A survey regarding the height (in cm) of 51 girls of class X of a school was conducted and the following data was obtained:
Find the median height.
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.
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