Question

Find the mode for the following: $36$, $32$, $31$, $31$, $29$, $31$, $30$, $32$, $40$, $46$, $31$, $32$, $35$, $37$, $40$. If one observation $31$ is replaced by $32$, will the modal value change? If yes, find it

• A. $31$, Yes, $32$
• B. $33$, No
  
• C. $37$, Yes, $30$
• D. $32$, No
  

Answer 1

The correct option is A $31$, Yes, $32$

By arranging the given data in increasing order, we get,
$29,30,31,31,31,31,32,32,32,35,36,37,40,40,46$
value that occurs most frequently is $31$
$\therefore$ Mode $=31$
if one $31$ is replaced by $32$ then the arranging data is:
$29,30,32,32,32,32,32,32,32,35,36,37,40,40,46$
Now the value that occurs most frequently is $32$
so, now modal value is change. i.e $32$