Solution:
Mean can be calculated as
Mean = Summation(Xi*P(Xi))
|
X
|
P(X)
|
Xi*P(Xi)
|
|
1
|
0.0303
|
0.0303
|
|
2
|
0.0639
|
0.1278
|
|
3
|
0.0197
|
0.0591
|
|
4
|
0.003
|
0.012
|
|
5
|
0.0164
|
0.082
|
|
6
|
0.0454
|
0.2724
|
|
7
|
0.0981
|
0.6867
|
|
8
|
0.0648
|
0.5184
|
|
9
|
0.0657
|
0.5913
|
|
10
|
0.0124
|
0.124
|
|
11
|
0.0118
|
0.1298
|
|
12
|
0.0539
|
0.6468
|
|
13
|
0.0497
|
0.6461
|
|
14
|
0.0648
|
0.9072
|
|
15
|
0.0373
|
0.5595
|
|
16
|
0.0475
|
0.76
|
|
17
|
0.0224
|
0.3808
|
|
18
|
0.0191
|
0.3438
|
|
19
|
0.0088
|
0.1672
|
|
20
|
0.0406
|
0.812
|
|
21
|
0.0445
|
0.9345
|
|
22
|
0.1202
|
2.6444
|
|
23
|
0.0597
|
1.3731
|
Mean = 12.809
Standard deviation = Sqrt(summation((Xi-mean)^2*P(Xi))
|
X
|
P(X)
|
Xi*P(Xi)
|
(Xi-Mean)
|
(Xi-mean)^2
|
(Xi-mean)^2*P(Xi)
|
|
1
|
0.0303
|
0.0303
|
-11.809
|
139.452481
|
4.2254101743
|
|
2
|
0.0639
|
0.1278
|
-10.809
|
116.834481
|
7.4657233359
|
|
3
|
0.0197
|
0.0591
|
-9.809
|
96.216481
|
1.8954646757
|
|
4
|
0.003
|
0.012
|
-8.809
|
77.598481
|
0.232795443
|
|
5
|
0.0164
|
0.082
|
-7.809
|
60.980481
|
1.0000798884
|
|
6
|
0.0454
|
0.2724
|
-6.809
|
46.362481
|
2.1048566374
|
|
7
|
0.0981
|
0.6867
|
-5.809
|
33.744481
|
3.3103335861
|
|
8
|
0.0648
|
0.5184
|
-4.809
|
23.126481
|
1.4985959688
|
|
9
|
0.0657
|
0.5913
|
-3.809
|
14.508481
|
0.9532072017
|
|
10
|
0.0124
|
0.124
|
-2.809
|
7.890481
|
0.0978419644
|
|
11
|
0.0118
|
0.1298
|
-1.809
|
3.272481
|
0.0386152758
|
|
12
|
0.0539
|
0.6468
|
-0.809
|
0.654481
|
0.0352765259
|
|
13
|
0.0497
|
0.6461
|
0.191
|
0.036481
|
0.0018131057
|
|
14
|
0.0648
|
0.9072
|
1.191
|
1.418481
|
0.0919175688
|
|
15
|
0.0373
|
0.5595
|
2.191
|
4.800481
|
0.1790579413
|
|
16
|
0.0475
|
0.76
|
3.191
|
10.182481
|
0.4836678475
|
|
17
|
0.0224
|
0.3808
|
4.191
|
17.564481
|
0.3934443744
|
|
18
|
0.0191
|
0.3438
|
5.191
|
26.946481
|
0.5146777871
|
|
19
|
0.0088
|
0.1672
|
6.191
|
38.328481
|
0.3372906328
|
|
20
|
0.0406
|
0.812
|
7.191
|
51.710481
|
2.0994455286
|
|
21
|
0.0445
|
0.9345
|
8.191
|
67.092481
|
2.9856154045
|
|
22
|
0.1202
|
2.6444
|
9.191
|
84.474481
|
10.1538326162
|
|
23
|
0.0597
|
1.3731
|
10.191
|
103.856481
|
6.2002319157
|
Standard deviation = sqrt(46.299) = 6.804
