Question

A student obtained the following marks percentage in an examination English – 50, Accounts – 75, 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. $\dfrac{{(50 \times 2) + (75 \times 3) + (60 \times 3) + (80 \times 2) + (55 \times 1)}}{5}$
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: According to the question given in the question we have to determine the mean when a student obtained the following marks percentage in an examination English – 50, Accounts – 75, B.Std – 80, Hindi – 55. If weights are $2,3,3,2,1$ respectively allotted to the subjects, his weight. So, first of all we have to understand about the mean which is as explained below:
Mean: The mean or we can say that the average of a data set which can be found by adding all the given numbers in the data set and then dividing by the number of the values in the set.
Now, we have to determine the table for the given data so that we can easily determine the mean for the given data.
Now, we have to multiply the weight with the marks obtained in the examination for the different subjects.
Now, to find the mean we just have to divide the obtained sum with the total number of terms.

Complete step-by-step solution:
Step 1: First of all we have to determine the table for marks obtained in the different subjects as English – 50, Accounts – 75, B.Std – 80, Hindi – 55 and their weights are $2,3,3,2,1$ respectively allotted to the subjects weighted. Hence,

Marks obtained (f)	Weight (x)
50	2
75	3
60	3
80	2
55	1

Step 2: Now, as from the table as obtained in the solution step 1 we have to determine $\sum {fx} $ and $\sum f $ which is as below:

Marks obtained (f)	Weight (x)	(fx)
50	2	$(50 \times 2)$
75	3	$(75 \times 3)$
60	3	$(60 \times 3)$
80	2	$(80 \times 2)$
55	1	$(55 \times 1)$

Hence,
$ \Rightarrow \sum {fx = (50 \times 2) + (75 \times 3) + (60 \times 3) + (80 \times 2) + (55 \times 1)} $
and,
$ \Rightarrow \sum f = 2 + 3 + 3 + 2 + 1$
Step 3: Now, to find the mean we just have to divide the obtained sum with the total number of terms as mentioned in the solution hint.
$ \Rightarrow $Mean$ = \dfrac{{\sum {fx} }}{{\sum f }}$
On substituting all the values in the expression just above,
\[ \Rightarrow \dfrac{{(50 \times 2) + (75 \times 3) + (60 \times 3) + (80 \times 2) + (55 \times 1)}}{{2 + 3 + 3 + 2 + 1}}\]
Hence, we have obtained the mean,
\[ \Rightarrow \dfrac{{(50 \times 2) + (75 \times 3) + (60 \times 3) + (80 \times 2) + (55 \times 1)}}{{2 + 3 + 3 + 2 + 1}}\] for the given data set.

Therefore option (C) is correct.

Note: Mean is basically the same as the average for the given data set in which first of all we have to determine the sum of all the given numbers or data and then we have to divide the sum by the total number of data sets.