Weighted arithmetic mean

2. Weighted Arithmetic Mean:
The mean of values when each value is weighted according to its
relative importance is called weighted mean or if x1, x2, …, xn here
weights w1, w2, …, wn, then the weighted mean is defined as:
Example-1:
The marks obtained by a student in Accounting, Statistics and
Economics were 82, 76 and 70 respectively. Find the weighted mean if
weight of 6, 5 and 4 are assigned to these marks.
Solution:
Let x denote the marks:
x w w x
82
76
70
6
5
4
492
380
280
Sum 15 1152
Marks

=
w
xw
xw

=
w
xw
xw
15
1152
=
8.76xw =

3. Example-2.
Areeba achieved 45% for her coursework and 62% in the written
exam paper. Using the weights 0.25 for coursework and 0.75 for the
written paper, find her overall mark
X %
Marks
W WX
45 0.25 11.25
62 0.75 46.5
1 57.75
%75.57
1
75.57
==


=
w
wx
Xw
Do yourself
1. An examination candidate’s percentages are: English 73, Urdu 82;
Mathematics 75; Science 62; History 60. Find the candidate’s
weighted mean if weights of 4, 3, 3, 1,1 respectively are allotted to
the subjects. (Answer = 73.75%)
2. In a company having 80 employees, 60 earn Rs.3 per hour and 20
earn Rs.2 per hour determine the mean earning per hour.
(Answer = 2.75 per hour)
3. What is the average for a student who received grades of 85, 76
and 82on 3 tests and a 79 on the final examination in a certain
course if the final examination counts three times as much as each
of the tests? (Answer = 80 )

4. 4. On a vacation trip a family bought 21.3 liters of gasoline at 39.9
cents per liter, 18.7 liters at 42.9 cents per liter, and 23.5 liters at
40.9 cents per liter. Find the mean price paid per liter.
(Answer = 41.15)
5. A savings and loan association makes one car loan of $5000 at
10.5% interest, a second car loan of $4500 at 11% interest & a
third car loan $6300 at 10.8% interest. What is the average
percentage return to the savings and loan associations for these 3
loans? (Answer = 10.76%)
6. A Professor has decided to use a weighted average in figuring final
grades for his seminar students. The homework average will count
for 20% of a student’s grade; the midterm 25%, the final 35%; the
term paper, 10% and quizzes, 10% from the following data,
compute the final average for the five students in the seminar.
Student Homework Quizzes Paper Midterm Final
Term
1 85 89 94 87 90
2 78 84 88 91 92
3 94 88 93 86 89
4 82 79 88 84 93
5 95 90 92 82 88
(Answers = 88.55, 87.75, 89.55, 86.65, 88.50).