Continuous Series

In a continuous series the data is grouped into class intervals, so the median is not a single listed value but lies inside a class. First locate the median class — the class in which the $\left(\dfrac{N}{2}\right)^{\text{th}}$ item lies (note: $\dfrac{N}{2}$, not $\dfrac{N+1}{2}$, for continuous data) — then interpolate:

where $L$ = lower limit of the median class, $c.f.$ = cumulative frequency of the class preceding the median class, $f$ = frequency of the median class, and $h$ = width (magnitude) of the median class interval. No adjustment is needed if the class sizes are unequal.

Example. Daily wages of factory workers:

Here $\dfrac{N}{2} = \dfrac{160}{2} = 80$, which lies in the 35–40 class. With $L = 35$, $c.f. = 75$, $f = 30$, $h = 5$: …