Mean, Median, Mode & Range Calculator

How to use the Mean, Median, Mode & Range Calculator

Enter or paste a list of numbers. Separate observations with commas, spaces, semicolons, tabs, or line breaks.

The calculator updates automatically and reports the mean, median, mode, range, count, sum, minimum, and maximum.

The default example 2, 3, 4, 5, 100 deliberately contains an extreme value so the difference between mean and median is immediately visible.

Open Dataset details & frequency to inspect distinct values, repeated observations, exact-value frequencies, copy the summary, or download the full frequency table as CSV.

Mean, median, mode, and range answer different questions

Mean, median, and mode are measures of location or central tendency, but they define centre in different ways.

The mean uses the numerical size of every observation. The median uses sorted position. The mode uses repetition.

Range is different: it is a measure of spread based only on the minimum and maximum.

Looking at all four together can reveal features that one summary value alone would hide.

Worked example: 2, 3, 4, 5, 100

This dataset shows why the mean and median should not automatically be treated as interchangeable versions of the same idea.

The first four observations lie between 2 and 5, but the value 100 raises the arithmetic mean to 22.8.

The median remains 4 because it depends on the middle sorted position rather than the numerical distance from the centre.

Every observation occurs once, so there is no mode. The observed range is 98.

How the arithmetic mean is calculated

The arithmetic mean is the sum of all observations divided by the number of observations.

For 4, 7, and 10, the sum is 21 and the count is 3, so the mean is 7.

Every observation affects the mean. Increasing one value by 30 increases the total by 30 and therefore increases the mean by 30 divided by the observation count.

Because every numerical value contributes to the total, unusually large or small observations can have substantial influence.

How the median is calculated

The median is determined after arranging the observations from lowest to highest.

With an odd number of observations, it is the single middle value. For 2, 4, 9, the median is 4.

With an even number of observations, it is the arithmetic average of the two middle values. For 1, 4, 7, 10, the median is 5.5.

Because it depends on position rather than the numerical distance of every observation, the median is often less influenced by a small number of extreme values than the mean.

How the mode is calculated

Mode is based on exact numerical frequency.

In 1, 2, 2, 3, the mode is 2 because it occurs twice while every other value occurs once.

In 1, 1, 2, 2, 3, both 1 and 2 are modes because they share the highest repeated frequency.

When every distinct value occurs exactly once, this calculator reports No mode.

Exact values, equivalent notation, and tied modes

Frequency counting happens after each valid input token has been converted to its numerical value.

The inputs 1, 1.0, and 1e0 therefore all become the number 1 and share one frequency count.

Negative zero is normalized to zero.

Nearby but unequal numbers remain distinct. For example, 1.2 and 1.2001 remain separate frequencies even if low display precision makes both appear as 1.2.

How range is calculated

Range equals the maximum observation minus the minimum observation.

For 3, 5, 8, and 11, the range is 11 − 3 = 8.

Range remains in the same measurement unit as the entered observations.

It is easy to interpret but uses only two observations. It says nothing about how the remaining values are distributed between the endpoints.

Why the calculator shows mean and median on the same range

The result visualization places the mean and median between the observed minimum and maximum.

When the two measures are close, they appear close together. When an extreme value moves the mean away from the central observations, their positions can separate substantially.

The line is not a histogram, box plot, density estimate, or distribution model.

It shows positions only; it does not tell you how many observations lie between those points.

Mean versus median when extreme values are present

Mean and median may be similar in balanced data and very different in skewed or long-tailed data.

In 2, 3, 4, 5, 100, the mean is 22.8 while the median is 4.

Neither statistic is mathematically wrong. The mean represents the arithmetic balance point, while the median identifies the middle sorted position.

For salaries, property prices, response times, and other datasets where a few observations may be much larger than most, reporting both can provide useful context.

How different datasets change the four measures

Different distributions can produce very different relationships among mean, median, mode, and range.

Repeated observations can produce one mode or several tied modes. Extreme observations can move the mean while leaving the median much less affected.

Two datasets may even share the same range while having very different centres and frequency patterns.

The examples below show how symmetry, extreme observations, repetition, tied modes, identical values, and negative values change the summary.

Count, sum, minimum, maximum, and distinct values

Count is the total number of observations included in the calculation.

Sum is their numerical total and is used in the arithmetic mean.

