1.1) Data distribution and histograms

Histograms are a powerful visual aid to determine the distribution of a dataset. 
They can be prepared in any statitics package as well as in most spreadsheet 
programs. However, they generally require manual setting of the class size, and
improper values for this parameter can easily mask the true nature of a dataset.
In this exercise we will explore this for a dataset of SiO2 content (wt%) in river
sediments from the French Massif Central.

A: Determine the range, mean, n and standard deviation of the dataset
B: Prepare a histogram for classes from 0 to 130 at a spacing of 10 wt% and 
    mark the mean and standard deviation
C: Do the same for classes: 4 to 124 at 5 wt% spacing; min to max at 20% 
    of the standard deviation and min to max at 10 samples per class
D: What is the ditribution of this dataset?

Data (SiO2 in wt %)

52.8
55.6
55.5
53.4
55.8
56.5
57.2
55
58.6
58
56.5
49.1
55.6
59
54.2
58.8
52
55.2
58.4
58.1
56.7
59.3
58.6
52.5
54.4
54.9
54.8
60.8
56.8
59.5
56.4
55.5
55.3
52.7
59.6
62.9
58.8
59.4
60
60.7
54.7
55
55.3
57.8
59.4
60.4
63.1
57.5
56.8
58.7
61.8
59.2
63.3
60.7
61.4
61
62.6
59.6
63.3
60.9
60.8
58.4
55.4
55.7
56
54.9
61.5
57
56.4
58.9
57.9
54.7
58.7
54.5
55.7
53.6
55.9
56
58.9
50.1
53.3
55.2
51.3
57.1
51.3
56.5
51.4
53.9
49.3
48.2
52.7
53.5
55
51.4
53.3
49.8
53.1
49.1
52.6
52.9
52.6
51.8
51.1
54.2
52.2
53.3
54.9
57.3
51.6
51.6
54.9
51.7
51.3
51.6
53.6
52
51.8
50.4
47.5
52.6
54.8
53.5
51.7
54.2
52.4
51.8
52.9
54.7
57.5
57.1
56.2
53.3
55.2
54.5
55.2
55.8
56.2
52.4
53.3
53.6
52.3
52.8
57
53.2
52.5
53.6
56.6
55.2
56.7
52.1
57.3
57.2
56.6
53.6
52.4
56.7
54.1
54.8
59
57.2
57.9
57.4
54.2
51.6
56.3
52.9
52.8
54.9
56.9
56.3
54.7
46.6
55.7
55.3
56.6
56.3
56
56.2
54.4
52.6
52.1
53.2
56
54
57.7
55.4
47.6
52.1
54.4
55.7
55.5
54.8
51.3
47.9
53.1
54.2
50.7
54.5
55.8
52.6
53.4
52.5
51.8
54.6
55.3
53.6
50.4
54.6
52.6
52.2
53.2
55.2
56.1
52.4
53.2
56.7
55.5
51.8
56.8
53.7
51.1
58.7
57.6
53.1
60.8
53.7
52.9
52.6
53.4
56.4
58
58
59.5
57.1
54.8
55.5
52.6
56.4
53.9
56.2
57.6
54.1
59.2
56.9
58.8
56.7
52.7
57
58
59.9
58.8
56.8
58.2
64.3
56.9
57.8
59.2
61.5
55.9
54
56.1
56.8
56.9
