A survey regarding the height (in cm) of 51 girls

We prepare the cumulative frequency, table as given below.

Now, we have

$N=51$

So, $\frac{N}{2}=25.5$

Now, the cumulative frequency just greater than $25.5$ is 40 and the corresponding class is $150-155$.

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

$l=150, f=11, F=29$ and $h=5$

We know that

Median $=l+\left\{\frac{\frac{N}{2}-F}{f}\right\} \times h$

$=150+\left\{\frac{25.5-29}{11}\right\} \times 5$

$=150-\frac{3.5 \times 5}{11}$

$=150-\frac{17.5}{11}$

$=150-1.59$

$=148.41$

Hence, the median height is 148.41 cm.