Question

The length of 40 leaves of a plant are measured correct to the nearest millimeter, 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 leaf.

Answer 1

SOLUTION :  

★★Here, the data is not in continuous form( exclusive) so we convert it into continuous form (inclusive).  For this subtract 0.5 from lower limit of each class interval and add 0.5 to upper limit of each class interval.

CUMULATIVE FREQUENCY TABLE is  in the attachment.  

Here, n = 40  

n/2 = 20

Since, the Cumulative frequency just greater than 20 is 29 and the corresponding class is 144.5 - 153.5.  Therefore 144.5 - 153.5  is the median class.

Here, l = 144.5  , f = 12, c.f = 17,  h = 7

MEDIAN = l + [(n/2 - cf )/f ] ×h

= 144.5  + [20 - 17)/12] × 9

= 144.5 + (3 × 9)/12

= 144.5 + 27/12

= 144.5 + 9/4

= 144.5 + 2.25

= 146.75

Hence, the Median length of leaf is 146.75 mm.  

★★ MEDIAN = l + [(n/2 - cf )/f ] ×h

Where,

l = lower limit of the median class

n = number of observations  

cf = cumulative frequency  of class interval preceding the  median class

f = frequency  of median class

h = class  size

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

$<big> <b> Answer :$

Refer the attachment for the answer.

Thus,

Median length of the leaves is 146.5 mm.

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