Find the standard deviation of the following data.
x | 1 | 2 | 3 | 4 | 5 | 6 | |
---|---|---|---|---|---|---|---|
P(X=x) | 0.1 | 0.1 | 0.1 | 0.2 | 0.3 | 0.2 |
X | P(X) | X×P(X) | (X^2)×P(X) |
1 | 0.1 | 0.1 | 0.1 |
2 | 0.1 | 0.2 | 0.4 |
3 | 0.1 | 0.3 | 0.9 |
4 | 0.2 | 0.8 | 3.2 |
5 | 0.3 | 1.5 | 7.5 |
6 | 0.2 | 1.2 | 7.2 |
ΣP(X) =1 | ΣX×PX) =4.1 | Σ(X^2)×P(X) =19.3 |
E(X) = ΣX×P(X) = 4.1
E(X^2) = Σ(X^2)×P(X) = 19.3
Variance= E(X^2) -[E(X)]^2
= 19.3 -(4.1^2)
= 19.3 - 16.81
= 2.49
Variance =2.49
Standard deviation =√variance
= √2.49
= 1.5780
=1.6 ...upto 1 decimal place.
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