Mean, Median, Mode & Range Calculator
Calculate the measures of central tendency: mean, median, mode, and range.
Quick Examples
Measures of Central Tendency
Mean (Arithmetic Average)
Median
The middle value when data is sorted. If there's an even number of values, take the average of the two middle values.
Mode
The most frequently occurring value. A data set can have one mode, multiple modes, or no mode.
Range
What Are Measures of Central Tendency?
A measure of central tendency is a single number that summarizes where the "middle" of a dataset lies. When you hear "the average house price" or "a typical test score," a central tendency is doing the work of compressing many numbers into one representative value. The three main measures — mean, median, and mode — each define "typical" differently, which is why they can disagree, and why choosing the right one matters.
The mean (arithmetic average) uses every value and is the right default for roughly symmetric data, like repeated measurements. The median, the middle value of sorted data, ignores extremes and is preferred for skewed data like incomes or house prices, where a few huge values would drag the mean away from what most people experience. The mode, the most frequent value, is the only one that works for categories — the "average" shirt size sold is a mode, not a mean.
Key Formulas
For the median, sort the data first: with an odd count n, the median is the value at position (n+1)/2; with an even count, average the two middle values at positions n/2 and n/2 + 1. The population-versus-sample distinction matters for variance and standard deviation, but the mean, median, and mode are computed the same way for both.
Step-by-Step: Mean, Median, and Mode of 4, 8, 6, 5, 3, 7
- Step 1 — Sort the data: 3, 4, 5, 6, 7, 8. Sorting is required before finding the median.
- Step 2 — Mean: sum = 3 + 4 + 5 + 6 + 7 + 8 = 33; count = 6; mean = 33 ÷ 6 = 5.5.
- Step 3 — Median: with 6 values (even), average the 3rd and 4th: (5 + 6) ÷ 2 = 5.5.
- Step 4 — Mode: every value appears exactly once, so this dataset has no mode.
- Step 5 — Range (bonus): 8 − 3 = 5.
Worked Examples
Example 1: Test scores 72, 85, 90, 85, 68
Sum = 400, n = 5, mean = 80. Sorted: 68, 72, 85, 85, 90 — the median (3rd value) = 85. Mode = 85 (the only repeated value). Range = 90 − 68 = 22.
Example 2: The effect of an outlier
Data: 10, 12, 11, 13, 100. Mean = 146 ÷ 5 = 29.2 — pulled far above most values by the single 100. Median of the sorted data (10, 11, 12, 13, 100) = 12, which still represents the bulk of the data. This resistance to outliers is why median income, not mean income, is the standard headline figure.
Common Mistakes
- Skipping the sort: the median of unsorted data is meaningless — always sort first.
- Forgetting to average two middles: with an even count, the median is the mean of the two center values, not one of them.
- Reporting the mean for skewed data: a few extreme values can make the mean misleading; check the median too.
- Claiming a mode where none exists: if every value is unique, the dataset has no mode.
Frequently Asked Questions
Which measure of central tendency should I use? Use mean for symmetric distributions without outliers. Use median for skewed data or when outliers are present. Use mode for categorical data or to find the most common value.
Which measure is best for salaries? The median — salaries are right-skewed by a few very high earners, so the median reflects the typical worker better than the mean.
Can a dataset have two modes? Yes — that is called bimodal. Data can even be multimodal, with three or more modes.
Must the mean be one of the data values? No. The mean of 1 and 2 is 1.5, which appears nowhere in the data.
When is the mode the right choice? For categorical data — colors, sizes, survey answers — where the mean and median cannot even be computed.
Midrange: A Fourth Quick Measure
The midrange is the value halfway between the minimum and maximum — the average of the two extremes:
For 3, 4, 5, 6, 7, 8 the midrange is (8 + 3)/2 = 5.5 — which here matches the mean and median exactly. It is fast to compute but fragile: a single outlier at either extreme moves it, since it ignores every value in between.
Which Measure Should You Use?
| Your data | Best measure | Why |
|---|---|---|
| Symmetric, no outliers (tight test scores) | Mean | Uses every value; most precise |
| Skewed or has outliers (incomes, house prices) | Median | Immune to extremes |
| Categories: colors, sizes, votes | Mode | The only one that works on labels |
| You need totals or rates | Mean | Mean × n recovers the sum; the median cannot |
| Quick estimate from min and max only | Midrange | Fast, but check for outliers first |
Where Each Measure Shows Up
- News and economics: "median household income" and "median home price" are standard because a few huge values would distort the means.
- Sports: a player's mean score per game uses every performance; the median game keeps one blowout from warping the picture.
- Retail: the modal shoe size — the one that sells out — drives restocking, not the average size.
- Quality control: the mean defect rate across a production run; the mode of defect types pinpoints what to fix first.
Computing Them in Spreadsheets
In Excel or Google Sheets: =AVERAGE(range) for the mean, =MEDIAN(range) for the median, =MODE.SNGL(range) for the mode (=MODE.MULT(range) reveals every tied mode), and =MAX(range)−MIN(range) for the range. All of them ignore text and blank cells, so they work directly on pasted raw data.