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BITSAT 2022

Exam: BITSAT
Year: 2022
Subject: Mathematics
Chapter: Statistics

BITSAT 2022 · Mathematics · Statistics

The mean of five observations is 4 and their variance is 5.2 . If...

The mean of five observations is

4

and their variance is

5.2

. If three of these observations are

1

,

2

and

6

, then the other two are

Options

A $2$ and $9$
B $3$ and $8$
C $4$ and $7$
D $5$ and $6$

Correct answer

C. $4$ and $7$

Step-by-step solution

Let the two unknown items be

x

and

y

. Then,

\operatorname{Mean}=4 \Rightarrow \frac{1+2+6+x+y}{5}=4\Rightarrow \quad x+y=11\dots(i)

and variance

=5.2\Rightarrow \frac{1^2+2^2+6^2+x^2+y^2}{5}-(\text{ mean })^2=5.2\Rightarrow \quad 41+x^2+y^2=5(5.2+16)

\begin{array}{ll}\Rightarrow & 41+x^2+y^2=106 \\ \Rightarrow & x^2+y^2=65\end{array}

On solving Eqs. (i) and (ii), we get

x=4, y=7

\text{ or }

x=7, y=4

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