57.2
53.9
56
56.1
59
54.1
59
60
57.4
53.6
53.4
51.3
58.7
60.7
53.1
54.1
57.8
58.4
56.3
54.9
58.2
57.8
55.6
52.9
62.9
58.3
60
59.9
58.1
53.2
55.2
57.5
52.4
56
56.3
54.1
53.7
52.2
53.8
56.9
56.3
57.6
54.3
54.8
58.8
59.4
62.8
57.1
55.9
54.7
57.5
61.9
57.9
62
58.5
61.9
59.9
54.2
58
57
51.5
52.4
52.5
56.5
53
54.8
54.5
51.4
53.5
54
54.3
50.4
54
50.5
50.2
48
56.3
51.7
50.5
51.5
53.7
55.9
59.5
56.4
55.3
56.6
56.6
53.4
47.2
52.3
58.6
55.8
57
55.1
55.4
58.7
61.9
58
62.8
57.3
49
55.5
57.1
51.8
52.5
60
55.2
57.1
57.1
60.2
57.9
56.7
57.4
57.9
58.2
61
53.8
56.6
60.3
64.2
61.8
63.1
62.3
58.8
61.3
55.6
56.8
59.6
63.7
62.9
57.7
62.2
63.4
61.6
60
60.6
61.9
62
54.5
56.1
57.9
52.8
50.1
58.8
55.3
52.7
51
56.6
54.3
55.4
53
52.1
53.9
60
57.2
53.5
48.9
51.3
52.8
58.8
53.1
51.2
54.6
51.3
51.5
51.3
55
55
55.7
46.5
46.4
52.8
52.7
60.4
55.5
52.8
57.1
59.1
54.4
56
53.5
52.6
53.5
51.2
55.1
57.9
49.5
58.6
59.7
57.5
55.7
57.4
58.6
56.4
60.2
60.2
53.9
58.7
59.3
64.6
63.1
66.4
64.7
60.7
59.6
56.4
53.7
63.8
62
59.2
60
59
53.6
57.6
55.4
58
59.2
62.1
60.1
63.2
64.9
59
57.5
59.7
58.7
54
57.1
55.1
58.1
61.5
61.2
59.7
59.1
59.3
60
58.5
63.1
58
60
52.6
49.6
52.8
57.5
57.7
63.5
59.7
62.6
53.8
57
59.6
55.3
54
54.9
56.8
63.8
63.1
55.4
56.5
56.4
53.7
56.8
56.1
56.1
59.2
56.1
56.6
57.1
53.5
57.1
57.1
58.2
57.8
55.4
54.1
52.7
54.4
52
50.9
50.7
52.4
55.8
55.6
58.4
51.6
56
55.3
54
54
52.8
53.5
52.9
49.9
51.4
53.3
50
52.8
54.6
53.7
55.6
55.2
52.4
51.6
54.1
53.6
50.2
59.6
52.2
57.3
55
60.8
54.1
51.8
52.3
58.4
60.1
51.7
49.8
50
54.3
66.2
56
56
56.5
57.2
54.7
57.9
63
61.2
63.6
62.2
59.4
64
61.7
59.1
53.1
52
50.4
54
61.4
63.2
62.8
56.1
56.5
58.1
58.4
58.4
60.4
58.6
61
60.3
61.8
58.8
60.9
65.7
66.3
65.9
62.5
69.2
60.6
72.5
64.8
59.3
55.1
60.9
66.2
64.8
64.2
61.3
56.6
63.6
57.2
64.4
62
60.4
58.5
62.5
66.4
64.2
57.1
61.5
67.2
56.9
62.6
53.5
60.4
63.5
60.2
61.1
63.1
65.9
71.2
69.7
62.3
63.3
55
63.2
58
56.6
57.5
62
57.1
58.7
61.8
60.2
62
64.7
66.3
62.5
62.9
58.8
54.5
61.4
53.8
57
57.4
56.8
57.1
56.3
55.7
57.5
57.5
53.1
58.8
57.5
58
58.5
55.8
55.3
61.3
59.8
59.6
52.3
57.7
54.3
56
57.6
52.6
54.2
55.4
54.9
56.9
57.5
59.9
57.4
56.2
60.6
56.8
57.2
57.6
51
54
52.3
54.1
55.2
53.1
53.9
