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Unformatted text preview: after giving proper weight to each
group.
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…n be the values of a variable x with respective
x
weights of w1, w2… n assigned to them, then
w
w x + w2 x2 + .... + wn xn
∑ wi xi
Weighted A.M = x w = 1 1
=
w1 + w2 + .... + wn
∑ wi
Uses of the weighted mean:
Weighted arithmetic mean is used in:
a. Construction of index numbers.
b. Comparison of results of two or more universities where
number of students differ.
c. Computation of standardized death and birth rates.
Example 5:
Calculate weighted average from the following data
Designation
Class 1 officers
Class 2 officers
Subordinate staff
Clerical staff
Lower staff Monthly salary
(in Rs)
1500
800
500
250
100
99 Strength of
the cadre
10
20
70
100
150 Solution:
Designation Monthly
salary,x
1,500
800
500 15,000
16,000
35,000 250
100 Class 1 officer
Class 2 officer
Subordinate
staff
Clerical staff
Lower staff Strength of
the cadre,w
10
20
70 wx 100
150
350 25,000
15,000
1,06,000 ∑ wx
∑w
106000
=
350
= Rs. 302.86 Weighted average, x w = Harmonic mean (H.M) :
Harmonic mean of a set of observations is defined as
the reciprocal of the arithmetic average of the reciprocal of the
given values. If x1,x2… n are n observations,
..x
n
n
1
∑ x i =1 i For a frequency distribution
H.M = HM. =
. N
1
∑1 f x i= i
n Example 6:
From the given data calculate H.M 5,10,17,24,30
100 X 1
x
0.2000
0.1000
0.0588
0.0417
0.0333
0.4338 5
10
17
24
30
Total
H.M = = n
1
∑ x 5
0.4338 = 11.526 Example 7:
The marks secured by some students of a class are given
below. Calculate the harmonic mean.
Marks
20
21
22 23
24
25
Number of
4
2
7
1
3
1
Students
Solution:
Marks
X
20
21
22
23
24
25 No of
students
f
4
2
7
1
3
1
18 1
x
0.0500
0.0476
0.0454
0.0435
0.0417
0.0400 101 ƒ( 1
)
x 0.2000
0.0952
0.3178
0.0435
0.1251
0.0400
0.8216 N
1
∑f x
18
=
= 21.91
0.1968
Merits of H.M :
1. It is rigi...
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 Winter '08
 Moshiri
 Business

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