Marks Calc
Glossary

Median

The median is the middle value when all data points are sorted in order — half score below, half score above.

The median is the value that sits exactly in the middle of an ordered dataset. To find it, sort all data points (smallest to largest), and take the middle value. If there is an even number of data points, the median is the average of the two middle values.

The median is robust to outliers in a way the arithmetic mean is not. A class with marks {30, 75, 80, 82, 85} has mean = 70.4 (pulled down by the 30) but median = 80 (unaffected). When summarising class performance, the median often gives a more representative "typical student" score than the mean.

In academic results analysis, the median appears whenever you compute percentile ranks (the median = 50th percentile by definition). Many state-level result statistics — for example the Pakistan BISE annual reports — quote both mean and median pass marks because the distributions are usually skewed by a long tail of low performers.

Worked example

In the set {30, 75, 80, 82, 85, 88, 95}, the median is 82. Adding one more value to get {30, 75, 80, 82, 85, 88, 92, 95} makes the median (82+85)/2 = 83.5.

Used by

  • Statistics
  • Class performance analytics