JEE Main · 2021 · 27 Aug 2021 · Shift 2 · Statistics

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An online exam is attempted by 50 candidates out of which 20 are boys. The average marks obtained by boys is 12 with a variance 2. The variance of marks obtained by 30 girls is also 2. The average marks of all 50 candidates is 15. If

μ

is the average marks of girls and

σ^{2}

is the variance of marks of 50 candidates, then

μ + σ^{2}

is equal to

Answer: 25

Solution

The overall mean gives

15 = \frac{20 ( 12 ) + 30 μ}{50}

, so

750 = 240 + 30 μ

and

μ = 17

. With deviations

d_{b} = 12 - 15 = - 3

and

d_{g} = 17 - 15 = 2

, the combined variance is

σ^{2} = \frac{20 ( 2 + 9 ) + 30 ( 2 + 4 )}{50} = \frac{220 + 180}{50} = 8.

Hence

μ + σ^{2} = 17 + 8 = 25

JEE Main · 2021 · 27 Aug 2021 · Shift 2 · Integer answer

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