Math

Mean Median Mode Calculator

Get the mean, median, and mode of any dataset in one go.

Paste a list of numbers and get all three measures of center at once: the mean (average), the median (middle value), and the mode (most frequent value). A must-have for statistics homework and quick data summaries.

Introduction

Mean, median, and mode are the three classic measures of central tendency — three different answers to 'what is a typical value?' The mean is the sum divided by the count; it uses every value and preserves the total. The median is the middle value when the data is sorted (or the average of the two middle values when the count is even); it resists distortion by extremes. The mode is the most frequently occurring value; a dataset can have no mode, one mode, or several (bimodal, trimodal), and it is the only measure that works for non-numerical categories like favorite colors or most common shoe size.

Each shines in different situations, and reporting all three gives the honest picture. The mean is dragged by outliers — one billionaire in an income survey skews the average — so it suits symmetric data like test scores or manufactured measurements. The median ignores outliers, which is why house prices, incomes, and commute times are usually reported as medians in the news. The mode flags the most typical single experience: the modal household size, the most common exam score. When mean, median, and mode agree, the data is nicely symmetric; when they diverge, the direction of the divergence tells you which way the data is skewed — a mean above the median means a rightward tail of high values, as the second example demonstrates. A quick diagnostic habit: compute all three, then compare. Mean well above median signals a right tail (income, house prices); mean below median signals a left tail (test scores with a few very low outliers, or ages in a retirement community). When someone quotes only the mean, ask for the median — the refusal to provide it is itself information. And remember the mode's unique talent: it is the only measure that works on categories, from the most common blood type (O positive) to the modal number of children per family.

How it's calculated

The mean is the sum divided by the count; the median is the middle value of the sorted list (average of the two middle values for even counts); the mode is the most frequent value, with ties broken by the smallest.

Worked examples

Dataset: 4, 8, 6, 5, 3, 7

Sort first: 3, 4, 5, 6, 7, 8. Mean: (3+4+5+6+7+8) = 33, divided by 6 = 5.5. Median: with an even count, average the two middle values (5 and 6): (5+6)/2 = 5.5. Mode: none — every value appears exactly once. Here the mean and median agree at 5.5, the signature of symmetric data with no outliers pulling either measure off center.

Dataset: 2, 3, 3, 5, 7 (skew demo)

Mean: (2+3+3+5+7) = 20, divided by 5 = 4. Median: the middle value of the sorted list is 3. Mode: 3, appearing twice. The single high value (7) pulls the mean up to 4 — above both the median and the mode. This is right skew in miniature: whenever the mean exceeds the median, suspect a tail of high values, exactly as in real income data where a few high earners lift the average above what most people make.

Frequently asked questions

What is the difference between mean, median, and mode?

The mean is the arithmetic average, the median is the middle value when sorted, and the mode is the value that appears most often. For 1, 2, 2, 3, 4 the mean is 2.4, the median is 2, and the mode is 2.

What if there are two middle numbers?

With an even count, the median is the average of the two middle values — e.g. the median of 1, 2, 3, 4 is 2.5.

What if no number repeats?

Then there is no true mode. The calculator shows the smallest value in that case, since every value is equally frequent.

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References