What is the median? State its merits and demerits.

The median. The median is a measure of central tendency: it is the value of the middle item when a set of observations is arranged in order of size (ascending or descending). It divides the distribution into two equal halves, so that one half of the items lie below it and the other half above it. For \( n \) arranged items, when \( n \) is odd the median is the \( \left(\frac{n+1}{2}\right)^{th} \) item; when \( n \) is even it is the average of the two middle items, the \( \left(\frac{n}{2}\right)^{th} \) and \( \left(\frac{n}{2}+1\right)^{th} \) items.

Merits.

• It is not affected by extreme values (very large or very small items), so it gives a good typical value for skewed data.
• It is easy to understand and compute, requiring only ordering of the data.
• It can be found even for open-ended classes, since only the middle position is needed.
• It can be determined graphically from an ogive (cumulative-frequency curve).

Demerits.

• It ignores the actual values of all items except the middle one, so it does not use all the data.
• It requires the data to be arranged in order first, which is tedious for large sets.
• It is not suitable for further algebraic treatment (unlike the mean).
• Where items cluster unevenly it may not truly represent the distribution, and for even \( n \) it may give a value that is not an actual item.

Examination reminder: its great strength is resistance to extreme values, which is exactly why the median is preferred to the mean for skewed data such as incomes.