Median Calculator

What is the median?

The median is the middle value of a data set once you line the numbers up in order. Half the values fall below it and half above. Because it ignores how extreme the outliers are and only cares about position, it often describes "typical" better than the mean does, which is why incomes and house prices are usually reported as medians.

If there is an odd number of values, the median is simply the one in the middle. If there is an even number, it is the average of the two middle values.

How to use this calculator

1. Enter the numbers in your data set, separated by commas or spaces.
2. Make sure the values are numbers only, then sort them from least to greatest if needed.
3. Count how many values you have, because the median depends on whether the count is odd or even.
4. Read the middle value, or the average of the two middle values, and compare it with the calculator result.

The formula explained

The median is the center of an ordered data set. If there is an odd number of values, it is the single middle number, and if there is an even number of values, it is the average of the two middle numbers.

• x = a value in the data set
• n = the number of values in the data set

Step by step method

1. Sort the data from smallest to largest.
2. Count the total number of values, n.
3. If n is odd, choose the middle value. If n is even, find the two middle values and average them.

Worked example

Problem. Find the median of the data set 4, 9, 2, 7, 5, 10.

1. First, order the numbers: 2, 4, 5, 7, 9, 10.
2. There are 6 values, so the data set has an even number of terms. The two middle values are 5 and 7.
3. Average the two middle values: (5 + 7) / 2 = 6.

Tips and common mistakes

• Always sort the data before looking for the middle value, because the median only works on ordered data.
• If there are two middle numbers, do not pick one of them, average them instead.

Frequently asked questions