Question

To see if a spinner that is divided into 100 equal sections labeled 1 to 100 is fair, a researcher spins the spinner 1000 times and records the result. Let X represent the outcome. The table below shows the probability distribution of the data. Find the mean and the standard deviation of the probability distribution using Excel. Round the mean and standard deviation to two decimal places.

Answer 1

The formulas are as follows:

The data is given below with the calculations:

X	P(X)	X*P(X)	X*X*P(X)
1	0.011	0.011	0.011
2	0.011	0.022	0.044
3	0.011	0.033	0.099
4	0.01	0.04	0.16
5	0.008	0.04	0.2
6	0.011	0.066	0.396
7	0.011	0.077	0.539
8	0.01	0.08	0.64
9	0.01	0.09	0.81
10	0.011	0.11	1.1
11	0.011	0.121	1.331
12	0.01	0.12	1.44
13	0.008	0.104	1.352
14	0.01	0.14	1.96
15	0.008	0.12	1.8
16	0.012	0.192	3.072
17	0.006	0.102	1.734
18	0.011	0.198	3.564
19	0.012	0.228	4.332
20	0.009	0.18	3.6
21	0.011	0.231	4.851
22	0.012	0.264	5.808
23	0.01	0.23	5.29
24	0.011	0.264	6.336
25	0.011	0.275	6.875
26	0.01	0.26	6.76
27	0.01	0.27	7.29
28	0.01	0.28	7.84
29	0.012	0.348	10.092
30	0.009	0.27	8.1
31	0.011	0.341	10.571
32	0.011	0.352	11.264
33	0.008	0.264	8.712
34	0.009	0.306	10.404
35	0.009	0.315	11.025
36	0.009	0.324	11.664
37	0.01	0.37	13.69
38	0.008	0.304	11.552
39	0.009	0.351	13.689
40	0.01	0.4	16
41	0.012	0.492	20.172
42	0.01	0.42	17.64
43	0.009	0.387	16.641
44	0.009	0.396	17.424
45	0.01	0.45	20.25
46	0.011	0.506	23.276
47	0.01	0.47	22.09
48	0.011	0.528	25.344
49	0.011	0.539	26.411
50	0.011	0.55	27.5
51	0.011	0.561	28.611
52	0.01	0.52	27.04
53	0.007	0.371	19.663
54	0.011	0.594	32.076
55	0.009	0.495	27.225
56	0.01	0.56	31.36
57	0.007	0.399	22.743
58	0.011	0.638	37.004
59	0.011	0.649	38.291
60	0.012	0.72	43.2
61	0.008	0.488	29.768
62	0.011	0.682	42.284
63	0.009	0.567	35.721
64	0.01	0.64	40.96
65	0.01	0.65	42.25
66	0.011	0.726	47.916
67	0.009	0.603	40.401
68	0.01	0.68	46.24
69	0.01	0.69	47.61
70	0.009	0.63	44.1
71	0.01	0.71	50.41
72	0.01	0.72	51.84
73	0.011	0.803	58.619
74	0.008	0.592	43.808
75	0.009	0.675	50.625
76	0.009	0.684	51.984
77	0.011	0.847	65.219
78	0.011	0.858	66.924
79	0.011	0.869	68.651
80	0.009	0.72	57.6
81	0.01	0.81	65.61
82	0.008	0.656	53.792
83	0.009	0.747	62.001
84	0.011	0.924	77.616
85	0.012	1.02	86.7
86	0.01	0.86	73.96
87	0.009	0.783	68.121
88	0.011	0.968	85.184
89	0.01	0.89	79.21
90	0.01	0.9	81
91	0.009	0.819	74.529
92	0.011	1.012	93.104
93	0.011	1.023	95.139
94	0.011	1.034	97.196
95	0.008	0.76	72.2
96	0.01	0.96	92.16
97	0.01	0.97	94.09
98	0.01	0.98	96.04
99	0.011	1.089	107.811
100	0.009	0.9	90
Total	1	50.28	3368.35
	mu = 50.28
	Variance = 3368.35 - 50.28*50.28	840.57
	Standard Deviation = Square root of variance	28.99

Mean = 50.28

Standard deviation = Square root of variance = 28.99