Statistics
Mean, Median & Mode Calculator
Paste a list of numbers and instantly get the mean, median, mode, and range — plus the full five-number summary, variance, standard deviation, and a distribution plot. Every figure updates as you type.
Enter your data set
8 valuesSeparate numbers with commas, spaces, or new lines. Decimals and negatives are fine.
Data represents a
Variance & std dev divide by n − 1 (Bessel's correction).
Mean
81.375
Arithmetic average
Median
85
Middle value
Mode
85
Unimodal
Range
28
Max − min
Distribution
value mean median
64
92
Tallest stack repeats 3× — that's the mode
Full breakdown
Count (n)8
Sum651
Minimum64
Maximum92
Q175
Q387.5
IQR12.5
Midrange78
Variance (s²)89.6964
Std dev (s)9.4708
Updates as you type
Try an example
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The basics
The three averages, and a measure of spread
“Average” can mean three different things, and they often disagree. Knowing which one to use — and pairing it with a measure of spread like the range or standard deviation — is the heart of describing any data set.
x̄ = (Σx) ÷ n
Mean — the balance point
Add every value and divide by the count. The mean uses all of the data, which makes it powerful — but also sensitive: one extreme value drags it along.
(2 + 4 + 9) ÷ 3 = 5
middle of sorted data
Median — the middle
Sort the data and take the centre. Because it only cares about position, the median shrugs off outliers that would distort the mean.
2, 4, 9 → 4
most frequent value
Mode — the most common
The value that occurs most often. It is the only average that works on categories, not just numbers, and a set can have one mode, several, or none.
2, 2, 5 → 2
max − min
Range — the spread
The distance from smallest to largest. A quick read on how spread out the data is, before reaching for variance and standard deviation.
9 − 2 = 7
Method
How to find each one by hand
The calculator does this instantly, but every measure follows a short, repeatable recipe.
- 1
Sort the data
Write the values from smallest to largest. Sorting is what makes the median, quartiles, and range easy to read off.
9, 4, 2 → 2, 4, 9 - 2
Mean — add, then divide
Sum every value to get Σx, then divide by the count n.
(2 + 4 + 9) ÷ 3 = 5 - 3
Median — take the middle
With an odd count, it's the single centre value. With an even count, average the two middle values.
2, 4, 9 → median = 4 - 4
Mode & range — count and subtract
The mode is the value seen most often; the range is the largest minus the smallest.
mode = none · range = 9 − 2 = 7
Worked examples
See it across the tricky cases
The median behaves differently for odd and even counts, and the mode can split. Switch tabs to watch each case computed from its data.
Data 7, 3, 9, 4, 5
Sorted 3, 4, 5, 7, 9
Mean: (7 + 3 + 9 + 4 + 5) ÷ 5 = 28 ÷ 5 = 5.6
Median: middle of 5 sorted values → position 3 = 5
Mode: every value is unique → no mode
Range: 9 − 3 = 6
Mean5.6Median5ModeNo modeRange6
Median is the single middle value.
Where it shows up
Why it matters
Choosing the right average changes the story the data tells. These are the everyday places it counts.
median income
Money & housing
Incomes and house prices are skewed by a few very large values, so the median is the honest “typical” figure — the mean would look richer than reality.
mean score
Grades & tests
Class averages and GPAs use the mean because every score should pull its weight, and outliers are rare on a fixed scale.
modal size
Retail & inventory
The mode tells a shop which size or colour sells most — the most-ordered, most-stocked choice, which a mean of arbitrary labels could never capture.
Reference
The full descriptive summary
Beyond the three averages, the calculator reports a complete descriptive picture. Here is what each figure means and when to reach for it.
Count (n)
How many values are in the set.
Sum (Σx)
Every value added together.
Minimum / Maximum
The smallest and largest values.
Range
Maximum minus minimum — the simplest spread.
Q1 / Q3
The medians of the lower and upper halves — the quartiles.
IQR
Q3 − Q1, the spread of the middle 50% (outlier-resistant).
