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
Solution
To calculate the standard deviation of a list of numbers, follow these steps:
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Find the mean (average) of the numbers: (34 + 1 + 23 + 4 + 3 + 3 + 12 + 4 + 3 + 1) / 10 = 8.8
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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)
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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)
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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
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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.
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