Average Calculator

Compute the mean of any list of numbers, plus sum, count and range.

About Average Calculator

The mean is the sum of all values divided by how many there are. The median is the middle value when sorted, the mode is the most frequent value, and the range is the difference between the largest and smallest values.

Formulas

Mean

Mean = Sum of all values ÷ Count

x̄: Arithmetic mean
xᵢ: Each individual value
n: Number of values

Median

Median = middle value of the sorted list (average of the two middle values when n is even)

n: Number of values

Range

Range = Maximum value − Minimum value

x_max: Largest value in the dataset
x_min: Smallest value in the dataset

Worked example

With the default values below, Average Calculator returns Mean (Average) of 30.0000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Numbers (comma or space separated): 10, 20, 30, 40, 50

Results

Mean (Average): 30.0000
Median: 30.0000
Mode: No mode
Sum: 150.00
Range: 40.00
Count: 5

Step by step

1Collect the values= 5 values
2Sum all values= 150.0000
3Divide sum by count to get the mean= 30.0000
4Sort the values, then find the median= 30.0000
5Find the range (max − min)= 40.0000
6Mode (most frequent value)= No modeEvery value appears the same number of times — no single mode exists.

Assumptions and limits

The result is derived only from the single input listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Six numbers from one list

Type or paste values separated by commas or spaces and you get Mean, Median, Mode, Sum, Range and Count together. The default list is 10, 20, 30, 40, 50. Seeing all six at once is the point: each describes the data differently, and comparing them tells you which one to quote.

The definitions, applied to the default list

Sum — everything added: 10 + 20 + 30 + 40 + 50 = 150.
Count — how many values: 5.
Mean — sum ÷ count = 150 ÷ 5 = 30.
Median — sort, then take the middle value. With five values that is the third, 30. With an even count, average the two middle ones: for 10, 20, 30, 40, 50, 60 the median is (30 + 40) ÷ 2 = 35.
Mode — the most frequent value. Each number here appears once, so there is no mode.
Range — maximum − minimum = 50 − 10 = 40.

Mean and median only agree on balanced data

Replace the 50 with 250 and watch what moves:

Result	10, 20, 30, 40, 50	10, 20, 30, 40, 250
Sum	150	350
Mean	30	70
Median	30	30
Range	40	240

The mean more than doubles while the median does not budge. Four of the five values now sit below the mean, so quoting 70 as typical would be misleading. The distance between mean and median is the fastest skew check available — when they separate, lead with the median and say so.

Choosing the right one

Use the mean when you will multiply it back up: average monthly spend times 12 gives the annual figure, which the median cannot do. Use the median for incomes, property prices, response times and anything with a long tail. Use the mode for repeated or categorical readings, such as the shoe size you sell most. The range is a one-second sanity check, but it rests on two values only and ignores everything between them; the sample standard deviation of the default list is 15.81 and uses all five.

Assumptions and traps

Check Count against how many values you meant to enter. It is the quickest way to spot a doubled separator or a number lost to a typo.
An average of averages is not the overall average unless every group is the same size. Averaging a 3-person team's mean with a 30-person team's mean gives both equal say.
Equal weighting is assumed. When items deserve different importance, you need a weighted calculation instead.
Means of 1-to-5 ratings are everywhere but shaky: the gap from 4 to 5 is not necessarily the same as 1 to 2.

For spread rather than centre, use the Standard Deviation Calculator. Weighted averages live in the Grade Calculator and the GPA Calculator, and the Percentage Calculator handles share-of-total questions.

Frequently Asked Questions

What's the difference between mean and median?

The mean averages every value and can be skewed by outliers. The median is the middle value and better represents a typical value when data is skewed.

Can data have more than one mode?

Yes. If several values tie for the highest frequency, the data is multimodal and all of them are listed.

One value is far larger than the rest — should I quote the mean or the median?

Quote the median and mention the outlier. Changing 10, 20, 30, 40, 50 to 10, 20, 30, 40, 250 moves the mean from 30 to 70 while the median stays at 30, and four of the five values fall under 70. Report the mean only when you need a figure that scales up, such as a total.

Do I need to sort my numbers before entering them?

No. Sorting happens internally for the median, so 40 10 50 30 20 gives the same results as the ordered list: median 30, mean 30, range 40. Enter the values in whatever order you collected them. Order never affects the mean, sum or count either.

Can I include negative numbers and decimals in the same list?

Yes. Both are handled, and the range is still maximum minus minimum — for −5, 0, 3.5, 12 the range is 17 and the mean is 2.625. Negative values matter for things like temperature readings or profit-and-loss figures, where dropping the sign would quietly change the mean.

The Mode result is empty — what does that mean for my data?

It means no value repeats, as with the default list where all five appear once. That is normal for measured or continuous data such as prices and times. The mode only earns its place with repeated or categorical values; if you want a typical figure for non-repeating data, use the median.