50.9
59.6
61
62.1
63.3
60.7
63.3
66.2
65.9
55.9
65.3
61.1
64
65.6
68.5
65
68.4
63.9
56.6
52.6
56.2
55.3
53.5
54.6
59.1
61.2
58.6
57.3
60.3
58.5
59.7
58.3
58.8
59.1
58.4
56.5
60.2
64.3
58.4
54.8
59.6
62.6
61.1
63.6
57.5
67.2
60
66.8
67.1
59.3
56.4
63.4
62.5
61.6
61.4
66.3
65.4
58.4
59.1
58.6
59.3
56.7
57.2
56
54.6
56.9
57.2
55.4
52.3
53.7
54.9
55.5
55.4
54.1
55.1
53.4
55
51.5
57.1
58
60.7
57.8
58.4
56.8
58.2
57.1
55.1
56.3
54.3
53.1
62.4
58.4
56.8
55.6
63.2
61.8
59
57.5
66.3
61
60.3
62.7
61.6
58
57.7
58.4
62.7
49.8
63
64
59.6
60.6
52.1
61.5
56.8
58.3
59.4
62.6
64.5
60.4
61.9
58
60.2
59.9
59.9
58.1
64.4
64.6
59.5
59.4
57.8
60.8
62.9
59.3
58.5
61.5
64.7
59.5
58.4
61.4
61.9
56.4
58.3
55.7
60.2
57.6
57.6
59.4
62.9
67.2
57.5
57.1
60.9
48
49.4
47.8
41.6
48.2
50.4
45.8
50.2
42.6
45.2
50.2
44.6
47.8
42.6
48
43
40.4
46.2
44.4
37.8
41.8
42.4
42.6
41.4
47.6
47.2
45.8
46.4
46.8
40.6
49
45.6
46.4
50.2
43.6
41
47.6
41.8
37.8
42.6
43.6
42.2
42.2
37.4
44
38.4
45.4
46.2
45.6
41.6
43.4
43.6
42.4
43
40.8
42.4
40.2
42.8
38.6
40.8
41.2
40.8
47.8
46.4
44
42.2
38
44
46.2
41.2
43.2
41
43.2
45.4
45.6
46.2
46.8
45.4
44.2
45.4
48.2
45.2
45
42.4
42.4
37.6
43.4
38.8
46.4
49.8
38.8
36.4
44.4
40.2
46.6
42
41.6
35.6
41.6
42
42.2
38.6
43.4
46
44
42.2
42
40.8
46.2
52.6
44
48.4
48.6
51.2
44.6
46.2
44.6
49.4
43.8
45.2
47.6
45.4
44.2
35.4
35.8
42.8
42
48.2
37
46.2
44.8
45.6
47.2
46.6
41.2
42.6
42.6
45.2
46.6
46
43
47.4
49.4
41.6
40.2
39.2
47
44.2
44.6
47.6
45.8
44.4
41
45.4
49.2
41.8
42.6
41.8
41.8
39
37.4
33.8
44.4
41.2
36.8
37
36.4
42
44.4
42.8
42.2
36
39.4
44
44.4
39.6
41.6
43.2
41
44.4
42.4
45
42.6
36.6
36.4
45.2
41.2
47.6
47
43.8
43
45.2
48
50
48
42.8
42.8
41.8
43.2
45.6
49.6
44.8
46.6
41.6
38.6
39.8
39.2
46.8
43.2
38.2
42.8
43.6
42.4
44.2
41
43
47.6
49.2
47.8
50
50.4
44.4
44.8
49
40.6
47.6
46
41
49.8
43.4
45
41.4
36.6
37.2
45.6
41.4
40.2
38.2
43.2
46.4
45
46.8
41.6
44.6
41.6
39
41
41.8
44.2
38.6
46.4
40.8
43.6
38.4
44.6
40.2
45.8
43.2
45
44.8
43.8
44.8
41.4
41.6
47.2
43
42.2
44.8
42
42.8
41
43.2
42.2
42.2
43
37.8
41
41.2
38.8
43.8
39
41.8
44.4
43.4
41.8
42.2
44.8
38.6
38.6
39.4
44.4
38.8
42.8
38
43.6
41.8
42.4
42.6
42.4
40
39
40.4
42.2
40.4
39.8
