Median Calculator

The median is the middle value once your numbers are sorted. Paste a list to get the median straight away, with the sorted list and the middle position shown for both odd and even counts.

6 values read.

Median
42.5
Position
3rd & 4th
Mean (compare)
42.8333
Q1 / Q3
38 / 47
Count
6
35404550
▲ mean 42.8333 · ◆ median 42.5

Step-by-step working

  1. Sort the values from smallest to largest35, 38, 41, 44, 47, 52
  2. There are 6 values (even), so average the two middle values at positions 3 and 4median = (41 + 44) ÷ 2 = 42.5

Formula odd n: median = value at position (n + 1) ÷ 2 even n: median = average of the values at positions n ÷ 2 and n ÷ 2 + 1

Ask the tutor about your result

An AI tutor reads your inputs and results above and explains them in plain English. The numbers come from the calculator; the explanation is AI-written, so check it against your notes.

Why the median ignores outliers

Eight quiz scores. Drag the slider to turn the last score into an outlier and watch which “average” gets pulled.

42444648505254
▲ mean 47.75 · ◆ median 47.5
Mean ▲
47.8
Median ◆
47.5
Gap
0.3

The mean uses every value’s size, so one extreme value drags it. The median only cares about order, so it stays put. That’s why house prices and incomes are reported as medians, and why a mean far from the median hints at skew or outliers.

How to find the median

  1. Sort the values from smallest to largest.
  2. If the count n is odd, the median is the value at position (n + 1) ÷ 2. For 7 values that is the 4th.
  3. If n is even, there are two middle values (positions n ÷ 2 and n ÷ 2 + 1). Add them and divide by 2.

Example: 35, 38, 41, 44, 47, 52 has n = 6, so average the 3rd and 4th values: (41 + 44) ÷ 2 = 42.5.

Median vs mean

The median depends only on order, so one huge value barely moves it, while the mean is pulled towards it. That is why household income and house prices are usually reported as medians. When mean and median are close, the data are roughly symmetric; a mean well above the median points to a long right tail. The skewness calculator puts a number on that.

Frequently asked questions

How do you find the median of an even set of numbers?

Sort the numbers, take the two in the middle and average them. For 2, 4, 7, 9 the middle pair is 4 and 7, so the median is 5.5.

Can the median be a number that is not in the data?

Yes. With an even count the median is the average of the two middle values, which often is not one of the original numbers.

Do I need to sort the numbers first?

Yes, by hand you must. This calculator sorts them for you and shows the sorted list so you can check the middle position.

Is the median the same as Q2?

Yes. The median is the second quartile (Q2) and the 50th percentile: half the data lie at or below it.