I am receiving a stream of numbers. I need to calculate the standard deviation of the last 100 numbers at each step. I don't have enough time for calculating it from scratch.
Is there a cheaper way of this calculation?
2026-03-26 04:30:53.1774499453
Calculating standard deviation of a moving window
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Assuming you are using SD with Bessel's correction, call $\mu_n$ and $SD_n$ the mean and standard deviation from $n$ to $n+99$. Then, calculate $\mu_1$ and $SD_{1}$ afterwards, you can use the recursive relation $\mu_{n+1}=\mu_n-\frac 1{99}x_n+ \frac 1{99}x_{n+100}$ and $SD_{n+1}=\sqrt{SD_n^2-\frac1{99}(x_n-\mu_n)^2+\frac1{99}(x_{n+100}-\mu_{n+1})^2}$.