41.2
40.2
37.6
39.2
38
44.4
43.8
41
42.6
38.2
41
42.2
44
42.4
42.8
44.8
45
42
46.2
45.6
43.8
43
45.6
41.6
40.4
41.8
43
42
43.2
45.6
47.8
54.4
56.2
46.4
43.2
51.2
47.8
50.2
48.4
45.4
47.6
48.4
48.8
46.4
49.2
51.4
38
44.6
46.4
46.4
40.8
41.6
44.6
45
38.2
46.8
42.8
38.6
35
41.8
43.6
45.4
45.6
43.4
45.8
43.2
48.8
45.2
49
44.8
39.6
43
46
44.6
48
41.2
48
43.4
43.4
44.4
43.2
45.2
44.4
48.8
47.4
50.6
39.8
43.6
47.8
41.6
43.4
45.2
43.6
45.2
43.2
44.4
43.8
44.6
38.6
39.4
40.2
41.4
50.6
50.6
40.8
45.8
42
43
46.2
47.8
40.2
39.8
41.2
44.4
44.6
49
43.2
37.6
42.4
44.8
50.2
51.2
48.6
49.4
44.8
47
44.4
37.2
41.8
46.4
45.4
41.8
46
44
42.8
37.6
48.2
41.2
42.2
47
39
34.8
42.8
43.2
37.2
42.8
45
44.2
48
44.2
42.8
49
42.6
42.8
50.6
47
46.6
36.8
40.2
32.8
35
43.2
41.6
46
44.4
36.2
38.6
41.8
45.4
45.2
49
42.6
45.8
47.6
45.2
40.8
47
41.4
40
40.6
39.4
42.6
43.4
49.2
46
48.6
47.2
41
41
43.4
42.8
47.4
40.6
43.4
39.8
46.4
41.2
48
50.2
46.4
46.4
46.6
41.2
45.8
40.8
46.2
45.2
44
48
49.2
49.6
44.6
42.4
40
39
40.4
40.4
43.4
45.6
42
39.2
44
46.8
43.6
45.2
43.4
44.8
45.6
45.6
40.4
39.2
41.6
48.6
46.8
42.2
50.2
46.8
48.4
41.6
44.2
41
41.6
46
42.2
45.8
43.4
44.8
44.2
44.6
44
46.4
42.4
44
43.4
41.6
40.6
44
39.8
47.4
46
44.8
44.8
46
49.2
43.2
42.6
44.4
41.4
42.4
48
43
45
42
47.2
47.2
43
40.4
33
44.2
41.4
45.2
45.8
42.2
44.6
31.4
31.6
36
34.8
44.2
37.2
38.6
41.6
44.4
46.6
49.4
45.8
42.2
38.8
37.2
39
45.2
43
44.6
39
41.8
47.2
44
44
39.2
46.2
38.2
37.2
36.6
34.8
39.4
37.2
44.2
30.2
39
49.4
34.8
45.8
41.2
39.8
36.6
44.4
50.2
38
49
45.8
40.2
45.2
45.2
45.6
37.4
34.4
46.2
41.8
35.6
47
33.2
48
46.4
38.2
44
44.6
41.4
38.6
33.2
34.8
38
42
49
43.6
44.8
46.4
47.6
43.4
47.4
44.4
43.6
37.8
43.4
41.6
38.8
38.2
42.2
47
50.4
43.6
43.8
47.2
47.2
46.4
48.2
47.6
49.8
47.2
46.4
51
44.6
40.4
45.2
44
47
47.6
42.4
43.8
39
48.8
44.8
46.2
46
44
48.8
49
45.2
50.6
41.2
46
42.2
47.2
48.4
43.2
43.2
41.4
45.2
49.8
44.4
50.2
48.2
43.8
45
43.2
43.4
39.8
39.2
35.4
37.8
35.6
32.8
36
32.6
43.6
39.2
46
42.2
40
36.8
40.8
34.4
39.2
46.6
51.2
48
45.4
49
49
42
39.8
41.8
45.4
43.6
43.4
45.6
44.4
43.2
43.2
47.6
43.8
45.6
41.8
44
53.8
43
43.6
46.6
38
46.2
37
43
35.6
38
43.8
38.2
44
42.8
47
45.2
38
