Question

A student obtained the following marks percentage in an examination English-50, Accounts-75, Economics-60, B. Std. -80, Hindi-55. If weights are 2,3,3,2,1 respectively allotted to the subjects, his weighted mean is
A. $\dfrac{{50 + 75 + 60 + 80 + 55}}{{2 + 3 + 3 + 2 + 1}}$
B. $\dfrac{{\left( {50 \times 2} \right) + \left( {75 \times 3} \right) + \left( {60 \times 3} \right) + \left( {80 \times 2} \right) + \left( {55 \times 1} \right)}}{5}$
C. \[\dfrac{{50 \times 2 + 75 \times 3 + 60 \times 3 + 80 \times 2 + 55 \times 1}}{{2 + 3 + 3 + 2 + 1}}\]
D. None

Answer 1

Hint: We will calculate the sum of all the percentages and the sum of all their weights. Then, we will calculate the weighted mean by using the formula, $M = \dfrac{{\sum {wx} }}{{\sum w }}$.

Complete step-by-step answer:
We are given the percentage of different subjects.
Let the weighted mean be $M$, where $M = \dfrac{{\sum {wx} }}{{\sum w }}$

Subject	$x$	$w$	\[wx\]
English	50	2	$50 \times 2$
Accounts	75	3	$75 \times 3$
Economics	60	3	$60 \times 3$
B. Std.	80	2	$80 \times 2$
Hindi	55	1	$55 \times 1$

Then, \[\sum {wx} \] is equal to \[50 \times 2 + 75 \times 3 + 60 \times 3 + 80 \times 2 + 55 \times 1\]
And $\sum w $ is equal to \[2 + 3 + 3 + 2 + 1\]
On substituting the value of \[\sum {wx} \] and $\sum w $, we get the weighted mean as,
$M = \dfrac{{50 \times 2 + 75 \times 3 + 60 \times 3 + 80 \times 2 + 55 \times 1}}{{2 + 3 + 3 + 2 + 1}}$
Hence, option C is correct.
Note: Here, do not calculate or solve the value of $M$ completely as the given options are of the same kind. Weighted mean is the mean where some values contribute more than the other values. To find the weighted mean, we multiply each value by its weight and take the sum of all such values and then divide it by the sum of weights.