Statistical Tables

Table1: Random Numbers One-digit Numbers

1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
3	3	2	6	1	6	8	0	4	5	6	0	8	0	0	7	3	5	4	5	5	4
2	7	0	7	3	6	0	7	5	1	2	4	6	1	9	9	6	7	3	8	1	8
1	3	5	5	3	8	5	8	5	9	8	8	6	7	0	0	3	7	2	6	7	1
5	7	1	2	1	0	1	4	2	1	8	8	6	5	2	2	4	2	8	6	7	3
0	6	1	8	4	4	3	2	5	3	2	3	0	9	2	7	8	5	0	0	9	4
8	7	3	5	2	0	9	6	4	3	8	4	6	7	4	2	9	6	3	7	2	7
2	1	7	6	3	3	5	0	2	5	8	3	3	0	8	7	8	6	1	0	4	8
1	2	8	6	7	3	5	8	0	7	4	4	1	7	5	5	7	3	9	5	2	5
1	5	5	1	0	0	1	3	4	2	9	9	3	2	0	0	8	2	8	0	0	4
9	0	5	2	8	4	7	7	2	7	0	8	1	3	1	3	7	5	6	9	2	9
0	6	7	6	5	0	0	3	1	0	5	5	2	6	7	2	5	1	9	2	7	5
2	0	1	4	8	5	8	8	4	5	1	0	2	3	8	1	7	0	5	0	0	3
3	2	9	8	9	4	0	7	7	2	9	3	2	8	3	4	5	0	3	4	1	4
8	0	2	2	0	2	5	3	5	3	8	6	4	0	6	6	8	9	2	0	8	7
5	4	4	2	0	6	8	7	9	8	3	5	1	7	3	1	8	8	9	2	2	9
1	7	7	6	3	7	1	3	0	4	0	7	0	0	8	8	3	8	7	9	3	1
7	0	3	3	2	4	0	3	5	4	9	7	2	4	3	3	9	3	4	8	6	6
0	4	4	3	1	8	6	6	7	9	9	4	9	7	7	2	7	8	0	5	7	3
1	2	7	2	0	7	3	4	4	5	9	9	6	1	9	9	1	3	9	5	0	9
5	2	8	5	6	6	6	0	4	4	3	8	5	7	0	0	4	5	0	5	0	9
0	4	3	3	4	6	0	9	5	2	6	8	5	0	4	2	4	2	4	6	7	7
1	3	5	8	1	8	2	4	7	6	1	5	5	8	2	7	7	4	4	7	6	2
9	6	4	6	9	2	4	2	4	5	9	7	3	2	8	5	3	8	2	7	5	7
1	0	4	5	6	5	0	4	2	6	1	1	1	2	1	8	7	7	3	4	9	6
3	4	2	5	2	0	5	7	2	7	4	0	5	1	7	2	7	5	9	5	4	1
6	0	4	7	2	1	2	9	6	8	0	2	5	4	6	7	0	2	6	5	5	4
7	6	7	0	9	0	3	0	8	6	3	8	3	9	4	7	4	8	2	5	8	7
1	6	9	2	5	3	5	6	1	6	0	2	7	6	3	9	9	2	2	5	0	4
4	0	0	1	7	4	9	1	6	2	4	8	8	6	7	4	8	3	3	1	2	7
0	0	5	2	4	3	4	8	8	5	2	7	8	4	6	4	5	9	7	9	4	9