31.6
46.2
43
45.8
45
45.8
46
43
46.8
49.4
44.6
49.2
52
46.8
50.2
49.2
40.8
49.2
47.4
49.6
48.8
45.6
45
44
41.2
42.8
42.8
37.2
40.8
45.2
46.8
48.8
50.8
38.8
41.4
45.6
50.8
43
41
40.4
41
41.2
35.4
37
42.6
36.2
39.8
46
43.8
42.6
40.2
51.6
35.2
37.4
38.6
40
49.6
40.4
46.2
40.6
45.4
38.4
38
41.2
42.6
42.2
39.8
37
36.4
40.6
35.6
39.6
40.6
42.6
40.2
42
41.6
36.6
43.4
41.6
37
39.8
41
36
39.2
41
38
41.2
39.6
39
42
40.4
41.8
31.2
42.2
44.4
40
67.2
60.9
64.4
54.6
60.2
55.3
61.6
61.6
54.6
53.9
54.6
120.4
66.5
58.1
66.5
60.9
88.2
69.3
51.8
31.5
55.3
53.2
35.7
52.5
55.3
58.8
57.4
39.2
56
39.9
61.6
66.5
70.7
74.2
53.9
40.6
53.2
35.7
25.9
44.8
49
46.2
45.5
29.4
35
28.7
21.7
45.5
48.3
37.1
30.1
48.3
37.1
28
39.2
46.2
35.7
20.3
23.1
25.9
37.1
37.1
43.4
48.3
49
56.7
23.1
40.6
45.5
53.9
49
53.9
52.5
60.9
62.3
63
54.6
62.3
51.1
60.2
65.1
63
61.6
45.5
79.1
46.2
62.3
52.5
69.3
70.7
51.8
61.6
67.9
58.8
61.6
64.4
62.3
80.5
62.3
60.9
72.1
82.6
69.3
67.2
65.1
63.7
48.3
51.8
72.8
77
57.4
65.1
71.4
60.9
56.7
55.3
56
71.4
63.7
65.1
63
58.8
75.6
60.9
66.5
64.4
57.4
66.5
56
57.4
69.3
70.7
52.5
69.3
60.2
67.2
56
67.9
45.5
56
81.2
67.2
60.9
75.6
114.1
77.7
48.3
59.5
50.4
72.1
69.3
46.9
42
53.9
49.7
49.7
60.9
60.2
48.3
47.6
53.9
43.4
53.2
75.6
53.9
79.1
67.2
63
45.5
48.3
72.8
107.8
63
55.3
50.4
53.2
59.5
67.2
55.3
74.9
58.1
58.1
45.5
73.5
56
55.3
77
63.7
60.9
59.5
61.6
61.6
64.4
69.3
62.3
53.2
56.7
58.1
57.4
69.3
67.2
65.8
65.8
69.3
53.2
58.8
61.6
63
65.8
77.7
60.2
56.7
52.5
60.2
66.5
69.3
71.4
67.9
60.9
66.5
73.5
50.4
56.7
72.1
43.4
68.6
64.4
52.5
65.8
46.9
55.3
63.7
50.4
58.1
64.4
66.5
66.5
51.1
74.9
60.9
58.8
64.4
54.6
65.1
57.4
52.5
76.3
51.8
54.6
47.6
50.4
55.3
53.9
29.4
56.7
44.8
54.6
32.9
60.2
59.5
56.7
58.8
50.4
39.2
66.5
56.7
56
44.8
56.7
53.9
46.2
58.1
56.7
58.8
59.5
39.9
47.6
57.4
50.4
56.7
48.3
55.3
67.2
46.9
46.9
55.3
64.4
39.2
40.6
38.5
50.4
46.2
56.7
54.6
54.6
60.2
52.5
51.1
52.5
57.4
65.8
55.3
49
47.6
46.9
56.7
51.1
37.8
40.6
40.6
58.1
53.2
50.4
48.3
37.8
49.7
49.7
58.8
48.3
54.6
62.3
52.5
46.2
69.3
60.2
58.8
51.8
64.4
56.7
52.5
57.4
60.9
55.3
54.6
67.9
58.8
64.4
66.5
77.7
55.3
59.5
61.6
58.8
56.7
60.9
47.6
52.5
58.8
61.6
56.7
58.1
82.6
