Weighted Average Calculator

About the Weighted Average Calculator

An ordinary average treats every value as equally important. Often they are not. A final exam may count for half of a course grade and homework for a fifth; a four-credit course affects a grade point average more than a two-credit one; shares bought in large quantities should count more than a few bought at a different price. A weighted average gives each value the influence it deserves by multiplying it by a weight before averaging.

This weighted average calculator combines a list of values with a matching list of weights. It shows the working, each value's share of the total weight, and the simple, unweighted mean for comparison, so you can see how much the weighting changes the result.

How to Use the Weighted Average Calculator

Enter the values, separated by commas, spaces or new lines — for example, the marks for each part of a course.

Enter the weights in the same order, one for each value. Weights can be percentages, credits, quantities or any non-negative numbers.

The weighted average appears with the working and a comparison with the simple mean.

The Formula

  weighted average = (v₁w₁ + v₂w₂ + … + vₙwₙ) ÷ (w₁ + w₂ + … + wₙ)
                   = Σ(value × weight) ÷ Σ weight

Dividing by the total weight means the weights do not need to add up to 100 or to 1 — only their proportions matter. Weights of 50, 30 and 20 give the same result as 5, 3 and 2, or 0.5, 0.3 and 0.2.

Step-by-Step Example

Course marks of 90, 80 and 70, weighted 50%, 30% and 20%.

  Products:     90 × 50 = 4,500
                80 × 30 = 2,400
                70 × 20 = 1,400
  Sum:          4,500 + 2,400 + 1,400 = 8,300
  Total weight: 50 + 30 + 20 = 100
  Average:      8,300 ÷ 100 = 83

The weighted average is 83. The simple average of the three marks is 80, so the weighting raises the result by 3, because the highest mark carries the most weight.

Grade points of 3.7, 3.0 and 4.0 on courses of 4, 3 and 2 credits.

  3.7 × 4 + 3.0 × 3 + 4.0 × 2 = 14.8 + 9 + 8 = 31.8
  31.8 ÷ (4 + 3 + 2) = 31.8 ÷ 9 = 3.53333

The weighted grade point average is about 3.53, a little below the simple average of 3.57, because the 4.0 grade was earned on the smallest course.

Where Weighted Averages Are Used

Weighting is everywhere once you start looking for it.

Grades. Course grades combine coursework, tests and exams with set percentages, and grade point averages weight each course by its credits.

Prices and costs. The average price paid for shares, fuel or stock bought at different prices is weighted by the quantity bought each time.

Surveys and polls. Results from groups of different sizes are weighted so each group counts in proportion to the population it represents.

Indices. Price indices such as inflation measures weight each item by how much people spend on it, so a rise in rent matters more than a rise in the price of salt.

Weighted Versus Simple Averages

A weighted average moves toward the values with the largest weights. If the heavily weighted values are high, the weighted average is above the simple average; if they are low, it is below. When all the weights are equal, the weighted average and the simple average are exactly the same.

Working Out a Missing Mark

Weighted averages are often used backwards, to find what score is needed. If the final exam is worth 40 percent and your marks so far average 75 on the other 60 percent, then to finish with 80 you need an exam mark of (80 − 0.6 × 75) ÷ 0.4 = 87.5. The same algebra works for any target average and any weights.

Averaging Averages Correctly

A common trap is averaging several averages that come from groups of different sizes. If one class of 10 pupils averages 70 and another of 30 averages 80, the combined average is not 75. Each class average must be weighted by its size: (10 × 70 + 30 × 80) ÷ 40 = 3,100 ÷ 40 = 77.5. The larger class pulls the result toward its own average. The same applies to combining survey results, sales figures from branches of different sizes, or prices from different-sized orders: whenever the groups are not equal, a weighted average is the only way to get the true overall figure, and a plain average of the group averages will be biased toward the smaller groups.

Understanding Your Result

The headline is the weighted average.

The working line shows the sum of value × weight divided by the total weight.

The share of each value line shows each value with its weight as a percentage of the total.

The simple mean line gives the unweighted average and the difference.

When Should You Use This Calculator?

Use it to work out course grades and grade point averages.

Use it to find the average price paid across several purchases.

Use it to combine survey results from groups of different sizes.

Use it to check how much a heavily weighted exam or item affects a total.

Common Mistakes

Dividing by the number of values. Divide by the total of the weights instead.

Mismatching values and weights. Enter them in the same order, one weight each.

Using percentages that do not add up. That is fine here, but check you have not left a component out.

Averaging averages from different-sized groups. Weight each group's average by its size.

Using negative weights. Weights must be zero or more; a negative weight would pull the average the wrong way.