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Calculate the variance for the following data: 3, 7, 7, 19. (2022)
Calculate the variance for the following data: 3, 7, 7, 19. (2022)
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Q1
Calculate the variance for the following data: 3, 7, 7, 19. (2022)
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25
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35
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Mean = (3 + 7 + 7 + 19) / 4 = 9. Variance = [(3-9)² + (7-9)² + (7-9)² + (19-9)²] / 4 = 25.
Questions & Step-by-step Solutions
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Q: Calculate the variance for the following data: 3, 7, 7, 19. (2022)
Solution:
Mean = (3 + 7 + 7 + 19) / 4 = 9. Variance = [(3-9)² + (7-9)² + (7-9)² + (19-9)²] / 4 = 25.
Steps: 9
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Step 1: Add all the numbers together: 3 + 7 + 7 + 19.
Step 2: Calculate the total: 3 + 7 + 7 + 19 = 36.
Step 3: Count how many numbers there are: There are 4 numbers.
Step 4: Calculate the mean (average) by dividing the total by the count: 36 / 4 = 9.
Step 5: Subtract the mean from each number to find the difference: (3-9), (7-9), (7-9), (19-9).
Step 6: Calculate the differences: -6, -2, -2, 10.
Step 7: Square each difference: (-6)² = 36, (-2)² = 4, (-2)² = 4, (10)² = 100.
Step 8: Add the squared differences together: 36 + 4 + 4 + 100 = 144.
Step 9: Divide the total of squared differences by the count of numbers to find the variance: 144 / 4 = 36.
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