Is the Dart Throwing Data a Gaussian Distribution?

[Dgray101]

Homework Statement

We threw a bunch of darts at a dart board to find the statistics of the positions. They ranged from -20 to 20 and the data is right here. ( each column corresponds to the dart number, it is just a syntax thing) The frequencies are below.

Dart 1 Dart 2 Dart 3 Dart 4 Dart 5
1 -7 -4 4 4 5
2 -19 -6 -5 -2 0
3 -10 -6 -5 6 7
4 -13 -8 -3 8 11
5 -8 -4 -2 0 7
6 -7 -1 0 1 2
7 -13 -11 -2 -2 0
8 -8 -4 -1 8 9
9 -13 -9 -6 -3 5
10 -6 7 12 12 14
11 9 -8 -2 -2 0
12 -12 -4 -4 3 10
13 -8 -7 -4 -3 4
14 -7 -4 2 4 4
15 -5 -3 0 6 11
16 -16 -5 -3 3 8
17 -11 -3 3 1 20
18 -6 -3 3 5 7
19 -4 -2 3 5 12
20 -4 0 3 4 6
21 -11 -9 -4 -5 3
22 0 1 2 7 11
23 -8 -7 -4 -4 0
24 -2 0 6 11 13
25 -10 -8 0 0 4
26 -2 0 3 5 9
27 -5 -1 -1 0 7
28 -13 -6 -5 5 12
29 -4 -8 -2 0 3
30 -15 -5 0 1 4
31 -10 -2 -2 0 4
32 -4 1 5 7 8
33 -10 1 2 6 -1.5
34 -6 -2.5 -2 -7 6
35 -9 -3 -2 5.5 6
36 -15 -7 1 0 3
37 -6 -1 -1 3 2
38 2 1 1 -7 -8
39 -4 -3 1 4 9
40 -3 -4 -2 1 -1
41 1 -2 -2 3 4
42 -4 -3 -1 3 3
43 -7 -4 -1 3 7
44 0 -1 -1 1 2
45 0 -7 -1 -3 7
46 -7 1 -1 -1 0
47 -6 2 -3 -2 6
48 -11 -8 -1 -3 2
49 -6 -3 -2 2 5
50 -7 -4 -3 1 1
51 -2 -2 4 4 11
52 0 -1 -4 -6 7
53 -3 -3 -1 1 2
54 -1 -1 -2 2 6
55 1 -3 4 4 2
56 -8 -8 -9 8 -3
57 2 6 -7 -3 -1
58 -5 -1 -1 1 2
59 3 1 2 -1 -3
60 2 0 -3 -4 -5



-20 0
-19 1
-18 0
-17 0
-16 1
-15 2
-14 0
-13 4
-12 1
-11 4
-10 4
-9 4
-8 12
-7 13
-6 11
-5 10
-4 21
-3 23
-2 23
-1 24
0 23
1 20
2 17
3 16
4 15
5 8
6 11
7 10
8 5
9 4
10 1
11 5
12 4
13 1
14 1
15 0
16 0
17 0
18 0
19 0
20 1

I graphed it, and I did a gaussian distribution and all the data fits fine and dandy. But when I perform the Chi squared test in excel, what ends up happening is that I will get CHITEST = 0
and then when I do CHIINV I get that the number isn't recognized by excel. Or when I mess around with bins I end up getting a number that's roughly around 300...


I honestly have no idea why I am not getting that this data is a gaussian distribution.

The Attempt at a Solution

 

[LCKurtz]

I'm not intending to address your question, but putting code tags around your data makes it much more readable.

Homework Statement

We threw a bunch of darts at a dart board to find the statistics of the positions. They ranged from -20 to 20 and the data is right here. ( each column corresponds to the dart number, it is just a syntax thing) The frequencies are below.

	Dart 1	Dart 2	Dart 3	Dart 4	Dart 5
1	-7	-4	4	4	5
2	-19	-6	-5	-2	0
3	-10	-6	-5	6	7
4	-13	-8	-3	8	11
5	-8	-4	-2	0	7
6	-7	-1	0	1	2
7	-13	-11	-2	-2	0
8	-8	-4	-1	8	9
9	-13	-9	-6	-3	5
10	-6	7	12	12	14
11	9	-8	-2	-2	0
12	-12	-4	-4	3	10
13	-8	-7	-4	-3	4
14	-7	-4	2	4	4
15	-5	-3	0	6	11
16	-16	-5	-3	3	8
17	-11	-3	3	1	20
18	-6	-3	3	5	7
19	-4	-2	3	5	12
20	-4	0	3	4	6
21	-11	-9	-4	-5	3
22	0	1	2	7	11
23	-8	-7	-4	-4	0
24	-2	0	6	11	13
25	-10	-8	0	0	4
26	-2	0	3	5	9
27	-5	-1	-1	0	7
28	-13	-6	-5	5	12
29	-4	-8	-2	0	3
30	-15	-5	0	1	4
31	-10	-2	-2	0	4
32	-4	1	5	7	8
33	-10	1	2	6	-1.5
34	-6	-2.5	-2	-7	6
35	-9	-3	-2	5.5	6
36	-15	-7	1	0	3
37	-6	-1	-1	3	2
38	2	1	1	-7	-8
39	-4	-3	1	4	9
40	-3	-4	-2	1	-1
41	1	-2	-2	3	4
42	-4	-3	-1	3	3
43	-7	-4	-1	3	7
44	0	-1	-1	1	2
45	0	-7	-1	-3	7
46	-7	1	-1	-1	0
47	-6	2	-3	-2	6
48	-11	-8	-1	-3	2
49	-6	-3	-2	2	5
50	-7	-4	-3	1	1
51	-2	-2	4	4	11
52	0	-1	-4	-6	7
53	-3	-3	-1	1	2
54	-1	-1	-2	2	6
55	1	-3	4	4	2
56	-8	-8	-9	8	-3
57	2	6	-7	-3	-1
58	-5	-1	-1	1	2
59	3	1	2	-1	-3
60	2	0	-3	-4	-5

