📏 Median

Step 1 is always sorting — many exam traps hand you unsorted data hoping you grab the middle of the raw list.

• Odd count: the median is the single value at position $\dfrac{n+1}{2}$. For $n=9$, that is the 5th value.

• Even count: there is no single middle, so average the two central values, at positions $\tfrac n2$ and $\tfrac n2+1$. For $n=6$, that is $\dfrac{3\text{rd}+4\text{th}}{2}$.

• Find a hidden value: if the median is given, drop the unknown into the middle position and read it off (odd $n$), or solve the small average equation (even $n$).

• Grouped data (class intervals): you cannot see single values, so interpolate inside the class holding the middle:

$\text{Median}=l+\dfrac{\frac n2-cf}{f}\times h$

where $l$ = lower limit of the median class, $cf$ = cumulative frequency before it, $f$ = its frequency, $h$ = class width. The median class is the first whose cumulative frequency reaches $\tfrac n2$.