The length of 40 leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table. Find the median length of the leaves.
The given series is in inclusive form. We may prepare the table in exclusive form and prepare the cumulative frequency table as given below :
Here, N = 40
$\therefore \quad \frac{\mathbf{N}}{\mathbf{2}}=20$
The cumulative frequency just greater than 20 is 29 and the corresponding class is 144.5- 153.5.
So, the median class is 144.5-153.5.
$\therefore \ell=144.5, \mathrm{~N}=40, \mathrm{C}=17, \mathrm{f}=12$ and $\mathrm{h}=9$
$\therefore \ell=144.5, \mathrm{~N}=40, \mathrm{C}=17, \mathrm{f}=12$ and $\mathrm{h}=9$
Therefore, median $=\ell+\left\{\frac{\frac{\mathbf{N}}{\mathbf{2}}-\mathbf{C}}{\mathbf{f}}\right\} \times \mathbf{h}$
$=144.5+\frac{(\mathbf{2 0}-\mathbf{1 7})}{\mathbf{1 2}} \times 9=144.5+\frac{\mathbf{3} \times \mathbf{9}}{\mathbf{1 2}}$
= 144.5 + 2.25 = 146.75
Hence, median length of leaves is 146.75 mm