Average Calculator
Paste or type your numbers – from Excel, a table or a list – and the average calculator shows the mean, median, mode and range. For weights, choose “weighted average”.
Source: 1.3.5.1, NIST/SEMATECH e-Handbook – Measures of location: mean, median, mode, trimmed mean. Updated: .
How it is calculated
To calculate the average (mean), add all the numbers and divide by how many there are: (12 + 15 + 11 + 18 + 15 + 20) ÷ 6 = 91 ÷ 6 ≈ 15.17. The median is the middle value of the sorted list (15) and the mode is the most frequent value (15).
Mean, median or mode?
- Mean (arithmetic average): uses every value but is pulled by outliers – one billionaire lifts a town’s average income.
- Median: splits the data into two halves and resists outliers; with an even count it is the average of the two middle values.
- Mode: the most common value – useful even for categories such as shoe sizes.
Weighted average
When values count differently, multiply each by its weight, add the products and divide by the sum of the weights: Σ(value × weight) ÷ Σ weights. Example: 3 lb at $2/lb and 1 lb at $6/lb average (3 × 2 + 1 × 6) ÷ 4 = $3/lb, not $4. For grades with credits use the GPA calculator.
Geometric and harmonic mean
Growth rates need the geometric mean (see the CAGR calculator); average speed over equal distances needs the harmonic mean: 60 mph out and 40 mph back average 48 mph, not 50. For positive numbers, harmonic ≤ geometric ≤ arithmetic ≤ root mean square. To see how spread out the data are, use the standard deviation calculator.
In Excel: =AVERAGE(A1:A10), =MEDIAN(…), =MODE.SNGL(…); weighted: =SUMPRODUCT(values,weights)/SUM(weights).
Frequently asked questions
How do you calculate the average?
Add all the values and divide by the number of values. For 4, 8 and 9: (4 + 8 + 9) ÷ 3 = 21 ÷ 3 = 7.
What is the difference between mean and median?
The mean is the arithmetic average; the median is the middle of the sorted list. For 1, 2, 3, 4, 100 the mean is 22 but the median is 3.
How do I calculate a weighted average?
Multiply each value by its weight, add the results and divide by the total weight: (2 × 1 + 3 × 2) ÷ 3 ≈ 2.67.
How do I find the mode?
Count how often each value appears; the one that appears most is the mode. A list can have several modes or none at all.
When should I use the geometric mean?
For factors and growth rates – investment returns or price increases over several years. It is the nth root of the product of the values.
Sources and legal basis
- 1.3.5.1: NIST/SEMATECH e-Handbook – Measures of location: mean, median, mode, trimmed mean
- Wolfram MathWorld – Geometric mean
- Wolfram MathWorld – Harmonic mean
- Wolfram MathWorld – Weighted mean
As of:
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