If the median of the following data is 19, find the value of p

Solution:

Preparing the cumulative frequency table to calculate median from the given data, we get

Here, median (Md) = 19 lies in (18 - 24)^th class

∴ Median class = 18 - 24

Median (Md) = \(L+\frac{{\displaystyle\frac N2}-cf}f\times i\)

Where, 

L = 18, \(\frac N2=\frac{24+p}2\), cf = 14, f = p, i = 6

∴ \(19=18+\frac{\left({\displaystyle\frac{24+p}2}-14\right)}p\times6\)
Or, \(19-18=\left(\frac{24+p-28}2\times\frac1p\right)\times6\)
Or, \(1=\frac{3\left(p-4\right)}4\)
Or, p = 3p - 12
Or, 2p = 12
Or, p = 6

Hence the required value of p is 6