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DayUtils

Average Calculator – Mean, Median, Mode and Range

Paste or type a list of numbers to find the average (mean), the median, the mode and the range, plus the sum, the count and the geometric mean. Numbers can be separated by commas, spaces or new lines — paste straight from a spreadsheet.

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How to use the average calculator

  1. Type or paste your numbers into the box. Separate them with commas, spaces or new lines.
  2. The results update as you type.

You’ll see the mean, median, mode, range (with the minimum and maximum), sum, count and geometric mean. Press Copy to copy a summary.

The formulas

Mean = Sum of values ÷ Number of values

Median: sort the numbers; take the middle one, or the average of the two middle ones.

Mode: the most frequent value or values.

Range = Largest value − Smallest value
Geometric mean = (x1 × x2 × … × xn)^(1/n)

Worked example

Test scores: 72, 85, 90, 66, 85, 78, 94

  • Sum = 570, count = 7
  • Mean = 570 ÷ 7 ≈ 81.43
  • Sorted: 66, 72, 78, 85, 85, 90, 94 → median = 85
  • Mode = 85 (appears twice)
  • Range = 94 − 66 = 28
  • Geometric mean ≈ 80.89

Mean, median or mode — which to use?

  • Mean uses every value and is best for symmetric data without outliers, such as heights or test scores in a large class.
  • Median resists outliers and suits skewed data such as incomes, house prices or waiting times.
  • Mode is the only average for categories (most popular shoe size, most common answer) and is useful when you want the typical value.

Here is how one large value changes things: for 30, 32, 35, 38 and 40 the mean and median are both 35. Replace 40 with 400 and the mean jumps to 107, while the median stays at 35.

Averages in everyday life

Averages turn up everywhere: a class’s average test score, a cricket or baseball batting average, average monthly spending, the average speed of a journey and average rainfall. Be careful with averages of rates — the average speed of a round trip at 60 km/h out and 40 km/h back is 48 km/h (the harmonic mean), not 50 km/h. And when someone quotes an “average”, it is worth asking whether they mean the mean or the median, because the two can be very different.

Weighted averages

If some values count more than others — such as course grades with different credit hours — you need a weighted average. Use the grade calculator for weighted course grades, or the GPA calculator for credit-weighted GPAs.

Going further

To measure how spread out your data is, use the standard deviation calculator, which also shows the variance and standard error. For percentages and changes between two numbers, try the percentage calculator. Your data stays in your browser and is never uploaded.

Frequently asked questions

How do I calculate the average?

Add all the numbers and divide by how many there are. For 72, 85, 90, 66, 85, 78 and 94: the sum is 570 and there are 7 numbers, so the mean is 570 ÷ 7 ≈ 81.43.

What is the median?

The middle value when the numbers are sorted. With an odd count it is the single middle number; with an even count it is the average of the two middle numbers. For the list above, sorted 66, 72, 78, 85, 85, 90, 94, the median is 85.

What is the mode?

The value that appears most often. In the example, 85 appears twice, so it is the mode. A list can have more than one mode, or none if every value appears once.

When should I use the median instead of the mean?

When the data has a few very large or very small values. Incomes and house prices are usually described by the median because a handful of very high values pull the mean up.

What is the range?

The largest value minus the smallest. In the example, 94 − 66 = 28. It is a quick measure of spread; the standard deviation is a better one.

What is the geometric mean?

The nth root of the product of n positive numbers. It is used for averaging growth rates and ratios, such as average investment returns over several years.

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