StATS: What is a weighted mean?

The weighted mean is a mean where there is some variation in the relative contribution of individual data values to the mean. Each data value (Xi) has a weight assigned to it (Wi). Data values with larger weights contribute more to the weighted mean and data values with smaller weights contribute less to the weighted mean. The formula is

There are several reasons why you might want to use a weighted mean.

1. Each individual data value might actually represent a value that is used by multiple people in your sample. The weight, then, is the number of people associated with that particular value.
2. Your sample might deliberately over represent or under represent certain segments of the population. To restore balance, you would place less weight on the over represented segments of the population and greater weight on the under represented segments of the population.
3. Some values in your data sample might be known to be more variable (less precise) than other values. You would place greater weight on those data values known to have greater precision.

Further reading

1. http://www.xycoon.com/weighted_mean.htm
2. http://en.wikipedia.org/wiki/Weighted_mean

This page was written by Steve Simon while working at Children's Mercy Hospital. Although I do not hold the copyright for this material, I am reproducing it here as a service, as it is no longer available on the Children's Mercy Hospital website. Need more information? I have a page with general help resources. You can also browse for pages similar to this one at Category: Definitions, Category: Definitions, Category: Descriptive statistics.