What is the variance of the data set: 2, 4, 4, 4, 5, 5, 7, 9?

What is the variance of the data set: 2, 4, 4, 4, 5, 5, 7, 9?

Correct Answer: 2.5

Step 1: List the data set: 2, 4, 4, 4, 5, 5, 7, 9.
Step 2: Calculate the mean (average) of the data set. Add all the numbers together: 2 + 4 + 4 + 4 + 5 + 5 + 7 + 9 = 40. Then divide by the number of values (8): 40 / 8 = 5.0.
Step 3: Subtract the mean from each number in the data set and square the result: (2-5)^2, (4-5)^2, (4-5)^2, (4-5)^2, (5-5)^2, (5-5)^2, (7-5)^2, (9-5)^2.
Step 4: Calculate each squared difference: (2-5)^2 = 9, (4-5)^2 = 1, (4-5)^2 = 1, (4-5)^2 = 1, (5-5)^2 = 0, (5-5)^2 = 0, (7-5)^2 = 4, (9-5)^2 = 16.
Step 5: Add all the squared differences together: 9 + 1 + 1 + 1 + 0 + 0 + 4 + 16 = 32.
Step 6: Divide the total by the number of values (8) to find the variance: 32 / 8 = 4.0.

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