Question

Calculate the median from the following data:

$\begin{array}{ccccccccc}\text{Height (in cm)}& 135-140& 140-145& 145-150& 150-155& 155-160& 160-165& 165-170& 170-175\\ \text{Number of days}& 6& 10& 18& 22& 20& 15& 6& 3\end{array}$

Answer 1

Lets form a frequency distribution table to find the median,

$\begin{array}{ccc}\text{Class}& \text{Frequency}& \text{Cumulative frequency}\\ 135-140& 6& 6\\ 140-145& 10& 16\\ 145-150& 18& 34\left(cf\right)\\ \left(L\right)150-155& 22\left(L\right)& 56\\ 155-160& 20& 76\\ 160-165& 15& 91\\ 165-170& 6& 97\\ 170-175& 3& 100\\ & N=\sum f=100& \end{array}$

From the table,

$N=\sum f=100$

$\Rightarrow \frac{N}{2}=50$

The cumulative frequency just greater than $50$ is $56$ and the corresponding class is $150-155$

Thus, the median class is $150-155$.

Now, $L=150$

Size of the class interval $h=5$

$F=22$

$cf=34$ (cumulative frequency of preceding class)

Median $=L+\left(\frac{\frac{N}{2}-c.f}{F}\right)\times h$

$=150+\left(\frac{50-34}{22}\right)\times 5$

$=150+\frac{16}{22}\times 5$

$=150+\frac{80}{22}$

$=150+3.64$ (Approximately)

$=153.64$ (Approximately)

Therefore, Median $=153.64$ (Approximately)