What is the variance of the following numbers: 1, 2, 3, 4, 5, 6? (2022)

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Question: What is the variance of the following numbers: 1, 2, 3, 4, 5, 6? (2022)

Options:

Correct Answer: 2.5

Exam Year: 2022

Solution:

Mean = (1 + 2 + 3 + 4 + 5 + 6) / 6 = 3.5. Variance = [(1-3.5)² + (2-3.5)² + (3-3.5)² + (4-3.5)² + (5-3.5)² + (6-3.5)²] / 6 = 2.92 (approx 2.5).

What is the variance of the following numbers: 1, 2, 3, 4, 5, 6? (2022)

What is the variance of the following numbers: 1, 2, 3, 4, 5, 6? (2022)

Step 1: Add all the numbers together: 1 + 2 + 3 + 4 + 5 + 6.
Step 2: Calculate the total: 1 + 2 + 3 + 4 + 5 + 6 = 21.
Step 3: Count how many numbers there are: There are 6 numbers.
Step 4: Find the mean (average) by dividing the total by the count: 21 / 6 = 3.5.
Step 5: Subtract the mean from each number and square the result: (1-3.5)², (2-3.5)², (3-3.5)², (4-3.5)², (5-3.5)², (6-3.5)².
Step 6: Calculate each squared difference: (1-3.5)² = 6.25, (2-3.5)² = 2.25, (3-3.5)² = 0.25, (4-3.5)² = 0.25, (5-3.5)² = 2.25, (6-3.5)² = 6.25.
Step 7: Add all the squared differences together: 6.25 + 2.25 + 0.25 + 0.25 + 2.25 + 6.25 = 17.5.
Step 8: Divide the total of squared differences by the count of numbers to find the variance: 17.5 / 6 = 2.9167.
Step 9: Round the variance to two decimal places: Variance ≈ 2.92.

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