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Question

Find the standard deviation of 40,42 and 48. If each value is multiplied by 3, find the standard deviation of the new data.

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Solution

Let us consider the given data 40,42,48 and find σ.
Let the assumed mean A be 44
x
d=x44
d2
40
4
16
42
2
4
48
4
16

d=2
d2=36
Standard deviation, σ= d2n(dn)2
=363(23)2
σ=1043
When the values are multiplied by 3, we get 120,126,144. Let the assumed mean A be 132.
Let σ1 be the S.D. of the new data.
x
d=x132
d2
120
12
144
126
6
36
144
12
144

d=6
d2=324
Standard deviation, σ1= d2n(dn)2
=3243(63)2
σ1=3123=104
In the example, when each value is multiplied by 3, the standard deviation also gets multiplied by 3.

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