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Question 691:



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  1. Q691_1_standardDeviationQ691.xls
To calculate the population standard deviation on a set of numbers we use the following procedure:
  1. Add up all the values 6+7+8+9+10 = 40
  2. Count the number of values = 5
  3. Divide the Sum by the the total number of values = 40/5 = 8
  4. Subtract each value from the mean. Then Square that result : (6-8)2+(7-8)2+(8-8)2+(9-8)2+(10-8)2 = 10
  5. Divide the Sum of Squared Deviations by n (this is the variance) = 10/5 = 2.
  6. Take the square root of the variance and this is the standard deviation = SQRT(2) = 1.414214
So the the population standard deviation is 1.414214 on the set of numbers. While it doesn't say in the question, if we wanted the sample standard deviation, in Step 5, we'd just divide by n-1 (called the degrees of freedom) and we'd get the sample standard deviation of 1.581139. 

For more information, such as the difference between the population and sample standard deviation, see the Standard Deviation Tutorial

I've also attached the calculations in an excel file, with the Excel formula =STDEV() which calculates the sample standard deviation.

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