# Finding standard deviation or error from normalized data.

by doublemint
Tags: data, deviation, error, normalized, standard
 Sci Advisor P: 3,297 What do you mean by "normalize"? For example, do you mean that multiply each datum in the data set x2 by the factor (a2/a1) ? Let the data be the $d_i$. Let the sample mean be $m$ . Let the scaling factor be $k$ The mean of the scaled data $k d_i$ is $m k$ The variance of the scaled data is: $\sum \frac { ( k d_i - m k )^2}{n} = \sum \frac{k^2 (d_i - k)^2 }{n} = k^2 \sum \frac{(d_i - m)^2}{n}$ This is $k^2$ times the variance of the original sample. So the sample standard deviation of the scaled data is $|k|$ times the standard deviation of the original data.