A weighted mean (or weighted average) is like an ordinary mean, but the observations don't contribute equally - more emphasis is placed on some data values than others; they are weighted by a bigger or smaller amount than 1/n.

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Determining true mean from noisy observations

I have a large set of data points of the form (mean, stdev). I wish to reduce this to a single (better) mean, and a (hopefully) smaller standard deviation. Clearly I could simply compute $\frac{\sum ...
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Bias correction in weighted variance

For unweighted variance $$\text{Var}(X):=\frac{1}{n}\sum_i(x_i - \mu)^2$$ there exists the bias corrected sample variance, when the mean was estimated from the same data: ...
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How do I calculate a weighted standard deviation? In Excel?

So, I have a data set of percentages like so: ...
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2k views

Weighted geometric mean vs weighted mean

I have a set of data, each element has a weight. I need to estimate the mean of this data. I found that there are two ways: A weighted geometric mean and a weighted mean. When should I use each of ...
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1k views

How to compute weighted means and SDs?

I want to calculate volume weighted average price and standard deviation for the following dataset: ...
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272 views

Estimate the population variance from a set of means

I have a set of measurements which is partitioned into M partitions. However, I only have the partition sizes $N_i$ and the means $\bar{x}_i$ from each partition. Because all measurements are assumed ...
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617 views

Weighted mean of two 2D Gaussian random variables

I have two 2D Gaussian random variables. I'd like to find the weighted average of the two (based on their covariance matrix around the mean, meaning that the mean of the final Gaussian should be ...
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204 views

Better method to estimate gender gap: difference between medians or median gap by occupation?

I'm doing some analysis of Bureau of Labor Statistics data on wages earned by men and women, and I'm trying to determine which of the two methods I've used is the better estimate of the gender wage ...