Height 160-162 163-165 166-168 169-171 172-174

frequency 15 117 x 118 14if the median of distribution is 167 . find the value of 'x'

Answer : 

We have  
 
Height 160 - 162 163 - 165 166 - 168 169 - 171  172 - 174  
Frequency 15 117 x  118 14 Total  = 264 + x

Let Median lies between 169 - 171  

And we know the formula for estimate median  = L + n2 - cfbfm × w
And
L is the lower class boundary of the group containing the median.  So here  = 169 
n is the total number of data  ( Here 264  + x ) 
cfb is the cumulative frequency of the groups before the median group ( Here 117 + 15 + x =  132 + x )
fm is the frequency of the median group  .     ( here 118 )
w is the group width. ( here 2 )

So,

167  = 169  + 264 +x2 - ( 132 + x )118 × 2 

167 = 169 + 132 + x2 - 132 - x118 × 2 

167 = 169  - x118

167 = 19942 - x118

19942 - x  = 19706 

x  = 19942 - 19706 

x  =  236                                                      (  Ans )

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