Business Statistics - II B.Com.

1. z
WEIGHTED
ARITHMETIC
MEAN
Dr. RMKV
ASST. PROF.

2. z
WEIGHTED ARITHMETIC MEAN
 For calculating simple mean, we suppose that all the values or the sizes of
items in the distribution have equal importance. But, in practical life this may
not be so. In case some items are more important than others, a simple
average computed is not representative of the distribution. Proper weightage
has to be given to the various items.
 For example, to have an idea of the change in cost of living of a certain group
of persons, the simple average of the prices of the commodities consumed by
them will not do because all the commodities are not equally important, e.g.
rice, wheat and pulses are more important than tea, confectionery etc., It is
the weighted arithmetic average which helps in finding out the average value
of the series after giving proper weight to each group.

3. z
Definition:
 The average whose component items are being multiplied by
certain values known as “weights” and the aggregate of the
multiplied results are being divided by the total sum of their
“weight”. If x1, x2…xn be the values of a variable x with
respective weights of w1, w2… wn assigned to them, then
 Xw =
𝚺𝐖𝑿
𝜮𝑾

4. z
ILLUSTRATION
 Ganesh is a rice merchant who sells FOUR types of rice in
Madurai. He wants you to calculate the average sale from
the following data:
Type of Rice Units Sold in KG Unit Price
A 100 60
B 60 50
C 50 40
D 10 30

5. z
Solution
X W XW
100 60 6000
60 50 3000
50 40 2000
10 30 300
𝑊
180 𝑊𝑋 = 11300
 Let us take unit sold as X
and Unit price as W
 Xw =
𝚺𝐖𝑿
𝜮𝑾
 =
11300
180
= 62.778
 AVERAGE SALES = 63 KG

6. z
Illustration
 Comment the performance of the students of three universities given below using
Simple and Weighted Average
University Mumbai Kolkata Chennai
Course of
study
% of pass No. of
Students
(‘00)
% of pass No. of
Students
(‘00)
% of pass No. of
Students
(‘00)
M.A. 71 3 82 2 81 2
M.Com. 83 4 76 3 76 3.5
B.A. 73 5 73 6 74 4.5
B.Com. 74 2 76 7 58 2
B.Sc. 65 3 65 3 70 7
M.Sc. 66 3 60 7 73 2

7. z
Solution
univers
ity
Mumbai Kolkata Chennai
course
s
x w wx x w wx x w wx
M.A. 71 3 213 82 2 164 81 2 162
M.Com
.
83 4 332 76 3 228 76 3.5 266
B.A. 73 5 365 73 6 438 74 4.5 333
B.Com. 74 2 148 76 7 532 58 2 116
B.Sc. 65 3 195 65 3 195 70 7 490
M.Sc. 66 3 198 60 7 420 73 2 146
𝑥
432
𝑤
20
𝑤𝑥
1451
𝑥
432
𝑤
28
𝑤𝑥
1977
𝑥
432
𝑤
21
𝑤𝑥
1513

8. z
 𝑥 is the same for all the three universities
 X =
𝑥
𝑁
=
432
6
= 72
 But the number of students(weight) is different. Therefore, we have to calculate
the weighted Arithmetic Mean
 Mumbai: Xw =
𝚺𝐖𝑿
𝜮𝑾
=
1451
20
= 72.55
 Kolkata: Xw =
𝚺𝐖𝑿
𝜮𝑾
=
1977
28
= 70.61
 Chennai: Xw =
𝚺𝐖𝑿
𝜮𝑾
=
1513
21
= 72.05
 Mumbai university is the best university, because the weighted arithmetic mean
is greater than the other two universities