Question

A survey regarding the height (in cm) of 51 girls of class X of a school was conducted and the following data was obtained:
Height in cm
Less than 140
Less than 145
Less than 150
Less than 155
Less than 160
Less than 165
Number of Girls
4
11
29
40
46
51
Find the median height.

Answer 1

SOLUTION :  

CUMULATIVE FREQUENCY TABLE is  in the attachment.  

Here, n = 51

n/2 = 25.5

Since, the Cumulative frequency just greater than 25.5 is 29 and the corresponding class is 145 - 150.  Therefore 145 - 150  is the median class.

Here, l = 145 , f =18 , c.f = 11,  h = 5

MEDIAN = l + [(n/2 - cf )/f ] ×h

= 145 + [25.5 - 11)/18] × 5

= 145 + (14.5 × 5)/18

= 145 + 72.5/18

= 145 + 4.03

= 149.03

Hence, the Median height is 149.03 cm.

★★ 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

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Answer 2

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