Question

I cannot figure out how to solve for the mean and standard deviation for this data set.

x   P(x)
1   0.01
2   0.01
3   0.04
4   0.02
5   0.02
6   0.09
7   0.08
8   0.04
9   0.07
10   0.02
11   0.04
12   0.04
13   0.16
14   0.08
15   0.08
16   0.02
17   0.02
18   0.08
19   0.04
20   0.04

Answer 1

x	P(x)	x*P(X)	X^2*P(X)
1	0.01	0.01	0.01
2	0.01	0.02	0.04
3	0.04	0.12	0.36
4	0.02	0.08	0.32
5	0.02	0.1	0.5
6	0.09	0.54	3.24
7	0.08	0.56	3.92
8	0.04	0.32	2.56
9	0.07	0.63	5.67
10	0.02	0.2	2
11	0.04	0.44	4.84
12	0.04	0.48	5.76
13	0.16	2.08	27.04
14	0.08	1.12	15.68
15	0.08	1.2	18
16	0.02	0.32	5.12
17	0.02	0.34	5.78
18	0.08	1.44	25.92
19	0.04	0.76	14.44
20	0.04	0.8	16
sum	1	11.56	157.2

Mean=E(x)=sum(x*P(X)=11.56

Mean=11.56

Standard deviation =sqrt(E(X^2)-E(X)^2)

E(X^2)=sum(x^2*P(X))

=157.2

Standard deviation =sqrt(157.2-11.56^2) =4.85

#standard deviation=4.85