(Q6) 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:

Length(in mm)	118-126	127-135	136-144	144-153	154-162	163-171	172-180
Number 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, 126.5-135.5,..., 171.5-180.5.)

Answer :

Since the formula, Median = l +

(

n

2

- cf )

f

× h assumes continuous classes, the data needs to be converted to continuous classes.

The classes then changes to 117.5-126.5; 126.5-133.5,.... 171.5-180.5.

Length (in mm) (C.I.)	Number of leaves [Frequency (f)]	c.f.
117.5-126.5	3	3
126.5-135.5	5	8
135.5-144.5	9	17 c.f
144.5-153.5	12 (f)	29
153.5-162.5	5	34
162.5-171.5	4	38
171.5-180.5	2	40

∑f = n =

∴ Median class = 144.5-153.5

Lower boundary, l =

Frequency of the median class, f = 12 , c.f. = 17, h = 9

∴ Median Length = mm