QJEEM20Mafa4d: JEE Main 2020 Mathematics - Class 11 JEEM20Mafa4d Solution: The mean and variance of 20 observations are found to be 10 and …

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QJEEM20Mafa4d: JEE Main 2020 Mathematics - Class 11 JEEM20Mafa4d Solution: The mean and variance of 20 observations are found to be 10 and …

The mean and variance of 20 observations are found to be 10 and 4, respectively. On rechecking, it was found that an observation 9 was incorrect and the correct observation was 11. Then the correct variance is

Multiple Choice Options

A 3.98
B 3.99
C 4.01
D 4.02

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Accepted Answer

Let 20 observation be x₁ , x₂ ,....., x₂₀

Mean =

x₁ + x₂ +, .....+ x₂₀

20

= 10

\Rightarrow

x₁ + x₂ +, .....+ x₂₀ = 200

Variance =

\frac{\sum_{i = 1}^{i = n} x_{i}^{2}}{n} - {(\overset{―}{x})}^{2}

\Rightarrow

4 =

\frac{x_{1}^{2} + x_{2}^{2} + . . . + x_{20}^{2}}{20}

- 10²

\Rightarrow

x_{1}^{2} + x_{2}^{2} + . . . + x_{20}^{2}

= 2080

Also x₁ + x₂ +, .....+ x₂₀ - 9 + 11 = 202

new variance will be

=

\frac{x_{1}^{2} + x_{2}^{2} + . . . + x_{20}^{2} - 81 + 121}{20}

-

{(\frac{202}{20})}^{2}

= 3.99

QJEEM20Mafa4d: JEE Main 2020 Mathematics - Class 11 JEEM20Mafa4d Solution: The mean and variance of 20 observations are found to be 10 and …

Multiple Choice Options

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