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Unformatted text preview: Example 11:
Calculate Standard deviation from the following data.
X:
20
22
25
31
35
40
42
f:
5
12
15
20
25
14
10
160 45
6 Solution:
Deviations from assumed mean
x
f
d = x –A
(A = 31)
11
5
20
9
12
22
6
15
25
0
20
31
4
25
35
9
14
40
11
10
42
14
6
45
N=107
σ= ∑ fd 2 ∑ fd − ∑f ∑f d2 fd fd2 121
81
36
0
16
81
121
196 55
108
90
0
100
126
110
84
∑fd=167 605
972
540
0
400
1134
1210
1176
∑fd2
=6037 2 2 =
=
= 6037 167 − 107 107 56.42 − 2.44
53.98 = 7.35 (c) Stepdeviation method:
If the variable values are in equal intervals, then we adopt
this method.
Steps:
1. Assume the center value of the series as assumed mean A
x−A
2. Find out d =
, where C is the interval between each
C
value
3. Multiply these deviations d’ by the respective frequencies
and get ∑fd
4. Square the deviations and get d 2
5. Multiply the squared deviation (d 2 ) by the respective
frequencies (f) and obtain the total ∑fd 2
161 6. Substitute the values in the following formula to get the
standard deviation. Example 12:
Compute Standard deviation from the following data
Marks
:
10
20
30
40
50
No.of students:
8
12
20
10
7
Solution:
Marks x
F
fd
x − 30
d=
10
16
2
8
10
12
1
12
20
0
0
20
30
10
1
10
40
14
2
7
50
9
3
3
60
N=60
Σ fd =5 60
3
fd 2 32
12
0
10
28
27
Σ fd 2
= 109 2 = 109 5  × 10
60 60 = 1.817  0.0069 × 10
= 1.8101 × 10
= 1.345 × 10
= 13.45
7.6.4 Calculation of Standard Deviation –Continuous series:
In the continuous series the method of calculating standard
deviation is almost the same as in a discrete series. But in a
continuous series, midvalues of the class intervals are to be found
out. The step deviation method is widely used.
162 The formula is, d= m−A
, C Class interval.
C Steps:
1.Find out the midvalue of each class.
2.Assume the center value as an assumed mean and denote
it by A
m−A
3.Find out d =
C
4.Multiply the deviations d by the respective frequencies and
get Σfd
5.Square the deviations and get d 2
6.Multiply the squared deviations (d 2) by the respec...
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 Winter '08
 Moshiri
 Business

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