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frequencies and get ∑fd 2
7.Substituting the values in the following formula to get the
standard deviation Example 13:
The daily temperature recorded in a city in Russia in a year
is given below.
Temperature C 0
No. of days
10
40 to –30
18
30 to –20
30
20 to –10
42
10 to
0
65
0 to 10
180
10 to 20
20
20 to 30
365
Calculate Standard Deviation.
163 Solution:
Temperature
40 to 30
30 to 20
20 to 10
10 to  0
0 to 10
10 to 20
20 to 30 Mid
value
(m)
35
25
15
5
5
15
25 No. of
days
f
10
18
30
42
65
180
20 d=
m− (−5n )
10n
3
2
1
0
1
2
3 N=365 fd
30
36
30
0
65
360
60 fd 2 90
72
30
0
65
720
180 ∑fd = ∑fd 2
389
=1157 2 1157
389 − × 10
365 365 = 3.1699  1.1358 × 10
= 2.0341 × 10
= 1.4262 × 10
= 14.26°c
= 7.6.5 Combined Standard Deviation:
If a series of N1 items has mean X1 and standard deviation σ1 and another series of N2 items has mean X 2 and standard
deviation σ2 , we can find out the combined mean and combined
standard deviation by using the formula. 164 Where d1 = X1 − X12
d2 = X2 − X12
Example 14:
Particulars regarding income of two villages are given
below.
Village
A
B
No.of people
600
500
Average income
175
186
Standard deviation of
10
9
income
Compute combined mean and combined Standard deviation.
Solution:
Given N1 = 600, X1 = 175, σ1 = 10
N2 = 500, X2= 186, σ2 = 9
Combined mean
= 600 × 175 + 500 × 186
600 + 500 105000 + 93000
1100
198000
=
= 180
1100
Combined Standard Deviation:
= 165 d1 = X1 − X12
= 175 − 180
= −5
d2 = X2 − X12
=186 – 180
=6
600 × 100 + 500 × 81 + 600 × 25 + 500 × 36
σ12 =
600 + 500
60000 + 40500 + 15000 + 18000
1100
133500
=
1100
= 121.364
= 11.02.
7.6.6 Merits and Demerits of Standard Deviation:
Merits:
1. It is rigidly defined and its value is always definite and
based on all the observations and the actual signs of
deviations are used.
2. As it is based on arithmetic mean, it has all the merits of
arithmetic mean.
3. It is the most important and widely used measure of
dispersion.
4. It is...
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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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