017. The length of 40 leaves of a plant are measures correctly to the nearest mm. Find
the median length of the leaves.

1 thought on “017. The length of 40 leaves of a plant are measures correctly to the nearest mm. Find<br />the median length of the leaves.<br />”

1. Answer:

   Step-by-she 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.)
   

   
   

   Converting the given table into exclusive form and preparing the cumulative frequency table, we get
   

   
   

   We have, n=40
   

   ⇒

   2
   

   n
   

   ​

   =20
   

   
   

   The cumulative frequency just greater than
   

   2
   

   n
   

   ​

   is 29 and the corresponding class is 144.5−153.5.
   

   
   

   Thus, 144.5−153.5 is the median class such that
   

   2
   

   n
   

   ​

   =20,l=144.5,cf=17,f=12, and h=9
   

   
   

   Substituting these values in the formula
   

   Median, M=l+

   ⎝
   

   ⎛
   

   ​

   
   

   f
   

   2
   

   n
   

   ​

   −cf
   

   ​

   
   

   ⎠
   

   ⎞
   

   ​

   ×h
   

   
   

   M=144.5+(

   12
   

   20−17
   

   ​

   )×9
   

   
   

   M=144.5+

   12
   

   3
   

   ​

   ×3=144.5+2.25=146.75
   

   Hence, median length =146.75 hourstep explanation:

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