What is the variance of the following data set: {5, 7, 8, 9, 10}?

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Question: What is the variance of the following data set: {5, 7, 8, 9, 10}?

Options:

Correct Answer: 3

Solution:

Mean = 7.8, Variance = [(5-7.8)² + (7-7.8)² + (8-7.8)² + (9-7.8)² + (10-7.8)²] / 5 = 3.

What is the variance of the following data set: {5, 7, 8, 9, 10}?

What is the variance of the following data set: {5, 7, 8, 9, 10}?

Step 1: Find the mean (average) of the data set {5, 7, 8, 9, 10}.
Step 2: Add all the numbers together: 5 + 7 + 8 + 9 + 10 = 39.
Step 3: Divide the total by the number of values (5): 39 / 5 = 7.8. This is the mean.
Step 4: Subtract the mean from each number in the data set and square the result:
(5 - 7.8)² = (-2.8)² = 7.84,
(7 - 7.8)² = (-0.8)² = 0.64,
(8 - 7.8)² = (0.2)² = 0.04,
(9 - 7.8)² = (1.2)² = 1.44,
(10 - 7.8)² = (2.2)² = 4.84.
Step 5: Add all the squared results together: 7.84 + 0.64 + 0.04 + 1.44 + 4.84 = 14.8.
Step 6: Divide the total of the squared results by the number of values (5): 14.8 / 5 = 2.96.
Step 7: The variance of the data set is 2.96.

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