What is the standard deviation of the data set {10, 12, 23, 23, 16, 23, 21, 16}?
Practice Questions
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What is the standard deviation of the data set {10, 12, 23, 23, 16, 23, 21, 16}?
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Questions & Step-by-Step Solutions
What is the standard deviation of the data set {10, 12, 23, 23, 16, 23, 21, 16}?
Step 1: Find the mean (average) of the data set. Add all the numbers together: 10 + 12 + 23 + 23 + 16 + 23 + 21 + 16 = 154. Then divide by the number of values (8): 154 / 8 = 19.25.
Step 2: Calculate the variance. For each number, subtract the mean and square the result: (10 - 19.25)², (12 - 19.25)², (23 - 19.25)², (23 - 19.25)², (16 - 19.25)², (23 - 19.25)², (21 - 19.25)², (16 - 19.25)². This gives: 85.5625, 52.5625, 14.0625, 14.0625, 10.5625, 14.0625, 3.0625, 10.5625.
