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=
N
Example 9:
Calculate the standard deviation from the following data.
14, 22, 9, 15, 20, 17, 12, 11
Solution:
Deviations from actual mean.
2 Values (X)
14
22
9
15
20
17
12
11
120
120
X=
=15
8
σ= 1
7
6
0
5
2
3
4 Σ(x − x)2
n 140
8
= 17.5 = 4.18 = 158 1
49
36
0
25
4
9
16
140 Example 10:
The table below gives the marks obtained by 10 students in
statistics. Calculate standard deviation.
Student Nos : 1 2 3
4
567
8
9 10
Marks
: 43 48 65 57 31 60 37 48 78 59
Solution: (Deviations from assumed mean)
Nos.
Marks (x)
d=XA (A=57)
1
2
3
4
5
6
7
8
9
10 = ∑d − n 14
9
8
0
26
3
20
9
21
2 196
81
64
0
676
9
400
81
441
4 ∑d=44 43
48
65
57
31
60
37
48
78
59 n = 10
∑d2
σ=
n d2 ∑d2 =1952 2 1952 −44 − 10 10 2 = 195.2 − 19.36
= 175.84 = 13.26
7.6.3 Calculation of standard deviation:
Discrete Series:
There are three methods for calculating standard deviation
in discrete series:
(a) Actual mean methods
(b) Assumed mean method
(c) Stepdeviation method.
159 (a) Actual mean method:
Steps:
1. Calculate the mean of the series.
2. Find deviations for various items from the means i.e.,
x x = d.
3. Square the deviations (= d2 ) and multiply by the respective
frequencies(f) we get fd2
4. Total to product (∑fd2 ) Then apply the formula:
∑ fd 2
∑f
If the actual mean in fractions, the calculation takes lot of
time and labour; and as such this method is rarely used in practice.
(b) Assumed mean method:
Here deviation are taken not from an actual mean but from
an assumed mean. Also this method is used, if the given variable
values are not in equal intervals.
Steps:
1. Assume any one of the items in the series as an assumed
mean and denoted by A.
2. Find out the deviations from assumed mean, i.e, XA and
denote it by d.
3. Multiply these deviations by the respective frequencies and
get the ∑fd
4. Square the deviations (d2 ).
5. Multiply the squared deviations (d2) by the respective
frequencies (f) and get ∑fd2.
6. Substitute the values in the following formula:
σ= ∑ fd 2 ∑ fd σ=
− ∑f ∑f Where d = X −A , N = ∑f.
2...
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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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