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The lengths of 40 leaves of a plant are n measured correct to the 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 |
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 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, 144.5 – 153.5 is the median class.
Therefore,
$l = 144.5, f = 12, F = 17$ and $h = (153.5 - 144.5) = 9$
Medain $=\mathrm{l}+\frac{\frac{\mathrm{N}}{2}-\mathrm{F}}{\mathrm{f}} \times \mathrm{h}$
$=144.5+\frac{20-17}{12} \times 9$
$=144.5+\frac{3}{4} \times 3$
$=144.5+\frac{9}{4}$
$= 144.5 + 2.25$
$= 146.75$
The mean length of the leaf is 146.75 mm.