The Mean Median Mode Calculator finds the three classic measures of centre from a pasted data set, and also returns the range, the sum and the count. Paste values separated by commas, spaces or line breaks; the calculator sorts the list, reports each measure and shows the arithmetic so a hand check is possible.
Mean, median and mode answer different questions about the same numbers. Choosing the wrong one for skewed data or categorical labels is a common coursework mistake, and the sections below spell out when each measure fits.
Calculate mean, median and mode from a data set
Three numbers summarise the centre of a list, and they only agree when the distribution is roughly symmetric with a single peak. Paste your values into the data field. Commas, spaces, tabs and line breaks all work, so a spreadsheet column pastes cleanly. The count under the field should match how many numbers you intended to enter.
The calculator sorts ascending before finding the median and mode. Sorting does not change the mean, but it is required for the middle value and for frequency counts. Empty tokens and non-numeric fragments are rejected with a clear message rather than silently dropped.
Calculate the mean, also called the average
The mean, also called the arithmetic mean, is the sum of the values divided by how many there are. In everyday speech that quantity is called the average; in statistics the two names refer to the same calculation.
Every value pulls the mean toward itself equally, which is why a single extreme observation can shift it a long way from a typical point.
x̄ = Σx / nAdd every value, then divide by n. For the set 4, 8, 15, 16, 23, 42 the sum is 108 and the mean is 108 ÷ 6 = 18. Every value pulls the mean toward itself equally, which is why a single extreme observation can shift it a long way. That sensitivity is useful when every observation should count, and a liability when outliers are noise.
Find the median of an odd or even data set
The median is the middle value once the data is sorted. Half the observations sit at or below it, and half sit at or above it. Outliers barely move it, which is why income and house-price summaries often quote the median rather than the mean.
Odd count. Position = (n + 1) / 2. For five sorted values the median is the third. Even count. Average the two central values, at positions n/2 and n/2 + 1.
For 4, 8, 15, 16, 23, 42 (already sorted, n = 6) the central pair is 15 and 16, so the median is (15 + 16) / 2 = 15.5.
Find the mode when a set has one, several or none
The mode is the value that appears most often. A set may be unimodal with one mode, bimodal with two, multimodal with several, or have no mode when every value appears once. Frequency is what matters, not magnitude, and categorical labels often have a meaningful mode even when a numeric mean would be nonsense.
Frequency is what matters, not magnitude. In 12, 15, 15, 18, 22 the mode is 15. In 4, 8, 15, 16, 23, 42 every value appears once, so there is no mode. Categorical data (favourite colour, blood type) often has a meaningful mode even when a mean would be nonsense.
Tied frequencies at the top produce multiple modes. The calculator lists all of them rather than picking one at random.
Calculate the range of a data set
Range is the simplest measure of spread: maximum minus minimum. For the worked list 4, 8, 15, 16, 23, 42 the range is 42 minus 4, which equals 38. Because it uses only two observations, a single extreme high or low value sets the entire result, so range is a quick screen rather than a durable summary.
It uses only two observations, so a single extreme high or low value sets the entire result. Range is a quick screen, not a durable summary. Variance and interquartile range describe spread with more of the data when the question demands it.
Find the sum and count of a data set
Sum and count are the building blocks beneath every other measure on this page. The mean is sum divided by count; the median position depends on count; mode frequencies compare against count. The calculator shows both explicitly so a paste error is obvious before anyone interprets the centre measures built on top of them.
The calculator shows both explicitly so a paste error is obvious: if you meant 20 values and the count reads 19, stop before interpreting the mean. Separators accepted include commas, spaces, tabs, line breaks, semicolons and pipes, matching how spreadsheets and notes actually export lists.
Calculate mean, median and mode for 4, 8, 15, 16, 23, 42
This six-value set is already sorted and yields mean 18, median 15.5, no mode and range 38. Count is 6 and sum is 108. Mean sits above median by 2.5 because the right side stretches to 42, a mild right skew that the mode cannot capture because every value appears once.
Count and sum. n = 6. Sum = 4 + 8 + 15 + 16 + 23 + 42 = 108.
Mean. 108 ÷ 6 = 18.
Median. Even n, so average the 3rd and 4th values: (15 + 16) / 2 = 15.5.
Mode. Each value appears once → no mode.
Range. 42 − 4 = 38.
