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

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

 3.4

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, 126.5 - 135.5, . . ., 171.5 - 180.5.)

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The data needs to be converted to continuous classes for finding the median, since the formula assumes continuous classes.

Class

Frequency

 f_i

Cumulative

Frequency

117.5-126.5 3 3
126.5-135.5 5 8
135.5-144.5 9 17
144.5-153.5 12 29
153.5-162.5 5 34
162.5-171.5 4 38
171.5-180.5 2 40


\dpi{100} N= 40 \implies \frac{N}{2} = 20
Therefore, Median class = 144.5-153.5

Lower limit, l = 144.5; Class height, h = 9
Frequency corresponding to median class, f = 12
Cumulative frequency of the class preceding the median class, c.f. = 17

Median = l + \left (\frac{\frac{n}{2}-c.f}{f} \right ).W
\\ = 144.5 + \left (\frac{20-17}{12} \right ).9 \\ \\

= 146.75

Thus, median length of the leaves is 146.75 mm

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