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# The lengths of 40 leaves of a plant are measured correct to nearest millimetre, and the data obtained is represented in the following table:

Length (in mm): | 118-126 | 127-135 | 136-144 | 145-153 | 154-162 | 163-171 | 172-180 |

No. of leaves: | 3 | 5 | 9 | 12 | 5 | 4 | 2 |

Find the median length of the leaves.

(Hint: The data needs to be converted to continuous classes for finding the median since the formula assumes continuous classes. The classes then change to 117.5 – 126.5

Given:

The lengths of 40 leaves of a plant are n measured correct to the nearest millimetre.

To do:

We have to find the mean length of the leaf.

Solution:

Arranging the classes in exclusive form and then forming its cumulative frequency table as below, we get,

Here,

$N = 40$

$\frac{N}{2} = \frac{40}{2} = 20$

The cumulative frequency just greater than $\frac{N}{2}$ is 29 and the corresponding class is 144.5 – 153.5.

This implies, that 144.5 – 153.5 is the median class.

Therefore,

$l = 144.5, f = 12, F = 17$ and $h = (153.5 - 144.5) = 9$

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

$=144.5+\frac{20-17}{12} \times 9$

$=144.5+\frac{3}{4} \times 3$

$=144.5+\frac{9}{4}$

$= 144.5 + 2.25$

$= 146.75$

The mean length of the leaf is 146.75 mm.

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