2026-08-07 9 min

Mean, Median, Mode, Range Calculator

Calculate mean, median, mode, range, trimmed mean, geometric mean, min, max, variance, and standard deviation for any dataset with a live dot plot.

Calculator

Data Values (comma or newline separated)

Trim Percent per Tail (%) Help

0–45 for trimmed mean

Results update automatically

Results update live as you type

Status:n = 8Mean 22.25Range 36

Center & Spread Summary

Mean22.25

Median23

Mode23

Range36

Extended Breakdown

Trimmed Mean (10%)22.25

Geometric Mean17.11985173

Minimum2

Maximum38

Sum178

Count8

Results

Optimal

Mean (Average)

22.25

Sum divided by count

Median

Middle of sorted values

Mode

Most frequent value

Range

Maximum minus minimum

Trimmed Mean (10%)

22.25

Mean after dropping 10% per tail

Geometric Mean

17.11985173

n-th root of the product

Minimum

Smallest value

Maximum

Largest value

Parses comma- or newline-separated numbers and summarizes them with exact order statistics. Trimming cuts equal shares from both sorted tails; the geometric mean assumes non-negative values.

Visualizations

Sorted Values

1010

2121

2323

3838

Value Share (positive values)

x=3823%

x=2314%

x=2113%

Range as Share of Maximum

Range36

Mean vs Maximum

Mean22.3

Formula

The four classical center-and-spread summaries share one pass over sorted data. The trimmed mean generalizes the idea by discarding tails, and the geometric mean handles multiplicative growth.

mean = Σx/n · median = middle of sorted x · mode = most frequent · range = max−min

Alternative Form

Trimmed mean = mean of middle (100−2t)% · Geometric mean = (Πx)^(1/n)

Variables

Symbol	Name	Unit	Description
x̄	Mean	data	Σx/n; uses every value
x̃	Median	data	Middle sorted value
x̂	Mode	data	Most frequent value
R	Range	data	max − min
t	Trim percent	%	Share dropped per tail
G	Geometric mean	data	(Πx)^(1/n)
n	Count	count	Dataset size

Explanation

Mean chases every value including outliers; median and trimmed mean buy robustness; mode reveals clustering. Range prices the extremes. Together they triangulate “typical” honestly.

Derivation

Mean minimizes squared error; median minimizes absolute error; mode maximizes the empirical mass function; range spans the support. Trimming replaces the full average with the average over central order statistics; the geometric mean is the exponential of the mean of logs.

Step-by-Step Calculation

Follow each step to understand how the result is calculated from your inputs.

Step 1

Parse comma- or newline-separated entries into numbers.

split, trim, drop non-numeric

Raw Input:10, 2, 38, 23, 38, 23, 21, 23

Intermediate: 8 values parsed

Result: n = 8

Step 2

Sum all values and divide by the count to get the mean.

mean = Σx / n

Sum:178

n:8

Intermediate: 178 / 8

Result: mean = 22.25

Step 3

Sort the values and take the middle (averaging the middle two when n is even).

median = middle of sorted x

n:8

Intermediate: sorted: 2, 10, 21, 23, 23, 23, 38, 38

Result: median = 23

Step 4

Count frequencies; the most frequent value is the mode.

mode = argmax frequency

Modes:23

Intermediate: single peak (or none)

Result: mode = 23

Step 5

Subtract the minimum from the maximum for the range.

range = max − min

Max:38

Min:2

Intermediate: 38 − 2

Result: range = 36

Step 6

Drop the trim percentage from each tail and average the rest.

trimmed = mean of middle 80%

Trim %:10% per tail

Intermediate: kept 8 of 8 values

Result: trimmed mean = 22.25

Final Answer

22.25

Worked Examples

See how the calculator works with different scenarios.

Scenario

Scores: 10, 2, 38, 23, 38, 23, 21, 23.

Inputs

n:8

Calculation

mean = 178/8 = 22.25 median = 23, mode = 23 range = 38 − 2 = 36

Result

mean 22.25 · median 23 · mode 23 · range 36

Interpretation

All centers agree near 22–23: a well-behaved, roughly symmetric class.

Understanding Your Result

Your Result: Mean (Average): 22.25

Typical range: Mean ≈ median within ~10% suggests symmetry; trimmed mean between them confirms mild tails.

What This Means

Mean locates the balance point, median the midpoint person, mode the most common value, and range the full span between extremes.

Why It Matters

“Average” without a named measure misleads: salaries, prices, and wait times routinely separate mean from median by multiples.

Professional Interpretation

Quote mean ± SD for symmetric data, median + range (or IQR) for skewed data, and always name multimodal peaks.

Recommendations

•Name which average you report
•Compare mean vs median before concluding
•Use trimming for contaminated measurements
•Use geometric mean for rates and ratios
•Show the dot plot to catch bimodality
•Never average averages without weights

Educational Content

Introduction

Mean, median, mode, and range are the oldest statistical summaries — four numbers that sketch any dataset’s center and span. This calculator adds trimmed and geometric means plus full spread statistics.

