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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
An investigator has missed a value while collecting data in an experiment. Denoting the missing value by $x$, the observations are: $10,4,11,6,17,15,9,8,x$. What should be the value of $x$, if he wants $\text{mean}=\text{median}=\text{mode}$ for this data set?
Solution
Given observations are:
$10,4,11,6,17,15,9,8,x$
Sum of known observations:
$10+4+11+6+17+15+9+8=80$
There are total $9$ observations.
Check option $2$, that is $x=10$.
Then data becomes:
$10,4,11,6,17,15,9,8,10$
Arranging in ascending order:
$4,6,8,9,10,10,11,15,17$
Median is the middle value.
Since there are $9$ observations, median is the $5^{\text{th}}$ value.
So,
$\text{Median}=10$
Mean is:
$\text{Mean}=\frac{80+10}{9}$
$\text{Mean}=\frac{90}{9}=10$
Also, $10$ occurs twice, so
$\text{Mode}=10$
Hence,
$\text{mean}=\text{median}=\text{mode}=10$
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