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Q.

A student obtained 60, 75 and 85 marks respectively in three monthly examinations in Mathematics and 95 marks in the final examination. The three monthly examinations are of equal weightage whereas the final examination is weighted twice as much as a monthly examination. The mean marks of Mathematics are

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a

80

b

81

c

82

d

85

answer is C.

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Detailed Solution

We have,

$x_{1} = 60, x_{2} = 75, x_{3} = 85, x_{4} = 95, w_{1} = 1, w_{2} = 1, w_{3} = 1,$ and $w_{4} = 2$

$\begin{array}{l} ∴ \bar{X_{w}} = \frac{w_{1} x_{1} + w_{2} x_{2} + w_{3} x_{3} + w_{4} x_{4}}{w_{1} + w_{2} + w_{3} + w_{4}} \\ \Rightarrow \bar{X_{w}} = \frac{1 \times 60 + 1 \times 75 + 1 \times 85 + 2 \times 95}{1 + 1 + 1 + 2} = \frac{410}{5} = 82 \end{array}$

Hence, mean marks in Mathematics $= 82 .$

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