MCQ
The mean of $6$ distinct observations is $6.5$ and their variance is $10.25$. If $4$ out of $6$ observations are $2,4,5$ and $7 ,$ then the remaining two observations are:
- ✓$10,11$
- B$8,13$
- C$1,20$
- D$3,18$
✓
Answer
Correct option: A.
$10,11$
a
Let other two numbers be $a$, (21-a)
Let other two numbers be $a$, (21-a)
Now,
$10.25=\frac{\left(4+16+25+49+a^{2}+(21-a)^{2}\right)}{6}$
(Using formula for variance)
$\Rightarrow 6(10.25)+6(6.5)^{2}=94+a^{2}+(21-a)^{2}$
$\Rightarrow a 2+\left(21-a^{2}\right)=221$
$\therefore a=10 \text { and }(21-a)=21-10=11$
so, remaining two observations are $10,11 .$
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