The mean is the average (sum ÷ count). The median is the middle value once sorted. The mode is the most frequent value. In skewed distributions the median often represents the "typical value" better.
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Descriptive statistics from a list of numbers, with a histogram.
Mean, median and mode are the three measures of central tendency that summarize a data set. The (arithmetic) mean is the sum of all values divided by the count: mean = sum ÷ n. The median is the middle value once the data is sorted, with an odd count it is the middle one; with an even count it is the average of the two middle values. The mode is the value that repeats most; it may not exist (all unique) or be a tie among several (bimodal, multimodal). Beyond that, the tool computes the range (maximum − minimum) and the quartiles Q1 and Q3 using linear interpolation (the numpy default and that of many textbooks), whose difference Q3 − Q1 is the interquartile range (IQR), a spread measure robust to outliers. You paste the list with any separator, comma, space, semicolon or line break, and also see the sum, count, minimum, maximum and a distribution histogram. Everything is computed in the browser.
The three measures of center answer the same question, what is the typical value?, in different ways. The mean adds everything and divides by the count (sum ÷ n), using every number. The median sorts the data and takes the middle one (or the average of the two middle values, if n is even). The mode simply counts repetitions and returns the most frequent value (or values).
For spread, the range is the distance between the largest and smallest value (max − min). The quartiles Q1 and Q3 mark the points leaving 25% and 75% of the data below: here they are computed by linear interpolation, placing the percentile at position (p ÷ 100) × (n − 1) in the sorted list and interpolating between neighbors. The interquartile range is IQR = Q3 − Q1.
Example 1, 4, 8, 15, 16, 23, 42. The sum is 108, so the mean = 108 ÷ 6 = 18. Sorted, the list has six values; the median is the average of the two middle ones, (15 + 16) ÷ 2 = 15.5. Every value is unique, so there is no mode; the range is 42 − 4 = 38. By linear interpolation, Q1 falls at position 1.25 between 8 and 15, giving Q1 = 8 + 0.25 × (15 − 8) = 9.75.
Example 2, 2, 4, 4, 4, 6, 8. The sum is 28, so the mean = 28 ÷ 6 ≈ 4.667. The median is (4 + 4) ÷ 2 = 4, and the mode is 4 (it appears three times). The range is 8 − 2 = 6. Here the mode and median coincide, a sign the data clusters around 4.
The mean uses every data point but is sensitive to extremes: a single very high outlier pulls it upward. The median ignores the magnitude of extremes and so better represents the "typical value" of skewed data, like income or house prices. When the mean and median are close, the distribution is fairly symmetric; when they diverge, there is skew.
It helps to know there is no single definition of a quartile: this tool uses linear interpolation, but some texts and software use the median-of-halves method, so Q1 and Q3 may differ slightly from another calculator. That is normal and not an error. These statistics underpin reports, school grades, quality control and any exploratory data analysis.
Paste the code into your HTML and the tool shows up on your page, without J-Kit's navigation and ads. It still runs in the browser of whoever visits your site.
<iframe
src="https://jkit.tools/embed/en-US/mean-median-mode-calculator"
width="100%"
height="600"
style="border:0"
loading="lazy"
title="Mean, Median & Mode Calculator"
></iframe>These references help contextualize formulas, standards, APIs and limitations used on this page. They do not replace professional validation when a result has legal, financial, medical or operational impact.
The mean is the average (sum ÷ count). The median is the middle value once sorted. The mode is the most frequent value. In skewed distributions the median often represents the "typical value" better.
Calculations run in your browser. No data is sent to a server.