Statistics & Data

Mean, Median & Mode Calculator

Paste or type your numbers separated by commas or spaces. You get the key averages and spread measures, plus the working behind each — including the squared-deviation table for standard deviation.

Updated October 3, 2026Written and reviewed by Mateuss M.Method: how we calculate

Try an example:

AnswerMean 6.142857 · Median 6

Mode: 8
Range: 6
Sample SD: 2.2678
Population SD: 2.0996

Step-by-step working 7 steps

1
Sort the data
```
3, 4, 5, 6, 8, 8, 9
```
7 values.
2
Mean = sum ÷ count
```
Sum = 43
Mean = 43 ÷ 7 = 6.142857
```
3
Median = middle value
```
Value 4 of 7 = 6
```
4
Mode = most frequent value
```
8 (appears 2 times)
```
5
Range = largest − smallest
```
9 − 3 = 6
```

Squared deviations from the mean

(4 − 6.142857)² = 4.5918
(8 − 6.142857)² = 3.449
(6 − 6.142857)² = 0.0204
(5 − 6.142857)² = 1.3061
(3 − 6.142857)² = 9.8776
(8 − 6.142857)² = 3.449
(9 − 6.142857)² = 8.1633
Sum of squares = 30.8571

Sum these for every value to get the total used below.

7
Variance and standard deviation
```
Population: σ² = 30.8571 ÷ 7 = 4.4082,  σ = 2.0996
Sample:     s² = 30.8571 ÷ 6 = 5.1429,  s = 2.2678
```
Use the sample version (÷ n−1) when your data is a sample from a larger group; use the population version when it is the whole group.

How to use the mean, median & mode calculator

Enter your data as a list.
Read the mean and median in the answer box.
Open the steps for the sorted list, mode, range and deviation table.
Use the sample or population SD depending on where the data came from.

Definitions

Mean = Σx / n
Median = middle value of the sorted list
Mode = most frequent value
Population σ = √(Σ(x − μ)² / n)
Sample s = √(Σ(x − x̄)² / (n − 1))

The median resists outliers; the mean does not.

Worked examples

Each example below is generated by the same calculator you used above, so the working always matches the answer.

4, 8, 6, 5, 3, 8, 9

AnswerMean 6.142857 · Median 6

Mode: 8
Range: 6
Sample SD: 2.2678
Population SD: 2.0996

Step-by-step working 7 steps

1
Sort the data
```
3, 4, 5, 6, 8, 8, 9
```
7 values.
2
Mean = sum ÷ count
```
Sum = 43
Mean = 43 ÷ 7 = 6.142857
```
3
Median = middle value
```
Value 4 of 7 = 6
```
4
Mode = most frequent value
```
8 (appears 2 times)
```
5
Range = largest − smallest
```
9 − 3 = 6
```

Squared deviations from the mean

(4 − 6.142857)² = 4.5918
(8 − 6.142857)² = 3.449
(6 − 6.142857)² = 0.0204
(5 − 6.142857)² = 1.3061
(3 − 6.142857)² = 9.8776
(8 − 6.142857)² = 3.449
(9 − 6.142857)² = 8.1633
Sum of squares = 30.8571

Sum these for every value to get the total used below.

7
Variance and standard deviation
```
Population: σ² = 30.8571 ÷ 7 = 4.4082,  σ = 2.0996
Sample:     s² = 30.8571 ÷ 6 = 5.1429,  s = 2.2678
```
Use the sample version (÷ n−1) when your data is a sample from a larger group; use the population version when it is the whole group.

2, 4, 4, 4, 5, 5, 7, 9

AnswerMean 5 · Median 4.5

Mode: 4
Range: 7
Sample SD: 2.1381
Population SD: 2

Step-by-step working 7 steps

1
Sort the data
```
2, 4, 4, 4, 5, 5, 7, 9
```
8 values.
2
Mean = sum ÷ count
```
Sum = 40
Mean = 40 ÷ 8 = 5
```

Median = middle value

Average of values 4 and 5: (4 + 5) ÷ 2 = 4.5

4
Mode = most frequent value
```
4 (appears 3 times)
```
5
Range = largest − smallest
```
9 − 2 = 7
```

Squared deviations from the mean

(2 − 5)² = 9
(4 − 5)² = 1
(4 − 5)² = 1
(4 − 5)² = 1
(5 − 5)² = 0
(5 − 5)² = 0
(7 − 5)² = 4
(9 − 5)² = 16
Sum of squares = 32

Sum these for every value to get the total used below.

7
Variance and standard deviation
```
Population: σ² = 32 ÷ 8 = 4,  σ = 2
Sample:     s² = 32 ÷ 7 = 4.5714,  s = 2.1381
```
Use the sample version (÷ n−1) when your data is a sample from a larger group; use the population version when it is the whole group.

With an outlier

AnswerMean 25.5 · Median 12

Mode: 12
Range: 85
Sample SD: 34.0632
Population SD: 31.0953

Step-by-step working 7 steps

1
Sort the data
```
10, 11, 12, 12, 13, 95
```
6 values.
2
Mean = sum ÷ count
```
Sum = 153
Mean = 153 ÷ 6 = 25.5
```

Median = middle value

Average of values 3 and 4: (12 + 12) ÷ 2 = 12

4
Mode = most frequent value
```
12 (appears 2 times)
```
5
Range = largest − smallest
```
95 − 10 = 85
```

Squared deviations from the mean

(10 − 25.5)² = 240.25
(12 − 25.5)² = 182.25
(11 − 25.5)² = 210.25
(13 − 25.5)² = 156.25
(12 − 25.5)² = 182.25
(95 − 25.5)² = 4830.25
Sum of squares = 5801.5

Sum these for every value to get the total used below.

7
Variance and standard deviation
```
Population: σ² = 5801.5 ÷ 6 = 966.9167,  σ = 31.0953
Sample:     s² = 5801.5 ÷ 5 = 1160.3,  s = 34.0632
```
Use the sample version (÷ n−1) when your data is a sample from a larger group; use the population version when it is the whole group.

Common mistakes to avoid

Using the wrong SD

Sample SD divides by n − 1; population SD divides by n. Exams and software default to different ones.

Forgetting to sort for the median

The median is the middle of the ordered list, not the middle of the list as written.

Assuming there is always a mode

If every value appears once, there is no mode; if two tie, there are two.

Frequently asked questions

Which average should I report?

Use the median when the data is skewed or has outliers, such as incomes or house prices. Use the mean when values are roughly symmetric.

How many numbers can I enter?

Up to 500. Only the first ten squared deviations are listed to keep the working readable; the totals use all of them.