mean and SD
Message posted by Jimmy on March 24, 2000 at 12:00 AM (ET)

I am trying to understand how standard deviations change. For example, if a population had salaries with a mean of $50,000 and a SD of $4000, would the SD change if all the salaries increased by $5000? What would happen to the SD if each salary in the population was increased by 10% instead of the flat $5000 amount?

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Re: mean and SD
Message posted by Phil Rosenkrantz on March 25, 2000 at 12:00 AM (ET)

So, if you just add 5000 to each value, the SD will end up the same mathematically.

However, if you add 10% to each value, you will slightly disburse the data a little more because the larger values in your data set will have larger increases. So in this case the SD will increase slightly.

You can take any data set and try it yourself.

Note:

Variance(x+5000)=Variance(x)
Variance(1.10x)= 1.21 Variance(x) where 1.21 represents 1.1 squared.

Take the square root of the variance to obtain the SD