Weighted Average of Three Values Calculator

Formula

Weighted mean = (First value × First weight+Second value × Second weight+Third value × Third weight) ÷ (First weight+Second weight+Third weight)

Worked example

With First value: 75, First weight: 2, Second value: 85, Second weight: 3, Third value: 90, Third weight: 5, weighted mean is 85.5.

Calculation method

The rule is Weighted mean = (First value × First weight+Second value × Second weight+Third value × Third weight) ÷ (First weight+Second weight+Third weight).

Multiply each value by its weight, add those products, then divide by the sum of the weights. The weights need not sum to 100 as long as they use the same scale.

For this weighted average of three values example, changing first value from 75 to 76 while keeping the other inputs fixed changes weighted mean from 85.5 to 85.7.

Reading weighted mean

Arithmetic mean adds and divides; weighted mean accounts for assigned weights; geometric and harmonic means suit multiplicative changes and rates respectively. Range is largest minus smallest. In the worked values on this page, first value 75, first weight 2, second value 85, second weight 3, third value 90, third weight 5 produce weighted mean 85.5.

Practical use

Use these summaries for small sets of measurements, scores, rates, or repeated results. The specific task here is to find weighted mean from first value, first weight, second value, second weight, third value, third weight.

Limits and common mistakes

Choose the summary that fits the question. An average can hide important differences between the original observations. Verify first value before interpreting weighted mean; a value measured on another basis would answer a different question.

Why the relationship works

A weighted mean allows observations to contribute unequally. Multiply every value by its own weight, add the products, and divide by the sum of weights. If weights are credits or counts, they must be assigned to the correct observations; swapping two weights can change the answer. The weighted average of three values rule uses first value, first weight, second value, second weight, third value, third weight in Weighted mean = (First value × First weight+Second value × Second weight+Third value × Third weight) ÷ (First weight+Second weight+Third weight); read each symbol as the field named on this page.

Interpreting another set of values

For weighted average of three values, the fields labeled first value, first weight, second value, second weight, third value, third weight are the known quantities. The calculator solves for weighted mean using Weighted mean = (First value × First weight+Second value × Second weight+Third value × Third weight) ÷ (First weight+Second weight+Third weight). The output summarizes the entered observations; it does not preserve every detail of them. Keep the original values alongside a mean or spread measure, especially when only three observations are used. When comparing two calculations, keep their units and input definitions identical.

For a second weighted average of three values check, keep the other default inputs fixed and change first value from 75 to 77. Weighted mean changes from 85.5 to 85.9. This is a comparison of two particular cases. Repeat it near the values relevant to your task; do not assume that every formula changes at a constant rate.

Checks and limits

For three values, inspect all three original observations as well as the summary. The same mean can describe very different spreads. A range can change when only an extreme changes, while the mean can change when any observation changes. These three-number examples demonstrate formulas but do not establish a population pattern. The reported weighted mean is 85.5 in the worked example. Keep its stated unit or counting convention when checking it against another calculation.