Chapter 13 · Question 5

State the formula for median of grouped data.

Answer

Median

=l+\frac{\frac n2-cf}{f}\times h

, where

l

is lower limit of median class,

n

total frequency,

cf

cumulative frequency before median class,

f

median class frequency, and

h

class size.

Find the class whose cumulative frequency first exceeds

n/2

, then apply the formula.

First compute cumulative frequencies and total frequency

n

. The median class is the class whose cumulative frequency is just greater than

\frac n2

. Then use

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

.

Median $=l+\frac{\frac n2-cf}{f}\times h$ , where $l$ is lower limit of median class, $n$ total frequency, $cf$ cumulative frequency before median class, $f$ median class frequency, and $h$ class size.