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Unformatted text preview: being used in further statistical
computations or processing. 94 Besides the above requisites, a good average should
represent maximum characteristics of the data, its value should be
nearest to the most items of the given series.
Arithmetic mean or mean :
Arithmetic mean or simply the mean of a variable is defined
as the sum of the observations divided by the number of
observations. If the variable x assumes n values x1, x2 …xn then the
mean, x, is given by
x + x + x + .... + xn
x= 1 2 3
n
n
1
= ∑ xi
n i =1
This formula is for the ungrouped or raw data.
Example 1 :
Calculate the mean for 2, 4, 6, 8, 10
Solution:
2 + 4 + 6 + 8 + 10
5
30
=
=6
5 x= ShortCut method :
Under this method an assumed or an arbitrary average
(indicated by A) is used as the basis of calculation of deviations
from individual values. The formula is
∑d
x = A+
n
where, A = the assumed mean or any value in x
d = the deviation of each value from the assumed mean
Example 2 :
A student’ s marks in 5 subjects are 75, 68, 80, 92, 56. Find his
average mark.
95 Solution:
X
75
A 68
80
92
56
Total
∑d
x = A+
n
31
= 68 +
5
= 68 + 6.2
= 74.2 d=xA
7
0
12
24
12
31 Grouped Data :
The mean for grouped data is obtained from the following formula:
∑ fx
x=
N
where x = the midpoint of individual class
f = the frequency of individual class
N = the sum of the frequencies or total frequencies.
Shortcut method :
∑ fd
×c
x = A+
N
x− A
where d =
c
A = any value in x
N = total frequency
c = width of the class interval
Example 3:
Given the following frequency distribution, calculate the
arithmetic mean
Marks
: 64 63
62
61
60
59
Number of
Students :8 18 12 9
96 7 6 Solution:
X
64
63
62
61
60
59 F
8
18
12
9
7
6 fx
512
1134
744
549
420
354 60 d=xA
2
1
0
−1
−2
−3 fd
16
18
0
−9
−14
−18 3713 7 Direct method 3713
∑ fx
=
= 61.88
N
60
Shortcut method
7
∑ fd
= 62 –
x = A+
= 61.88
N
60
Example 4 :
Following is the distribution of persons according to
different income groups. Calculate arithmetic mean.
x= Income
Rs(100) Number of
per...
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This note was uploaded on 01/18/2014 for the course BUS 100 taught by Professor Moshiri during the Winter '08 term at UC Riverside.
 Winter '08
 Moshiri
 Business

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