Table2: Random Numbers Two-digit Numbers

1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
51	51	00	83	63	22	55	39	65	36	63	70	77	45	85	50
68	97	87	64	81	07	83	73	71	98	16	04	29	18	94	51
30	79	20	69	22	40	98	72	20	56	20	11	72	65	71	08
81	69	40	23	72	51	39	75	17	26	99	76	89	37	20	70
90	60	73	96	53	97	86	37	48	60	82	29	81	30	15	39
46	15	38	26	61	70	04	68	08	02	80	72	83	75	46	30
99	05	48	67	26	43	18	14	23	98	61	67	70	52	85	01
98	35	55	03	36	67	68	49	08	96	21	44	25	27	99	41
11	53	44	10	13	5	57	78	37	06	08	43	63	61	62	42
06	71	95	06	79	88	54	37	21	34	17	68	86	96	83	23
83	45	19	90	70	99	00	14	29	09	34	04	87	83	07	55
49	90	65	97	38	20	46	68	43	28	06	36	49	52	83	51
39	84	51	67	11	52	49	10	43	67	29	70	80	62	80	03
16	17	17	95	70	45	80	44	38	88	39	54	86	97	37	44
13	74	63	52	52	01	41	90	59	59	19	51	85	39	52	85
68	93	60	61	97	22	61	41	47	10	25	62	97	05	31	03
01	07	98	99	46	50	47	91	94	14	63	19	75	89	11	47
74	97	76	38	03	29	63	80	06	54	18	66	09	18	94	06
19	33	53	05	70	53	30	67	72	77	63	48	84	08	31	55
43	70	02	87	40	41	45	59	40	24	13	27	79	26	88	86
95	80	35	14	97	35	33	05	90	35	89	95	01	61	16	96
82	15	94	51	33	41	67	44	43	80	69	98	46	68	05	14
65	31	91	51	80	32	44	61	81	31	96	82	00	57	25	60
85	23	65	09	29	75	63	42	88	07	10	05	24	98	65	63
65	79	20	71	53	20	25	77	94	30	05	39	28	10	99	00
81	06	01	82	77	45	12	78	83	19	76	16	94	11	68	84
00	52	53	43	37	15	26	87	76	59	61	81	43	63	64	61
50	28	11	39	03	34	25	91	43	05	96	47	55	78	99	95
53	32	40	36	40	96	76	84	97	77	72	73	09	62	06	65
69	84	99	63	22	32	98	87	41	60	76	83	44	88	96	07

Table3: (F-Variance ratio) at 5% level of significance

n1 n2	1	2	3	4	5	6	8	12	24
1	161.4	199.5	215.7	224.6	230.2	234.0	238.9	243.9	249.0	254.3
2	18.51	19.00	19.16	19.25	19.30	19.33	19.37	19.41	19.45	19.50
3	10.13	9.55	9.28	9.12	9.01	8.94	8.84	8.74	8.64	8.53
4	7.71	6.94	6.59	6.39	6.26	6.16	6.04	5.91	5.77	5.63
5	6.61	5.79	5.41	5.19	5.05	4.95	4.82	4.68	4.53	4.36
6	5.99	5.14	4.76	4.53	4.39	4.28	4.15	4.00	3.84	3.67
7	5.59	4.74	4.35	4.12	3.97	3.87	3.73	3.57	3.41	3.23
8	5.32	4.46	4.07	3.84	3.69	3.58	3.44	3.28	3.12	2.93
9	5.12	4.26	3.86	3.63	3.48	3.37	3.23	3.07	2.90	2.71
10	4.96	4.10	3.71	3.48	3.33	3.22	3.07	2.91	2.74	2.54
11	4.84	3.98	3.59	3.36	3.20	3.09	2.95	2.79	2.61	2.40
12	4.75	3.88	3.49	3.26	3.11	3.00	2.85	2.69	2.50	2.30
13	4.67	3.80	3.41	3.18	3.02	2.92	2.77	2.60	2.42	2.21
14	4.60	3.74	3.34	3.11	2.96	2.85	2.70	2.53	2.35	2.13
15	4.54	3.68	3.29	3.06	2.90	2.79	2.64	2.48	2.29	2.07
16	4.49	3.63	3.24	3.01	2.85	2.74	2.59	2.42	2.24	2.01
17	4.45	3.59	3.20	2.96	2.81	2.70	2.55	2.38	2.19	1.96
18	4.41	3.55	3.16	2.93	2.77	2.66	2.51	2.34	2.15	1.92
19	4.38	3.52	3.13	2.90	2.74	2.63	2.48	2.31	2.11	1.88
20	4.35	3.49	3.10	2.87	2.71	2.60	2.45	2.28	2.08	1.84
21	4.32	3.47	3.07	2.84	2.68	2.57	2.42	2.25	2.05	1.81
22	4.30	3.44	3.05	2.82	2.66	2.55	2.40	2.23	2.03	1.78
23	4.28	3.42	3.03	2.80	2.64	2.53	2.38	2.20	2.00	1.76
24	4.26	3.40	3.01	2.78	2.62	2.51	2.36	2.18	1.98	1.73
25	4.24	3.38	2.99	2.76	2.60	2.49	2.34	2.16	1.96	1.71
26	4.22	3.37	2.98	2.74	2.59	2.47	2.32	2.15	1.95	1.69
27	4.21	3.35	2.96	2.73	2.57	2.46	2.30	2.13	1.93	1.67
28	4.20	3.34	2.95	2.71	2.56	2.44	2.29	2.12	1.91	1.65
29	4.18	3.33	2.93	2.70	2.54	2.43	2.28	2.10	1.90	1.64
30	4.17	3.32	2.92	2.69	2.53	2.42	2.27	2.09	1.89	1.62
40	4.08	3.23	2.84	2.61	2.45	2.34	2.18	2.00	1.79	1.51
60	4.00	3.15	2.76	2.52	2.37	2.25	2.10	1.92	1.70	1.39
120	3.92	3.07	2.68	2.45	2.29	2.17	2.02	1.83	1.61	1.25
	3.84	2.99	2.60	2.37	2.21	2.10	1.94	1.75	1.52	1.00

