StatReason

Median Calculator

Enter a list of numbers to find the middle value, the point where half your data falls below and half falls above.

Separate values with commas, spaces, tabs, or one per line.

What this answers

The median answers "what is the middle value of this data, once sorted?" Unlike the mean, it does not care how far above or below the center an extreme value sits, only that it is above or below. This makes the median a more reliable summary than the mean whenever your data is skewed or contains a handful of extreme values.

How it is calculated

Values are sorted, and the median is the middle value for an odd count, or the average of the two middle values for an even count. This calculator also reports the first and third quartiles using the same Hyndman-Fan Type 7 interpolation convention used throughout this site (R's and most spreadsheets' default), so the median and quartiles here always agree with the quartiles shown by the Quartile and IQR engine on the same data.

Worked example

For the values 1, 2, and 100: sorted, the middle value is 2, so the median is exactly 2, completely unaffected by how large 100 is. Compare this with the mean of the same three values, about 34.3, and the difference shows exactly why the median is the safer choice when a dataset has an extreme value like this one.

Assumption audit

Calculated from your data: the count of values and whether the count is even or odd, which determines whether the median is interpolated between two middle values or taken directly.
Evidence to review: how far apart Q1 and Q3 sit relative to the median. A wide gap suggests real spread in your data that the median alone will not convey.
You must verify: that every value is measured on the same scale and that ordering them meaningfully answers your question, since the median only ever reflects rank order, never magnitude.

Common mistakes

Assuming the median and mean will be close is only safe for roughly symmetric data. Reporting only the median can also hide real variability; pairing it with Q1 and Q3, or checking the full spread with the Standard Deviation Calculator, gives a fuller picture.

Limitations

The median discards information about exactly how far values sit from the center, only their relative order. Two very differently shaped datasets can share the same median.