A random variable X has the following discrete probability
distribution.
x |
12 |
19 |
22 |
24 |
27 |
32 |
p(x) |
0.13 |
0.25 |
0.18 |
0.17 |
0.11 |
0.16 |
Calculate σ = standard deviation of X (up to 2 decimal places).
Solution:
Given in the question
that data is discrete data
For standard deviation, first we need to calculate Mean
X |
P(X) |
X.P(X) |
12 |
0.13 |
1.56 |
19 |
0.25 |
4.75 |
22 |
0.18 |
3.96 |
24 |
0.17 |
4.08 |
27 |
0.11 |
2.97 |
32 |
0.16 |
5.12 |
Mean = 1.56+4.75+3.96+4.08+2.97+5.12 = 22.44
Standard deviation can be calculated as
SD = sqrt(summation(Xi-mean)^2 *P(Xi))
X |
P(X) |
X.P(X) |
Xi-Mean |
(Xi-mean)^2 |
(Xi-mean)^2*P(X) |
12 |
0.13 |
1.56 |
-10.44 |
108.9936 |
14.169168 |
19 |
0.25 |
4.75 |
-3.44 |
11.8336 |
2.9584 |
22 |
0.18 |
3.96 |
-0.44 |
0.1936 |
0.034848 |
24 |
0.17 |
4.08 |
1.56 |
2.4336 |
0.413711999999999 |
27 |
0.11 |
2.97 |
4.56 |
20.7936 |
2.287296 |
32 |
0.16 |
5.12 |
9.56 |
91.3936 |
14.622976 |
SD = sqrt(14.169+2.9584+0.0348+0.4137+2.287+14.62) =
sqrt(34.4864) = 5.87
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