Find the standard deviation of the following distribution
X | -9 | -6 | -3 | 0 | 3 |
P(x) | 0.2 | 0.1 | 0.2 | 0.3 | 0.2 |
Solution,
X | P(x) | X * P(x) | X2 * P(x) |
-9 | 0.2 | -1.8 | 16.2 |
-6 | 0.1 | -0.6 | 3.6 |
-3 | 0.2 | -0.6 | 1.8 |
0 | 0.3 | 0 | 0 |
3 | 0.2 | 0.6 | 1.8 |
1.00 | -2.4 | 23.4 |
a) mean = u = x * p(x) = -2.4
b) standard deviation = = x2 * p(x) - (u)2
standard deviation = = 23.4 - ( -2.4)2
standard deviation = = 23.4 - 5.76
standard deviation = = 17.64
standard deviation = = 4.2
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