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What is the standard deviation of the following list?34,1,23,4,3,3,12,4,3,1Please enter at least 3 digits after the decimal

Question

What is the standard deviation of the following list?34,1,23,4,3,3,12,4,3,1Please enter at least 3 digits after the decimal

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Solution

To calculate the standard deviation of a list of numbers, follow these steps:

  1. Find the mean (average) of the numbers: (34 + 1 + 23 + 4 + 3 + 3 + 12 + 4 + 3 + 1) / 10 = 8.8

  2. Subtract the mean from each number to get the list of deviations: (34-8.8, 1-8.8, 23-8.8, 4-8.8, 3-8.8, 3-8.8, 12-8.8, 4-8.8, 3-8.8, 1-8.8) = (25.2, -7.8, 14.2, -4.8, -5.8, -5.8, 3.2, -4.8, -5.8, -7.8)

  3. Square each deviation to get the list of squared deviations: (25.2^2, -7.8^2, 14.2^2, -4.8^2, -5.8^2, -5.8^2, 3.2^2, -4.8^2, -5.8^2, -7.8^2) = (634.24, 60.84, 201.64, 23.04, 33.64, 33.64, 10.24, 23.04, 33.64, 60.84)

  4. Find the mean of these squared deviations. This is called the variance: (634.24 + 60.84 + 201.64 + 23.04 + 33.64 + 33.64 + 10.24 + 23.04 + 33.64 + 60.84) / 10 = 106.4

  5. Take the square root of the variance to get the standard deviation: sqrt(106.4) = 10.316

So, the standard deviation of the list is 10.316.

This problem has been solved

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