Concept Explanation

Different centers optimize different losses: squared error (mean), absolute error (median), zero-one match (mode). Range simply spans the observed support.

Applications

▸Reporting test scores and grades

▸Summarizing salaries and prices

▸Describing survey responses

▸Quality measurements on a line

▸Sports averages and records

▸Everyday data literacy in the news

Benefits

•Four classic summaries in one paste
•Trimmed mean resists outliers automatically
•Geometric mean handles growth correctly
•Dot plot reveals clusters and gaps
•Multimodal detection via frequency table

Limitations

•Range leans entirely on two extremes
•Mode is unstable in continuous data
•Geometric mean fails on negative values
•Summaries never replace the plot

Best Practices

•Sort data mentally before trusting median
•Check mode count for hidden subgroups
•Trim symmetrically and disclose the percent
•Log-transform before geometric means of ratios
•Pair every center with a spread

Common Misconceptions

Myth: Average always means arithmetic mean.

Truth: News “averages” are often medians (house prices, incomes) — ask which one.

Myth: A higher range means a higher average.

Truth: Range measures spread only; two datasets can share a mean with opposite ranges.

Myth: Mode is useless for numbers.

Truth: A strong mode exposes rounding, thresholds, or genuine subpopulations.

Myth: Trimming is cheating.

Truth: Disclosed symmetric trimming is a standard robust estimator, not data cooking.

Practical Tips

•Paste with commas or line breaks
•Compare mean and median first
•Raise trim % for noisy sensors
•Use geometric mean for percent changes
•Expand multimodal hints in the breakdown
•Keep full precision until the final report
•Screenshot the dot plot for presentations

Common Mistakes

Quoting “average” without naming it

Say mean, median, or mode explicitly — they can differ by multiples.

Averaging percentages arithmetically

Convert to growth factors and take the geometric mean.

Letting one outlier set the range story

Report trimmed range or percentiles alongside the full range.

Reading a continuous mode literally

Bin continuous data first; raw-value modes are often noise.

Over-trimming small datasets

Keep trim ≤ 20% under n=10 or little data remains.

Assumptions

This calculator makes the following assumptions to provide estimates:

Numeric Input: Non-numeric tokens are skipped silently.

Equal Weights: Each value contributes once.

Symmetric Trim: Equal shares are cut from both tails.

Non-negative GM: Geometric mean assumes non-negative values.

Static Snapshot: One dataset per calculation; no time modeling.

Limitations

Be aware of these limitations when using this calculator:

No Inference: No confidence intervals or tests.

Range Fragility: Two extremes fully determine the range.

Mode Ties: Only the first mode headlines; see breakdown for all.

Single Group: Mixed populations should be split first.

Frequently Asked Questions

Answers to common questions about this calculator.

What is the mean?

The arithmetic average: add all values and divide by the count. It uses every data point, which makes it efficient but sensitive to outliers and skew.

What is the median?

The middle value of sorted data (or the average of the middle two for even counts). It resists outliers, so it best represents skewed data like incomes.

What is the mode?

The most frequently occurring value. A dataset can have no mode (all unique), one mode, or several (bimodal, multimodal) — multiple modes hint at mixed groups.

What is the range?

Maximum minus minimum. It is the quickest spread measure but depends on just two values, so a single outlier can dominate it.

Mean vs median: which should I report?

Report both. When they agree, the data is roughly symmetric. When the mean exceeds the median, expect right skew (a high outlier); the reverse signals left skew.

What is a trimmed mean?

The mean after dropping a fixed percentage from each tail (e.g. 10%). It keeps the efficiency of averaging while resisting outliers — a compromise between mean and median.

What is the geometric mean?

The n-th root of the product of values. Use it for growth rates, returns, and ratios — anywhere multiplication, not addition, accumulates.

Can data have more than one mode?

Yes. Two equal peaks make it bimodal (often two overlapping groups, like test scores from two classes). This calculator reports the first mode and the full list in the breakdown.

How do outliers change mean, median, mode, and range?

One extreme value drags the mean and explodes the range, barely moves the median, and usually leaves the mode untouched — which is why robust summaries pair median with range.

What is the difference between average and mean?

In everyday speech they are synonyms for the arithmetic mean. Strictly, “average” can mean any center measure — mean, median, or mode — so name the one you used.

How do you find the median of an even-sized dataset?

Sort the values and average the two middle ones. For 2, 10, 21, 23, 23, 23, 38, 38 the middle pair is 23 and 23, so the median is 23.

Why does this calculator also show variance and SD?

Center without spread is half the story: identical means can hide opposite variability. The breakdown includes variance and standard deviation so every dataset gets center plus spread.