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Average Calculator (Mean, Median, Mode and Weighted Average)

Average a list of numbers with the working shown: mean, sum, count, median, mode, range, geometric, harmonic and trimmed means, plus a weighted-average mode for grades and prices.

Type of average

Numbers

Weights

Trimmed mean: drop from each end

Round results to

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How it works

mean = Σx ÷ n · weighted mean = Σ(w × x) ÷ Σw · median = middle sorted value · geometric mean = (x₁ × x₂ × … × xₙ)^(1/n) · harmonic mean = n ÷ Σ(1/x) · RMS = √(Σx² ÷ n)

The everyday average, or arithmetic mean, adds every value together and divides by how many there are — it marks the single balance point of the data. Next to it you get the sum, count, smallest and largest values, the range, the median (the middle value once the list is sorted) and the mode (the value that appears most often), so you can see at a glance whether a few extreme values are pulling the mean. A second table lists the other kinds of average: the geometric mean for growth rates and ratios, the harmonic mean for rates such as speeds or prices per unit, the root mean square, the mid-range and a trimmed mean that drops a chosen share of the smallest and largest values. Switch to Weighted average when the numbers do not count equally — course grades with different credits, or prices bought in different quantities — and enter one weight per number. Every result comes with the working, and you can round the answers or use a decimal comma under More options.

Worked example

For 10, 20, 30, 40 and 50: the sum is 150 and there are 5 values, so the average is 150 ÷ 5 = 30. The median is also 30, there is no mode because no value repeats, and the range is 50 − 10 = 40. The geometric mean is (10 × 20 × 30 × 40 × 50)^(1/5) ≈ 26.05 and the harmonic mean is 5 ÷ (1/10 + 1/20 + 1/30 + 1/40 + 1/50) ≈ 21.90. With weights 1, 2, 3, 2, 1 the weighted average is (10 + 40 + 90 + 80 + 50) ÷ 9 = 270 ÷ 9 = 30 — the same here because the weights are symmetric.

Sources: NIST/SEMATECH e-Handbook of Statistical Methods — measures of location

Frequently asked questions

Is the average the same as the mean?

In everyday use, yes — “average” almost always means the arithmetic mean: add the values and divide by how many there are. The median and mode are other kinds of average, and both are shown in the results.

How do outliers affect the average?

A single very large or very small value pulls the mean toward it. When your data has extremes, the median or the trimmed mean (which ignores a share of the smallest and largest values) often describes the typical value better than the mean does.

How do I calculate a weighted average?

Multiply each number by its weight, add those products, then divide by the sum of the weights. For grades of 90, 80 and 70 worth 3, 4 and 2 credits: (270 + 320 + 140) ÷ 9 = 81.1. Choose Weighted average above and enter the weights in the same order as the numbers.

Can I average numbers that are themselves averages?

Only if each represents the same number of items. Averaging the averages of different-sized groups gives the wrong answer — use the weighted average with each group’s size as its weight.

When should I use the geometric or harmonic mean?

Use the geometric mean for things that multiply, such as yearly growth rates or investment returns. Use the harmonic mean for rates over a fixed amount, such as the average speed over equal distances. Both need every value to be above zero.