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Statistics Part 1

Section: Mathematics

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Question : 37 of 100

Marks: +1, -0

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 observationsare:

[20 Jul 2021 Shift 1]

10,11
3,18
8,13
1,20

Solution:

Let other two numbers be a, (21-a)

Now,

10.25

= \frac{4+16+25+49+a^{2}+(21-a)^{2}}{6}

-(6.5)^{2}

(Using formula for variance)

\Rightarrow 6(10.25)+6(6.5)^{2}=94+a^{2}+(21-a)^{2}

\Rightarrow a^{2}+(21-a)^{2}=221

\therefore a=10

and

(21-a)=21-10=11

So, remaining two observations are 10,11 .

\Rightarrow

Option (1) is correct.

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