Source: Fisher and Yates Statistical Tables

Table4: (F-Variance ratio) at 1% level of significance

n1 n2	1	2	3	4	5	6	8	12	24
1	4052	4999	5403	5625	5764	5859	5982	6106	6234	6366
2	98.50	99.00	99.17	99.25	99.30	99.33	99.37	99.42	99.46	99.50
3	34.12	30.82	29.46	28.71	28.24	27.91	27.49	27.05	26.60	26.12
4	21.20	18.00	16.69	15.98	15.52	15.21	14.80	14.37	13.93	13.46
5	16.26	13.27	12.06	11.39	10.97	10.67	10.29	9.89	9.47	9.02
6	13.74	10.92	9.78	9.15	8.75	8.47	8.10	7.72	7.31	6.88
7	12.25	9.55	8.45	7.85	7.46	7.19	6.84	6.47	6.07	5.65
8	11.26	8.65	7.59	7.01	6.63	6.37	6.03	5.67	5.28	4.86
9	10.56	8.02	6.99	6.42	6.06	5.80	5.47	5.11	4.73	4.31
10	10.04	7.56	6.55	5.99	5.64	5.39	5.06	4.71	4.33	3.91
11	9.65	7.20	6.22	5.67	5.32	5.07	4.74	4.40	4.02	3.60
12	9.33	6.93	5.95	5.41	5.06	4.82	4.50	4.16	3.78	3.36
13	9.07	6.70	5.74	5.20	4.86	4.62	4.30	3.96	3.59	3.16
14	8.86	6.51	5.56	5.03	4.69	4.46	4.14	3.80	3.43	3.00
15	8.68	6.36	5.42	4.89	4.56	4.32	4.00	3.67	3.29	2.87
16	8.53	6.23	5.29	4.77	4.44	4.20	3.89	3.55	3.18	2.75
17	8.40	6.11	5.18	4.67	4.34	4.10	3.79	3.45	3.08	2.65
18	8.28	6.01	5.09	4.58	4.25	4.01	3.71	3.37	3.00	2.57
19	8.18	5.93	5.01	4.50	4.17	3.94	3.63	3.30	2.92	2.49
20	8.10	5.85	4.94	4.43	4.10	3.87	3.56	3.23	2.86	2.42
21	8.02	5.78	4.87	4.37	4.04	3.81	3.51	3.17	2.80	2.36
22	7.94	5.72	4.82	4.31	3.99	3.76	3.45	3.12	2.75	2.31
23	7.88	5.66	4.76	4.26	3.94	3.71	3.41	3.07	2.70	2.26
24	7.82	5.61	4.72	4.22	3.90	3.67	3.36	3.03	2.66	2.21
25	7.77	5.57	4.68	4.18	3.86	3.63	3.32	2.99	2.62	2.17
26	7.72	5.53	4.64	4.14	3.82	3.59	3.29	2.96	2.58	2.13
27	7.68	5.49	4.60	4.11	3.78	3.56	3.26	2.93	2.55	2.10
28	7.64	5.45	4.57	4.07	3.75	3.53	3.23	2.90	2.52	2.06
29	7.60	5.42	4.54	4.04	3.73	3.50	3.20	2.87	2.49	2.03
30	7.56	5.39	4.51	4.02	3.70	3.47	3.17	2.84	2.47	2.01
40	7.31	5.18	4.31	3.83	3.51	3.29	2.99	2.66	2.29	1.80
60	7.08	4.98	4.13	3.65	3.34	3.12	2.82	2.50	2.12	1.60
120	6.85	4.79	3.95	3.48	3.17	2.96	2.66	2.34	1.95	1.38
	6.64	4.60	3.78	3.32	3.02	2.80	2.51	2.18	1.79	1.00

Source: Fisher and Yates Statistical Tables

Table5: Values of and t at 1%, 5% and 10% level of significance.