Minimum and maximum are the smallest and largest observations after numerical parsing.

Distinct count records how many different numerical values appear. Repeated observations counts entries beyond the first occurrence of each distinct value.

How the exact-value frequency table works

The frequency table records each distinct numerical value, how many times it occurs, and its percentage of the full dataset.

For example, if the value 4 appears three times in a dataset of 12 observations, its count is 3 and its relative frequency is 25%.

The on-page table previews the first 50 distinct values in numerical order when the dataset contains more than 50 distinct values.

Frequency CSV exports the complete table, including rows that are not displayed in the preview.

Display decimal places do not change the data

The Additional control changes the maximum number of decimal places shown in the interface.

It does not round the entered observations before the mean, median, mode, range, or frequency calculations are performed.

This means two distinct values can look identical at low display precision while still remaining separate in the underlying frequency table.

Choose a display precision appropriate for the source measurements rather than displaying more digits than the data justify.

Accepted input and the comma rule

The calculator accepts ordinary decimal notation, negative values, leading decimals such as .5, and scientific notation such as 1e3.

Whitespace, commas, semicolons, tabs, and line breaks can separate observations.

Because a comma always separates observations, 1,234 is interpreted as two values: 1 and 234.

Enter 1234 without the grouping comma when one thousand two hundred thirty-four is intended as a single observation.

Scientific notation and negative values

Scientific notation is useful for entering very large or very small values. For example, 1e3 is parsed as 1,000 and 2.5e-4 as 0.00025.

Negative observations are handled normally when sorting, summing, finding the mean and median, counting frequencies, and calculating the range.

The range itself cannot be negative because it is defined as maximum minus minimum.

Numerical stability and the 50,000-value limit

The calculator uses finite double-precision floating-point arithmetic.

Compensated summation reduces avoidable accumulation and cancellation error, and scaled fallback arithmetic helps avoid some intermediate-overflow cases when calculating the sum.

The mean is calculated in a way that can remain finite even when a direct raw total would overflow, and the even-count median avoids adding two enormous middle observations before dividing by two.

These techniques improve robustness but do not provide arbitrary-precision decimal mathematics. Values or results outside the supported finite numerical range are rejected.

The 50,000-observation limit bounds local parsing, sorting, frequency counting, memory usage, rendering, and CSV generation.

Check the dataset before interpreting the result

Confirm that all observations represent the same quantity and compatible units. Do not combine metres with centimetres, monthly figures with annual figures, or scores from different scales without first converting them appropriately.

Check pasted data for headings, units, placeholders, duplicated records, missing periods, impossible measurements, and decimal-format mistakes.

A missing observation is not automatically zero.

Investigate apparent outliers before removing them. An extreme value may be an error, but it may also be a genuine and important observation.

Common uses for descriptive statistics

Mean, median, mode, range, and frequency counts are useful for compactly summarizing test scores, prices, salaries, measurements, response times, delivery times, survey results, sales figures, and experimental observations.

The most useful measure depends on the type of data and the question being asked.

A calculation can be mathematically correct while still being misleading when observations use inconsistent units, periods, definitions, or collection methods.

When mean, median, mode, and range are not enough

These statistics provide a compact descriptive summary but do not reveal the complete distribution.

Use variance or standard deviation when spread across all numerical observations matters.

Use quartiles, percentiles, or interquartile range when positional summaries or robust spread are important.

Use an appropriate chart when clusters, gaps, skewness, several peaks, or other distributional features need to be seen.

Use inferential statistical methods when the goal is to draw conclusions beyond the entered observations.

Mean, median, mode, range, and frequency formulas

Let the observations be x₁ through xₙ and the sorted observations be x₍₁₎ ≤ … ≤ x₍ₙ₎. Mode uses exact parsed numerical frequencies.

$x_i$

Each entered observation

$x_{(i)}$

Observation in sorted position i

$n$

Number of observations

$S$

Sum of all observations

$\bar{x}$

Arithmetic mean

$f(v)$

Exact frequency of numerical value v

$p(v)$

Percentage of observations equal to value v

$R$

Range

Examples

Frequently Asked Questions

References

• NIST/SEMATECH e-Handbook — Measures of Location
• NIST/SEMATECH e-Handbook — Measures of Scale
• NIST/SEMATECH e-Handbook — Exploratory Data Analysis
• NIST Dictionary of Algorithms and Data Structures — Mode