Mean, Median, Mode Calculator
Find the mean, median, mode and range of a list of numbers.
Results update as you type.
About this calculator
The mean, median and mode calculator returns the three measures of central tendency for a data set — the mean (arithmetic average), the median (middle value) and the mode (most frequent value) — plus the count, sum, range and the full five-number summary (minimum, first quartile, median, third quartile and maximum). Enter your numbers separated by commas or spaces.
The mean is the sum of all the values divided by how many there are. The median is found by sorting the data and taking the middle value, or the average of the two middle values when the count is even. The mode is whichever value appears most often; when every value is unique there is no mode, and when several values tie for the highest frequency the set is multimodal and all of them are shown.
Worked example: for 4, 8, 15, 16, 15, 23, 42 the sum is 123 across 7 values, so the mean is 123 ÷ 7 ≈ 17.57. Sorting gives 4, 8, 15, 15, 16, 23, 42, so the median (the fourth of seven values) is 15, and 15 is also the mode because it occurs twice while every other value occurs once. A frequency table and distribution chart break the data down value by value, which is useful for grades, survey scores, prices or any list where you need the typical value at a glance.
Frequently asked questions
When is there no mode?
A data set has no mode when every value occurs exactly once. If two or more values share the highest frequency, the set is bimodal or multimodal and each of those values is a mode.
Should I report the mean or the median?
Use the median for skewed data or when outliers are present, because it is not dragged toward extreme values. The mean is best for roughly symmetric data with no strong outliers.
What is the difference between the mean and the median?
The mean adds every value and divides by the count, so each number pulls on it and a single extreme value can shift it a lot. The median is just the middle value once the data is sorted, so it ignores how far away the extremes are. In symmetric data the two nearly coincide; in skewed data they separate.
How is the median found when there is an even number of values?
With an even count there is no single middle value, so the median is the average of the two central values. For 2, 4, 6, 8 the two middle numbers are 4 and 6, giving a median of 5.
Can a data set have more than one mode?
Yes. If two or more values tie for the highest frequency the set is bimodal or multimodal, and this mean, median and mode calculator lists every value that reaches that top frequency rather than picking just one.
What does the range tell me?
The range is the difference between the largest and smallest values, a quick but crude measure of spread. For 4, 8, 15, 16, 15, 23, 42 it is 42 − 4 = 38. Because it uses only the two extremes it is very sensitive to outliers.
What are the quartiles shown below the results?
The first and third quartiles are the 25th and 75th percentiles, so the middle half of your data lies between them. Together with the minimum, median and maximum they make up the five-number summary that describes the shape of the distribution.
API — use this calculator from code
Call this calculator as a free JSON endpoint — no key required. Send the field values below as query parameters or JSON. Read the full API docs →
Endpoint
GET https://calculator.free/api/v1/mean-median-mode/curl
curl "https://calculator.free/api/v1/mean-median-mode/?numbers=4, 8, 15, 16, 15, 23, 42"JavaScript fetch()
const r = await fetch(
"https://calculator.free/api/v1/mean-median-mode/?" + new URLSearchParams({
"numbers": "4, 8, 15, 16, 15, 23, 42"
}));
const data = await r.json();
console.log(data.results);Results are estimates for general guidance only, not financial, medical or tax advice.