Mean, Median & Mode Calculator

Paste or type the numbers

Paste a column from a spreadsheet or type the numbers by hand. Commas, spaces, and line breaks all count as separators, and you can mix them in one list. There is no calculate button. Count, sum, mean, median, mode, and range update as soon as the box holds at least one valid number.

Decimals are allowed, including values such as .5 and 3.25. Negative numbers are written with the minus sign attached, as in -4. A trailing exponent such as 1.2e3 is read as 1200. A comma is only a separator, so one thousand is written 1000, not 1,000, and a space splits numbers the same way. Anything that is not a plain number is skipped, and the line under the box names what was left out.

Under the six figures, one line says how the median was chosen, and another line explains the mode, including when a list has several modes or no mode. The sorted list follows, with the middle value or values marked in violet. The math stays in your browser. Nothing is uploaded, there is no account, and closing the tab clears the list.

How the mean is calculated

The mean is the arithmetic average. Add the numbers, then divide by how many there are. For 70, 80, 90, and 100 the sum is 340 and the count is 4, so the mean is 85. The count and the sum sit beside the mean so you can check that division yourself.

Every value pulls on the mean, including a value that sits far from the rest. In 2, 3, 3, 4, 100 the sum is 112 and the mean is 22.4, even though four of the five numbers are 4 or below. That is why one very low quiz can drag a class average down, and why the mean price of houses in a town can sit well above what most of those houses sold for.

Integers are shown in full. A result that is not a short decimal is shown with up to 12 significant digits. The mean of 1, 2, and 2 is 1.66666666667, which is 5 divided by 3 stopped at that length.

How the median is calculated

The median is the middle of the list after the numbers are sorted from least to greatest. The order you typed does not matter, because a copy of the list is sorted before the middle is chosen. With an odd count, the median is that middle number. Sorted, 3, 7, 8, 12, 15 has five values, and the third one is 8, so the median is 8.

With an even count there are two middle numbers, and the median is their average. Sorted, 3, 7, 8, 12 has four values. The two in the middle are 7 and 8, and their average is 7.5. The line under the results names which case you are in. Violet in the sorted list marks the value, or the two values, that went into the median.

How the mode is calculated

The mode is the number that appears most often. In 6, 7, 7, 8, 8, 8, 9 the number 8 appears three times and every other number appears less often, so the mode is 8. Shoe sizes sold this week, answers on a multiple-choice item, and the most common number of pets in a class survey are the sorts of questions a mode answers, because you want the value that came up most.

A list can have more than one mode. In 4, 4, 6, 6, 9 both 4 and 6 appear twice, which is more than 9 appears, so the modes are 4 and 6. A list with two modes is called bimodal. A list with more than two modes is called multimodal. The mode card shows up to three of them, and the sentence underneath names every mode and says how many times each one appears.

A list has no mode when no number is more common than the others. If every number appears once, as in 3, 5, 8, 12, nothing was repeated. The same is true when every distinct number appears equally often, as in 2, 2, 5, 5, where both values appear twice. The mode card reads None, and the sentence under the results says which of those situations you have. A single unrepeated number also has no mode, because a mode is a value that was repeated.

When each measure is the useful one

The mean asks what the total would be if it were shared evenly. The median asks what sits in the middle once the list is in order. The mode asks what showed up most. For a tight cluster of test scores the three often land near one another. For a skewed list they separate, and that gap is part of the description.

Take 2, 3, 3, 4, 100. The mode is 3, the median is 3, and the mean is 22.4. The mean is the right summary when the total matters, such as five sales added together. The median is the better picture of a typical sale, because one large sale does not move the middle. The mode is the better picture when the question is which value occurred most.

Range is a measure of spread, not of center. It is the largest value minus the smallest. In that same list the range is 98, which says the values are widely scattered even though the median is 3. A small range means the numbers sit close together. A large range means they do not, even when the mean looks ordinary.

Checking the result by hand

The sorted list is the same numbers, ordered from least to greatest. Use it when you want to find the median yourself. Count in from either end until you reach the middle. On an odd count you land on one number. On an even count you land on two numbers and average them. The violet highlight marks that spot.

A solid homework check is to cover the result and work one measure on paper, then compare. Add the list and divide for the mean. Sort and take the middle for the median. Tally the repeats for the mode. Subtract the smallest from the largest for the range. When the two answers disagree, the usual cause is a number left out of the sum, or a comma that turned 1000 into 1 and 0.