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Relations and Functions Ncert Solutions Maths class 12th Maths Class 12th

The mean and standard 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:

Option 1 -

Option 2 -

Option 3 -

Option 4 -

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Vishal Baghel | Contributor-Level 10

2 months ago

Correct Option - 3

Detailed Solution:

$\bar{x} = 15, σ = 2 \Rightarrow σ^{2} = 4$

$∴ x_{1} + x_{2} + . . . . + x_{50} = 15 \times 50 = 750$

$4 = \frac{x_{1}^{2} + x_{2}^{2} + . . . . . + x_{50}^{2}}{50} - 225$

Let a be the correct observation and b is the incorrect observation then a + b = 70 and

$16 = \frac{75 - b + a}{50}$

$= \frac{50 \times 229 + 6 0^{2} - 1 0^{2}}{50} - 256 = 43$

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The mean and standard 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:

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