Find the standard deviation of the given data sets 7,47,8,42,47,95,42,96,3(1 Point)29.0930.0931.0932.09
Question
Find the standard deviation of the given data sets
Data set: 7, 47, 8, 42, 47, 95, 42, 96, 3
(1 Point)
29.09
30.09
31.09
32.09
Solution
To find the standard deviation of a data set, follow these steps:
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Find the mean (average) of the data set. Add all the numbers together and divide by the number of data points. For your data set (7,47,8,42,47,95,42,96,3), the mean is (7+47+8+42+47+95+42+96+3)/9 = 38.67.
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Subtract the mean from each data point to get the deviation of each point. This gives you: -31.67, 8.33, -30.67, 3.33, 8.33, 56.33, 3.33, 57.33, -35.67.
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Square each deviation to get the squared deviations: 1003.59, 69.39, 941.09, 11.09, 69.39, 3171.31, 11.09, 3286.21, 1272.35.
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Find the mean of these squared deviations. This is called the variance. So, (1003.59+69.39+941.09+11.09+69.39+3171.31+11.09+3286.21+1272.35)/9 = 1037.06.
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The standard deviation is the square root of the variance. So, the standard deviation is √1037.06 = 32.21.
So, the standard deviation of your data set is approximately 32.21.
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