Average Calculator

How to use the average calculator

1. Pick Simple average, Weighted average or Score needed.
2. For a simple average, type the numbers separated by commas, spaces or new lines.
3. For a weighted average, put one value and its weight on each line, such as 88 20% or 3.7, 4.
4. For the score needed, enter the scores so far, your target and how many scores are still to come.

Average formulas

In the simple average every value counts once. In a weighted average each value xᵢ is multiplied by its weight wᵢ, and the total is divided by the sum of the weights rather than by the number of values. A simple average is just a weighted average in which every weight is 1. In the last formula, n is the number of scores so far and k the number still to come.

Worked examples

Simple average. The test scores 85, 92, 78, 90, 88 add up to 433, so the average is 433 ÷ 5 = 86.6.

Weighted course grade. A course is graded on homework, quizzes, a midterm and a final with different weights:

The weighted average is 8,550 ÷ 100 = 85.5. The plain average of the four scores would be 86; the heavily weighted final pulls the grade towards its own score.

Score needed. After three tests of 82, 76, 91 (total 249), how much do you need on the fourth to average 85? The four tests must total 85 × 4 = 340, so you need 340 − 249 = 91.

Score needed on the next test

Each cell shows the score needed on a fourth equally weighted test, given the average of the first three (rows) and the target average (columns). Values above 100 mean the target cannot be reached on a test marked out of 100.

Notice the pattern: with three tests behind you, every point you want to add to your average costs four points on the next test.

Weighted average tips

• Weights do not have to add up to 100. The calculator divides by the total weight, so credit hours (3, 4, 4), counts or percentages all work.
• Do not average averages. If 20 students average 80 and 30 students average 70, the combined average is 74, not 75. Weight each group's average by its size.
• GPA is a weighted average. Multiply each grade point by the course's credit hours, add them up and divide by the total credits.
• Prices by quantity. The average price paid for stock bought in several lots is the weighted average of the prices, with the number of units as weights.
• Check that the weights match the syllabus. A category weighted 35% must have weight 35 (or 0.35), whichever scale you use for the others.

Which average is this?

"Average" usually means the arithmetic mean, which is what this calculator works out. It is not always the best summary: for skewed data such as incomes the median is more typical, and for growth rates the geometric mean is the right choice. The mean, median, mode and range calculator compares the basic measures with working, and the statistics calculator adds the geometric and harmonic means. For percentage changes, see the percentage calculator.