Test Index

Statistics Part 1

Section: Mathematics

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Question : 22 of 100

Marks: +1, -0

The mean and standard deviation of 50 observations are 15 and 2 respectively. It was found that one incorrect observation was taken such that the sum of correct and incorrect observations is 70 . If the correct mean is 16 , then the correct variance is equal to :

[26-Jun-2022-Shift-2]

10
36
43
60

Solution: 👈: Video Solution

Given

\overline{x}=15, \sigma=2 \Rightarrow \sigma^2=4

\therefore x_2+x_2+\dots+x_{50}=15 \times 50=750

4=\frac{x_1^2+x_2^2+\dots+x_{50}^2}{50}-225

\therefore x_1^2+x_2^2+\dots+x_{50}^2=50 \times 229

Let a be the correct observation and

b

is the incorrect observation

then

a+b=70

and

16=\frac{750-b+a}{50}

\therefore a-b=50 \Rightarrow a=60, b=10

\therefore

Correct variance

=\frac{50 \times 229+60^2-10^2}{50}-256=43

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