Mean and median disagree by 2.5 because the right side of the list stretches farther than the left. That pattern is a mild right skew: the mean sits above the median, pulled by 42.
Choose between mean, median and mode
Use the mean when every value should influence the summary equally and extremes are not dominating the story. Use the median when skew or outliers would pull the mean away from a typical value, as with income. Use the mode for categorical data or when the most common value is the decision that matters.
When mean and median diverge sharply, report both.
Use the median when the distribution is skewed or contains outliers you do not want to dominate the story. Household income is the textbook case: a few very high earners lift the mean far above what a typical household earns, while the median stays near the middle earner.
Use the mode for categorical data, or when the most common value is the decision that matters (most frequent defect code, most common shoe size in a shipment).
When mean and median diverge sharply, report both and say why. Suppressing one of them hides the shape of the data.
Calculate a weighted or geometric mean
A weighted mean multiplies each value by a weight, sums the products and divides by total weight; course grades and portfolio holdings are typical uses. A geometric mean takes the n-th root of a product of positive values and fits compounding growth factors.
Equal weights reduce the weighted mean to the ordinary mean; a zero or negative value blocks the geometric mean.
Weighted mean. Multiply each value by its weight, sum those products, and divide by the total weight:
x̄w = Σ(wᵢxᵢ) / ΣwᵢCourse grades with category weights, and portfolio returns with position sizes, both use this form. A score of 90 at weight 0.2 and a score of 70 at weight 0.8 yields (18 + 56) / 1.0 = 74, not the simple average of 80.
Geometric mean. Multiply the values, then take the n-th root. All values must be positive.
GM = (x₁ × x₂ × … × xₙ)^(1/n)Growth rates and returns compounded over periods are the usual use. The geometric mean of 1.10 and 1.20 (10% then 20% growth factors) is √(1.32) ≈ 1.149, a 14.9% compounded rate, not the arithmetic 15%.
Outliers and reporting habits
A single mistyped extra zero can move the mean dramatically while barely touching the median. When a result looks surprising, sort the list and glance at the extremes before rewriting a whole lab report. The Descriptive Statistics Calculator adds variance, quartiles and a box plot when the question grows beyond centre alone.
Frequently asked questions
What is the difference between mean, median and mode?
The mean is the arithmetic average (sum ÷ count). The median is the middle value after sorting. The mode is the most frequent value. They coincide on a symmetric unimodal distribution and diverge when the data is skewed, has outliers, or is categorical.
How do I find the median of an even number of values?
Sort the list, then average the two central values. For n = 6 those are positions 3 and 4. For 4, 8, 15, 16, 23, 42 the median is (15 + 16) / 2 = 15.5.
Can a data set have more than one mode?
Yes. Two values sharing the highest frequency make the set bimodal; more than two make it multimodal. If every value appears once, the set has no mode.
Is the average the same as the mean?
In ordinary usage, yes: both refer to the arithmetic mean. Statisticians sometimes say "average" for any measure of centre, so coursework that asks for "the average" usually wants the mean unless it specifies otherwise.
When should I use the median instead of the mean?
Use the median when outliers or skew would pull the mean away from a typical value. Income, house prices and reaction times with long right tails are common cases. The median stays at the middle observation even if the largest value doubles.
How is range calculated?
Range = maximum − minimum. For 4, 8, 15, 16, 23, 42 the range is 38. It ignores everything between the extremes, so it is a rough spread screen rather than a full description.
What is a weighted mean?
A weighted mean multiplies each value by a weight, sums the products, and divides by the sum of weights. Category grades and portfolio holdings are typical applications. Equal weights reduce it to the ordinary mean.
What is a geometric mean?
The geometric mean is the n-th root of the product of n positive values. It is the right average for compounding growth factors. It is undefined if any value is zero or negative.
Does the Mean Median Mode Calculator change my data?
No. Values are parsed and sorted for display; nothing is stored or sent. A copy button exports the sorted list and the summary figures for pasting into a report.
Summary
The Mean Median Mode Calculator returns the mean, median, mode, range, sum and count from any pasted list, with the sorted data visible for checking. The mean divides the sum by n; the median takes the middle of the sorted list (or averages the central pair when n is even); the mode is the most frequent value, if any.
Prefer the median on skewed data, the mean when every point should count equally, and the mode for categorical frequency. Weighted and geometric means cover grades and growth rates when the simple average is the wrong tool.