Question

Find the median of the following:
$38$, $46$, $64$, $87$, $41$, $58$, $77$, $35$, $90$, $25$, $92$, $33$, $91$. If $58$ is replaced by $97$ and $35$ by $23$, find the new median

• A. $57$, $66$
• B. $58$, $64$
• C. Data insufficient
  
• D. None of these
  

Answer 1

Answer: (B)

$58$, $64$

By arranging the given data in increasing order, we get:
$25,33,35,38,41,46,58,64,77,87,90,91,92$
Total terms = 13
since, the middle most term is $7^{th}$.
$\therefore$ value of median is 58
If 58 is replaced by 97 and 35 by 23 then given data becomes:
$38,46,64,87,41,97,77,23,90,25,92,33,91$
By arranging this new data in increasing order, we get:
$23,25,33,38,41,46,64,77,87,90,91,92,97$
since, the middle most term is $7^{th}$.= 64
$\therefore$ new median is 64