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

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

Correct Answer: 2.56

Step 1: Find the mean (average) of the data set {4, 8, 6, 5, 3}. Add all the numbers together: 4 + 8 + 6 + 5 + 3 = 26. Then divide by the number of values (5): 26 / 5 = 5.2.
Step 2: Calculate the variance. For each number in the data set, subtract the mean (5.2) and square the result: (4-5.2)², (8-5.2)², (6-5.2)², (5-5.2)², (3-5.2)².
Step 3: Calculate each squared difference: (4-5.2)² = 1.44, (8-5.2)² = 7.84, (6-5.2)² = 0.64, (5-5.2)² = 0.04, (3-5.2)² = 4.84.
Step 4: Add all the squared differences together: 1.44 + 7.84 + 0.64 + 0.04 + 4.84 = 14.8.
Step 5: Divide the total by the number of values (5) to find the variance: 14.8 / 5 = 2.96.
Step 6: Find the standard deviation by taking the square root of the variance: √2.96 ≈ 1.72.

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