Midrange
The average of the minimum and maximum.
Variance & std dev
Average squared distance from the mean, and its square root.
Worth knowing
Rules and gotchas
A handful of facts that explain why the three averages can disagree — and how to avoid the common mistakes.
sort first
Always sort for the median
The median is about position, so an unsorted list gives the wrong answer. The calculator sorts for you, but by hand it is the step people skip.
mean ≠ median
Skew pulls them apart
When the mean sits well above the median, the data is skewed right (a long tail of large values); below, skewed left. Equal means a roughly symmetric set.
no mode is valid
No mode is a real answer
If every value appears once, there is genuinely no mode — that is not an error. Two or more tied values give a bimodal or multimodal set.
outlier sensitivity
The mean feels every outlier
Because it uses every value, one extreme number can swing the mean a long way while the median barely moves. Spread measures react the same way.
n vs n − 1
Variance depends on the model
Population variance divides by n; sample variance divides by n − 1. Pick the wrong one and your spread is slightly off.
units matter
Std dev shares the data's units
Variance is in squared units, which is hard to read, so its square root — the standard deviation — is reported in the same units as the data.
Glossary
Key terms, plainly
The vocabulary you'll meet alongside these measures.
- Outlier
- A value far from the rest of the data, able to distort the mean and range.
- Quartile
- A value splitting sorted data into quarters; Q2 is the median itself.
- Skew
- Asymmetry in the data — a longer tail on one side, which separates mean from median.
- Bimodal
- Having exactly two modes — two values tied as most frequent.
- Dispersion
- How spread out the data is, measured by range, IQR, or standard deviation.
- Bessel's correction
- Dividing a sample's variance by n − 1 to remove bias when estimating a population.
FAQ
Common questions
They are three measures of a typical value, often all called the 'average'. The mean is the arithmetic average — add every value and divide by how many there are. The median is the middle value once the data is sorted. The mode is the value that appears most often.
Sort the values, then take the two in the middle and average them. For 4, 8, 15, 16, 23, 42 the middle two are 15 and 16, so the median is (15 + 16) ÷ 2 = 15.5.
Yes. A set with two most-frequent values is bimodal, and one with several is multimodal. If every value appears exactly once, the set has no mode at all.
Use the median when the data has outliers or is skewed — like incomes or house prices. A single very large value pulls the mean up but barely moves the median, so the median better reflects a 'typical' value.
The range is the simplest measure of spread: largest value minus smallest. Standard deviation measures the typical distance of values from the mean, using every data point, so it is less sensitive to a single extreme than the range.
When your data is the entire group, divide the squared deviations by n (population, σ). When it's a sample you're using to estimate a larger group, divide by n − 1 (sample, s). Dividing by n − 1 — Bessel's correction — corrects the slight underestimate a sample produces. Use the toggle in the calculator to switch.
No. You can enter decimals and negative numbers in any order, separated by commas, spaces, or new lines. The calculator sorts them for you before finding the median, quartiles, and range.
Repeats are kept and counted. They affect the mean and are exactly how the mode is found — the value (or values) repeated most often. They also shift the median toward the busier part of the data.
Keep going
Related calculators
Keep reading
Further reading
Calculator
What Is the Mean? Definition, Formula, and How to Calculate It
The mean is the average of a set of numbers: add them all up and divide by how many there are. This guide shows the formula, a worked example, and how the mean differs from the median and mode.
Ugo Charles
Statistics
How to Calculate Standard Deviation in Excel
Use STDEV.S or STDEV.P in Excel, choose the right one for your data, and check the result against a worked example.
Ugo Charles
Calculator
How to Calculate Range in Statistics (Beginner’s Guide with Real-Life Examples)
A friendly, beginner-focused guide to understanding and calculating range in statistics. Learn what range means, how to compute it, real-life applications, and common mistakes to avoid.
Ugo Charles
Written by
UC
Author
Ugo CharlesBuilt and fact-checked against our editorial standards · Last updated June 2026
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