The standard deviation is a commonly used measure of the degree of variation within a set of data values.
#CAN YOU CALCULATE WEIGHTED STANDARD DEVIATION HOW TO#
As for modifying the MAD formula on wikipedia to be weighted somehow, I would imagine it would appear in much the same way, though it is not immediately obvious to me how to modify that formula in an unbiased manner. Base R has a function you can use to calculate standard deviation in R. This is a tedious exercise to show, but it is accessible to an undergraduate level statistics student.Īs for your second comment, if you are calculating weighted absolute standard deviation as in the first paper you linked, then yes of course, $N'$ appears directly in the formula. It just so happens that by using this strange looking formula, it actually turns out that $s,s_w$ are unbiased estimators of $\sigma$. That is, we want $E=\sigma$, and we want $E = \sigma$ where $\sigma$ is the true population standard deviation, and $E$ denotes the expected value. If you used a simple average, then all groups would have had an equal effect. Because the pooled standard deviation uses a weighted average, its value (5.486) is closer to the standard deviation of the largest group. The reason that this isn't just ignored in the first paper you cited is because we like our estimators to be unbiased. The fourth group is much larger (n200) and has a higher standard deviation (6.8). Investors most commonly use it to measure the risk of a stock (a measure of stock volatility over a period of time). You are also correct that $(N'-1)/N'$ will be close to one if $N$ is large. Sample (STDEV.S) Standard Deviation in Excel Standard Deviation function can be used as a worksheet function & can also be applied by using VBA code. If we have $w_i=0$ then we are ignoring the $i$th observation, so it doesn't really count as part of our sample. The number of nonzero weights is effectively the sample size.
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