What is the variance of the data set {4, 8, 6, 5, 3}?

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Question: What is the variance of the data set {4, 8, 6, 5, 3}?

Options:

Correct Answer: 2.5

Solution:

Mean = 5.2; Variance = [(4-5.2)² + (8-5.2)² + (6-5.2)² + (5-5.2)² + (3-5.2)²] / 5 = 2.56.

What is the variance of the data set {4, 8, 6, 5, 3}?

What is the variance of the data set {4, 8, 6, 5, 3}?

Step 1: Find the mean (average) of the data set {4, 8, 6, 5, 3}.
Step 2: Add all the numbers together: 4 + 8 + 6 + 5 + 3 = 26.
Step 3: Count how many numbers are in the data set. There are 5 numbers.
Step 4: Divide the total (26) by the count (5) to find the mean: 26 / 5 = 5.2.
Step 5: Now, calculate the squared differences from the mean for each number.
Step 6: For 4: (4 - 5.2)² = (-1.2)² = 1.44.
Step 7: For 8: (8 - 5.2)² = (2.8)² = 7.84.
Step 8: For 6: (6 - 5.2)² = (0.8)² = 0.64.
Step 9: For 5: (5 - 5.2)² = (-0.2)² = 0.04.
Step 10: For 3: (3 - 5.2)² = (-2.2)² = 4.84.
Step 11: Add all the squared differences together: 1.44 + 7.84 + 0.64 + 0.04 + 4.84 = 14.8.
Step 12: Divide the total squared differences (14.8) by the number of data points (5) to find the variance: 14.8 / 5 = 2.96.

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