-20	0
-19	1
-18	0
-17	0
-16	1
-15	2
-14	0
-13	4
-12	1
-11	4
-10	4
-9	4
-8	12
-7	13
-6	11
-5	10
-4	21
-3	23
-2	23
-1	24
0	23
1	20
2	17
3	16
4	15
5	8
6	11
7	10
8	5
9	4
10	1
11	5
12	4
13	1
14	1
15	0
16	0
17	0
18	0
19	0
20	1

I graphed it, and I did a gaussian distribution and all the data fits fine and dandy. But when I perform the Chi squared test in excel, what ends up happening is that I will get CHITEST = 0
and then when I do CHIINV I get that the number isn't recognized by excel. Or when I mess around with bins I end up getting a number that's roughly around 300...


I honestly have no idea why I am not getting that this data is a gaussian distribution.

The Attempt at a Solution

 

[Ray Vickson]

Homework Statement

We threw a bunch of darts at a dart board to find the statistics of the positions. They ranged from -20 to 20 and the data is right here. ( each column corresponds to the dart number, it is just a syntax thing) The frequencies are below.

Dart 1 Dart 2 Dart 3 Dart 4 Dart 5
1 -7 -4 4 4 5
2 -19 -6 -5 -2 0
3 -10 -6 -5 6 7
4 -13 -8 -3 8 11
5 -8 -4 -2 0 7
6 -7 -1 0 1 2
7 -13 -11 -2 -2 0
8 -8 -4 -1 8 9
9 -13 -9 -6 -3 5
10 -6 7 12 12 14
11 9 -8 -2 -2 0
12 -12 -4 -4 3 10
13 -8 -7 -4 -3 4
14 -7 -4 2 4 4
15 -5 -3 0 6 11
16 -16 -5 -3 3 8
17 -11 -3 3 1 20
18 -6 -3 3 5 7
19 -4 -2 3 5 12
20 -4 0 3 4 6
21 -11 -9 -4 -5 3
22 0 1 2 7 11
23 -8 -7 -4 -4 0
24 -2 0 6 11 13
25 -10 -8 0 0 4
26 -2 0 3 5 9
27 -5 -1 -1 0 7
28 -13 -6 -5 5 12
29 -4 -8 -2 0 3
30 -15 -5 0 1 4
31 -10 -2 -2 0 4
32 -4 1 5 7 8
33 -10 1 2 6 -1.5
34 -6 -2.5 -2 -7 6
35 -9 -3 -2 5.5 6
36 -15 -7 1 0 3
37 -6 -1 -1 3 2
38 2 1 1 -7 -8
39 -4 -3 1 4 9
40 -3 -4 -2 1 -1
41 1 -2 -2 3 4
42 -4 -3 -1 3 3
43 -7 -4 -1 3 7
44 0 -1 -1 1 2
45 0 -7 -1 -3 7
46 -7 1 -1 -1 0
47 -6 2 -3 -2 6
48 -11 -8 -1 -3 2
49 -6 -3 -2 2 5
50 -7 -4 -3 1 1
51 -2 -2 4 4 11
52 0 -1 -4 -6 7
53 -3 -3 -1 1 2
54 -1 -1 -2 2 6
55 1 -3 4 4 2
56 -8 -8 -9 8 -3
57 2 6 -7 -3 -1
58 -5 -1 -1 1 2
59 3 1 2 -1 -3
60 2 0 -3 -4 -5



-20 0
-19 1
-18 0
-17 0
-16 1
-15 2
-14 0
-13 4
-12 1
-11 4
-10 4
-9 4
-8 12
-7 13
-6 11
-5 10
-4 21
-3 23
-2 23
-1 24
0 23
1 20
2 17
3 16
4 15
5 8
6 11
7 10
8 5
9 4
10 1
11 5
12 4
13 1
14 1
15 0
16 0
17 0
18 0
19 0
20 1

I graphed it, and I did a gaussian distribution and all the data fits fine and dandy. But when I perform the Chi squared test in excel, what ends up happening is that I will get CHITEST = 0
and then when I do CHIINV I get that the number isn't recognized by excel. Or when I mess around with bins I end up getting a number that's roughly around 300...


I honestly have no idea why I am not getting that this data is a gaussian distribution.

The Attempt at a Solution

You need to include more details. How did you obtain the Chi-squared values; that is, what are the individual "bins" that you used in submitting the data to the Chi-squared package?

I looked at your data in maple, and found that in some ways of presenting the data the normality hypothesis was rejected (at some reasonable level of significance), while in other ways of presenting the data the normality hypothesis was accepted at the same level of significance. The point is that it is easy to "misuse" the Chi-squared test if you don't really know what you are doing. There are certain rule of thumb restrictions that typically accompany descriptions of chi-squared usage, and we have no way of knowing whether or not you paid attention to these restrictions. If you violate the restrictions the chi-squared test simply does not apply; that is, the use of a Chi-squared table is inaccurate and ill-advised.