FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 5.55Solution :
Table : Calculation of Standard Deviation
Devn. From
Ass. Mean (12)
X f d fd d^2 fd^2
(1) (2) (3) (4) = (5) = (6)
(2) × (3) (3) × (3) (2) × (5)
10 3 –2 –6 4 12
11 12 –1 –12 1 12
12 18 0 0 0 0
13 12 1 12 1 12
14 3 2 6 4 12
Total 48 0 48
fd^2 fd^2(^480) 1 1
f f 48 48
σ = − = − = =
∑ ∑
∑ ∑
For (c) the following formula is used.
The idea will be clear from the example shown below :
Formula is,
fd^2 fd^2
i
f f
σ = ′ −^ ′^ ×
(^) where d′ = step deviation, i = common factor.
Example 52: Find the standard deviation for the following distribution :
x f
4.5 2
14.5 3
24.5 5
34.5 17
44.5 12
54.5 7
64.5 4