 + 9 = 21, 21 + 11 = 32.
Step 3: Count how many numbers there are: There are 4 numbers (5, 7, 9, 11).
Step 4: Calculate the mean (average) by dividing the total by the count: 32 / 4 = 8.
Step 5: Subtract the mean from each number and square the result: (5-8)², (7-8)², (9-8)², (11-8)².
Step 6: Calculate each squared difference: (5-8)² = 9, (7-8)² = 1, (9-8)² = 1, (11-8)² = 9.
Step 7: Add all the squared differences together: 9 + 1 + 1 + 9 = 20.
Step 8: Divide the total of squared differences by the count of numbers to find the variance: 20 / 4 = 5.
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