# How does standard deviation depend on data?

I've got a problem: I take a random variable, assign values to it and than I have to invent two different probability distribution functions with similar mean values (+-5%), but in the second function I have to reduce standard deviation by 50% in respect to the first case. How do I change the PDF so that standard deviation is reduced in a most optimal way?

Thanks.

Sample data:

x: 1 2 3 4 5 6 7 8 9 10

pdf1: 0.15 0.2 0.1 0.12 0.09 0.07 0.11 0.06 0.051 0.049

stdev1: 0.047844656

I need a pdf2 with stdev2 <= 0.0235.

• Since standard deviation is a measure of how far the data is from the mean, adjust all the values in pdf1 so that they are closer to the mean to get pdf2. Then the standard deviation should be lower. – Pratyush Sarkar Mar 3 '13 at 16:08