Can I increase the standard deviation of a series without increasing its mean?

Question

I have a series of values. Can I modify them in a consistent manner such that it's mean remain the same but standard deviation increase by 1? 1 is just arbitrary in this example

score 2 · Answer 1 · answered Jul 27 '18 at 07:40

2

If $\mu$ denotes the mean and $\sigma$ the standard deviation then replace value $x$ by value: $$(1+\frac1{\sigma})(x-\mu)+\mu$$

The new mean will be $\mu$ and the new standard deviation will be: $(1+\frac1{\sigma})\sigma=\sigma+1$.

answered Jul 27 '18 at 07:40

drhab

151,093

2

In effect this would be adding $\frac{x-\mu}{\sigma}$ to each $x$ – Henry Jul 27 '18 at 08:18

coffeemath · Answer 2 · 2018-07-27T14:47:33.333

0

You can insert mean $\pm c$ which won't change the mean but will change the variance by a calculatable amount in terms of $c$ and the original population size.

Note this only works on probability distributions on finite sets.

edited Jul 27 '18 at 14:47

answered Jul 27 '18 at 07:37

coffeemath

7,403

Can I increase the standard deviation of a series without increasing its mean?

2 Answers2