Glossary term
Weighted Mean: Meaning and Definition
Reviewed and approved by Dr. Anamika ShrivastavaPublished Last updated
The weighted mean is an average in which each item is multiplied by a weight showing its relative importance before the total is divided by the sum of the weights. It is used when items differ in importance, as with marks in papers of different weights or prices in an index number.
In more detail
Weights are chosen to reflect importance: credit hours for grades, spending shares for prices, or population for state data. When all weights are equal, the weighted mean becomes the simple mean. Consumer price indices are weighted averages of price changes, where food has a larger weight than recreation because households spend more on it.
Example
Scores of 70, 60 and 80 in papers with weights 5, 3 and 2 give (350 + 180 + 160) ÷ 10 = 69, while the simple mean is 70.
Key points
- Weighted mean = ΣwX ÷ Σw.
- Heavier weights pull the result towards that item.
- Basis of price index numbers.
Common mistake
Using the simple mean of percentages from groups of different sizes.
Related terms
Where it is explained
This term is explained in Class 11 Statistics Chapter 5: Measures of Central Tendency.