Mathematics CalcyZone Calculator

Median Calculator

Find the exact middle number of a sorted set of numbers.

Enter Numbers (Comma Separated)

Calculation Solution

Median = 30

Sorted: 10, 20, 30, 40, 50

Mathematical Formula

Median = Middle value of ordered dataset (or average of two middle values if count is even)

Overview & Explanation

The median is the middle value in a list of numbers sorted in ascending order. It is less affected by extreme outliers than the mean.

How It Works

Sort all dataset values in ascending numerical order.
If dataset length is odd, pick the exact center number.
If dataset length is even, compute the average of the two central numbers.

Practical Applications

Determining median household income.
Analyzing real estate median home sale prices.

Finding the median

The median is the middle value of a data set sorted from smallest to largest. For 3, 7, 9, 15, 40 the median is 9. With an even number of values, take the average of the two middle ones: for 3, 7, 9, 15 the median is (7 + 9) ÷ 2 = 8.

Always sort first. Forgetting to sort is the most common error.

Median versus mean

The mean of 3, 7, 9, 15, 40 is 74 ÷ 5 = 14.8, pulled upwards by the single large value 40. The median, 9, is not affected by how extreme the largest or smallest values are, which makes it the better summary for skewed data.

This is why household incomes and house prices are usually reported as medians: a few very high values would make the mean look unrepresentative of a typical household. If the mean is much larger than the median, the data has a long tail of high values.

Related measures

The median splits data into two halves; the quartiles split it into four. The interquartile range, the gap between the first and third quartile, describes spread in a way that, like the median, resists outliers. For grouped data in frequency tables, the median is estimated by interpolating within the class that contains the middle position.