What is the variance of the following numbers: 5, 7, 9, 11? (2020)

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Question: What is the variance of the following numbers: 5, 7, 9, 11? (2020)

Options:

Correct Answer: 4

Exam Year: 2020

Solution:

Mean = (5 + 7 + 9 + 11) / 4 = 8. Variance = [(5-8)² + (7-8)² + (9-8)² + (11-8)²] / 4 = 4.

What is the variance of the following numbers: 5, 7, 9, 11? (2020)

What is the variance of the following numbers: 5, 7, 9, 11? (2020)

Step 1: Add all the numbers together: 5 + 7 + 9 + 11.
Step 2: Calculate the total: 5 + 7 = 12, then 12 + 9 = 21, and finally 21 + 11 = 32.
Step 3: Count how many numbers there are: There are 4 numbers (5, 7, 9, 11).
Step 4: Find the mean (average) by dividing the total by the count: 32 / 4 = 8.
Step 5: Subtract the mean from each number to find the difference: (5 - 8), (7 - 8), (9 - 8), (11 - 8).
Step 6: Calculate the differences: 5 - 8 = -3, 7 - 8 = -1, 9 - 8 = 1, 11 - 8 = 3.
Step 7: Square each difference: (-3)² = 9, (-1)² = 1, (1)² = 1, (3)² = 9.
Step 8: Add the squared differences together: 9 + 1 + 1 + 9 = 20.
Step 9: Divide the total of squared differences by the count of numbers to find the variance: 20 / 4 = 5.

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