d.f.	Significance level of t			Significance level of
	.01	.05	.10	.01	.05	.10
1	63.66	12.71	6.31	6.63	3.84	2.71
2	9.92	4.30	2.92	9.21	5.99	4.61
3	5.84	3.18	2.35	11.34	7.81	6.25
4	4.60	2.78	2.13	13.28	9.49	7.78
5	4.03	2.57	2.02	15.09	11.07	9.24
6	3.71	2.45	1.94	16.81	12.59	10.64
7	3.50	2.36	1.90	18.50	14.07	12.02
8	3.36	2.31	1.86	20.09	15.51	13.36
9	3.25	2.26	1.83	21.67	16.92	14.68
10	3.17	2.23	1.81	23.21	18.31	16.00
11	3.11	2.20	1.80	24.72	19.68	17.28
12	3.06	2.18	1.78	26.22	21.03	18.55
13	3.01	2.16	1.77	27.69	22.36	19.81
14	2.98	2.14	1.76	29.14	23.68	21.06
15	2.95	2.13	1.75	30.58	25.00	22.31
16	2.92	2.12	1.75	32.00	26.30	23.54
17	2.90	2.11	1.74	33.41	27.59	24.77
18	2.88	2.10	1.73	34.80	28.87	25.99
19	2.86	2.09	1.73	36.19	30.14	27.20
20	2.84	2.09	1.72	37.57	31.41	28.41
21	2.83	2.08	1.72	38.93	32.67	29.62
22	2.82	2.07	1.72	40.29	33.92	30.81
23	2.81	2.07	1.71	41.64	35.17	32.01
24	2.80	2.06	1.71	42.98	36.42	33.20
25	2.79	2.06	1.71	44.31	37.65	34.38
26	2.78	2.06	1.71	45.64	38.88	35.56
27	2.77	2.05	1.70	46.96	40.11	36.74
28	2.76	2.05	1.70	48.28	41.34	37.92
29	2.76	2.04	1.70	49.59	42.56	39.09
30	2.75	2.04	1.70	50.89	43.77	40.26
70				100.42	90.53	85.53
	2.58	1.96	1.64

Source: Fisher and Yate�s Statistical Tables

TABLE 6. FACTORS USEFUL IN THE CONSTRUCTION OF CONTROL CHARTS *

Mean Chart				Standard deviation chart			Range chart
Samples factors for control limits Size				Factor for central line factors for control limits			Factor for central line Factors for control limits.
n	A	A1	A2	c2	B3	B4	d2	D3	D4
2	2.121	3.760	1.880	0.5642	0	3.267	1.128	0	3.267
3	1.732	2.394	1.023	0.7236	0	2.568	1.693	0	2.575
4	1.500	1.880	0.729	0.7979	0	2.266	2.059	0	2.282
5	1.342	1.596	0.577	0.8407	0	2.089	2.326	0	2.115
6	1.225	1.410	0.483	0.8686	0.030	1.970	2.534	0	2.004
7	1.134	1.277	0.419	0.8882	0.118	1.882	2.704	0.076	1.924
8	1.031	1.175	0.373	0.9027	0.185	1.815	2.847	0.136	1.864
9	1.000	1.094	9.337	0.9139	0.239	1.761	2.970	0.184	1.816
10	0.949	1.028	0.308	0.9227	0.284	1.716	3.078	0.223	1.777
11	0.905	0.973	0.285	0.9330	0.321	1.679	3.173	0.256	1.744
12	0.866	0.925	0.266	0.9359	0.354	1.646	3.258	0.284	1.716
13	0.832	0.884	0.249	0.9410	0.382	1.618	3.336	0.308	1.692
14	0.802	0.848	0.235	0.9453	0.406	1.594	3.407	0.329	1.671
15	0.775	0.816	0.223	0.9490	0.428	1.572	3.472	0.348	1.652
16	0.750	0.788	0.212	0.9523	0.448	1.552	3.532	0.364	1.636
17	0.728	0.762	0.203	0.9551	0.466	1.534	3.588	0.379	1.621
18	0.707	0.738	0.194	0.9576	0.482	1.518	3.640	0.392	1.608
19	0.688	0.717	0.187	0.9599	0.497	1.503	3.689	0.404	1.596
20	0.671	0.697	0.180	0.9619	0.510	1.490	3.735	0.414	1.586
21	0.655	0.679	0.173	0.9638	0.523	1.477	3.778	0.425	1.575
22	0.640	0.662	0.167	0.9655	0.534	1.466	3.819	0.434	1.566
23	0.626	0.647	0.162	0.9670	0.545	1.455	3.858	0.443	1.557
24	0.612	0.632	0.157	0.9684	0.555	1.445	3.895	0.452	1.548
25	0.600	0.619	0.153	0.9696	0.565	1.435	3.931	0.459	1.541

* Reproduced from Table B2, ASTM SPT � 15C, Manual on Quality control of Materials, with the kind permission of the American Society for Testing and Materials.