Weighted Standard Deviation Calculator

About this calculator

The weighted standard deviation measures spread around a weighted mean rather than a plain average, giving each data point influence in proportion to a weight you assign it, a reliability score, sample size, or measurement precision, instead of treating every value as equally trustworthy.

This matters whenever the data points being combined aren't equally reliable: meta-analyses in research combine results from studies of different sizes by weighting larger, more precise studies more heavily; survey analysts weight responses to correct for over- or under-sampled demographic groups; and lab scientists combine repeated measurements with different precisions using weights based on their measurement uncertainty. Using an unweighted standard deviation in these cases would let noisy or unreliable data points distort the result just as much as trustworthy ones.

Enter your values along with a matching weight for each one, and this calculator computes the weighted mean and weighted standard deviation.