Weighted arithmetic mean
Also called: Weighted average · Topic: Economic Data: Census, NSS, Surveys and Statistical Tools · NCERT: Class 11, Ch 5 "Measures of Central Tendency"; Class 11, Ch 7 "Index Numbers"; Class 11, Ch 8 "Use of Statistical Tools"
Meaning
A weighted arithmetic mean gives each item a weight, a number showing how important that item is, instead of treating all items as equal. The formula is Weighted mean = Σwx/Σw, where x is each value and w its weight. It matters because a simple average can mislead when items differ in importance. It is the basis of price indices such as the CPI, where each item's weight is its share in the household budget.
Example
Suppose a household spends much more on potatoes than on mangoes. When you average the change in their prices, the potato price should count for more. So each price is weighted by its budget share. The trade-weighted average tariff and the revenue-neutral GST rate work the same way.
Don't confuse with
- Simple arithmetic mean: the simple mean (ΣX/N) gives every item equal importance. It is the special case where all weights are equal.
Related concepts
- Measures of central tendency
- Arithmetic mean
- Median
- Quartiles
- Decile
- Percentiles
- Mode
- Bimodal and multimodal distribution
- Modal class
- Relative position of mean, median and mode