1332.0.55.002 - Statistical Language!, 2008
Latest ISSUE Released at 11:30 AM (CANBERRA TIME) 27/06/2008 First Issue
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The are six steps to calculating the standard deviation:
1. Calculate the mean
The mean of the salaries in the above table is $55,555
2. Subtract the mean from each observation
This has been calculated in the above table under the heading 'Difference'. For example, the difference from the mean for the CEO's salary is 100,000 minus 56,555 which equals 44,444.
3. Square each result
This has been calculated in the above table under the heading 'Difference Squared'. For example the difference squared for the CEO's salary is 44,444 times 44,444 which equals 1,975,308,247.
4. Add these squares
In the example this is 1,975,308,246 + 19,753.047 + 19,753.047 + 30,864,247 + 30,864,247 +30,864,247 + 30,864,247 + 241,975,447 + 241,975,447 = 2,622,222,222.
5. Divide this sum by the number of observations (the result at this stage is called the "variance").
In this example this is 2,622,222,222 divided by nine (number of observations) which equals 291,358,024.69.
6. Take the positive square root
In this example the square root of 291,358,024.69 is 17,069.21. Therefore, the standard deviation is 17,069.21.
The standard error of the mean of a sample from a population is the standard deviation of the sample divided by the square root of the sample size.
Relative Standard Error
The RSE is generally calculated by with the following formula.