What it means
The middle number after arranging the values from smallest to largest. If there are two middle numbers, use their average.
Examples on this page are illustrations, not findings from the research cards.
Worked example
For the values 2, 4 and 12, the middle value is 4. The median is 4.
Hypothetical example: three amounts are 2, 4 and 12. They are already in order. The middle amount is 4, so the median is 4. The mean is (2 + 4 + 12) ÷ 3 = 6. The large value, 12, pulls the mean above the median.
For 2, 4, 8 and 12, the middle values are 4 and 8, so the median is (4 + 8) ÷ 2 = 6. For 2, 4 and 4, the median is 4 even though no value is strictly above it. Repeated values do not change the method.
A closer look
To find the median, arrange the values from smallest to largest and locate the middle. With an odd number of values, one value occupies that position. With an even number, there are two middle values: add them and divide by two. Repeated values stay in the list, because each observation still counts. Ties mean there need not be equal numbers strictly above and strictly below the median.
The median describes the centre by position. The mean uses the sizes of all the values: add them and divide by how many there are. A very large or small value can therefore pull the mean away from the median. Neither figure alone tells you how widely people's circumstances differ.
A common misunderstanding
The median is not always the mean, and it does not always have exactly half the observations strictly above it and half strictly below.
Check the explanation
Sources
The wording and examples are original explanations informed by these references.
Cite this explanation
Median. aikyam school. https://aikyam.school/glossary/median/
Used in these cards
47 cards use this term
The original research wording is preserved in these cards.