65.1
44.8
47.6
32.9
26.6
37.8
29.4
21.7
21.7
22.4
49
100.1
49
37.8
49
45.5
30.1
46.9
42.7
42
33.6
40.6
35.7
32.9
36.4
35.7
36.4
45.5
24.5
37.1
16.1
19.6
21.7
21.7
41.3
38.5
47.6
45.5
36.4
37.1
43.4
39.9
18.9
28.7
34.3
23.1
23.1
28
37.1
46.9
50.4
39.2
63
99.4
36.4
60.9
60.9
95.9
51.1
61.6
44.8
58.8
51.8
42
21
29.4
55.3
76.3
58.1
56.7
30.1
61.6
72.1
56.7
58.8
56.7
59.5
51.1
45.5
56
105
81.9
58.8
55.3
46.9
49
58.1
45.5
41.3
60.9
48.3
52.5
56.7
56
60.9
52.5
44.1
81.2
49
54.6
60.2
58.8
58.8
66.5
53.2
45.5
52.5
64.4
49
51.1
48.3
49.7
36.4
42.7
48.3
60.9
60.2
58.8
28
32.9
59.5
49.7
51.1
58.8
51.1
52.5
49
54.6
48.3
53.2
43.4
33.6
49
48.3
39.2
32.9
53.9
37.8
46.9
36.4
36.4
37.1
37.8
46.9
45.5
45.5
34.3
28
45.5
57.4
70.7
67.2
70
52.5
45.5
34.3
42.7
28.7
65.1
48.3
37.1
49.7
56
52.5
60.2
28.7
30.8
67.9
49.7
53.2
61.6
58.1
55.3
47.6
56
65.1
66.5
63
55.3
51.8
64.4
63.7
66.5
53.9
69.3
78.4
63.7
56.7
64.4
62.3
62.3
54.6
49.7
38.5
56
62.3
58.1
54.6
57.4
56
53.9
66.5
54.6
63.7
53.9
63
57.4
56.7
51.8
59.5
55.3
65.1
64.4
56.7
59.5
70
44.8
75.6
46.2
57.4
26.6
52.5
64.4
58.1
49.7
36.4
61.6
58.8
56
55.3
38.5
57.4
54.6
53.2
69.3
53.2
37.8
36.4
41.3
42.7
42.7
53.2
35
44.8
66.5
65.8
61.6
53.2
60.2
49
32.2
38.5
48.3
56
44.1
56.7
39.2
46.9
50.4
55.3
49.7
46.2
59.5
46.9
43.4
32.9
39.9
45.5
18.9
43.4
26.6
40.6
45.5
68.6
48.3
22.4
35.7
42.7
49.7
59.5
32.9
60.2
26.6
34.3
49
63
28.7
36.4
42.7
58.1
52.5
28.7
64.4
31.5
53.2
32.2
23.8
41.3
31.5
45.5
25.9
12.6
9.1
22.4
22.4
58.8
23.8
57.4
67.9
55.3
34.3
56
49
30.1
19.6
31.5
42.7
26.6
50.4
44.1
52.5
60.2
41.3
54.6
59.5
57.4
65.1
62.3
60.9
62.3
60.9
56
69.3
58.1
51.1
64.4
50.4
60.9
61.6
49
37.8
35
67.9
57.4
61.6
50.4
49
67.9
66.5
58.1
63.7
47.6
58.1
36.4
57.4
59.5
53.9
52.5
44.8
60.9
66.5
62.3
67.9
65.1
53.2
61.6
57.4
56
43.4
33.6
37.1
35.7
38.5
37.8
25.2
29.4
51.8
32.9
46.2
39.9
37.1
28.7
35
33.6
43.4
58.8
65.1
57.4
63
60.9
63.7
53.2
37.1
53.9
62.3
49.7
61.6
48.3
63
64.4
53.2
48.3
64.4
51.1
38.5
51.1
56.7
43.4
45.5
41.3
34.3
39.2
30.1
32.9
30.8
30.1
36.4
105
35
40.6
39.2
47.6
30.1
39.2
60.2
58.8
58.1
46.2
57.4
62.3
55.3
63
56
52.5
57.4
70
59.5
61.6
59.5
67.9
66.5
58.1
63
58.8
70
58.1
57.4
49
56
53.2
42
46.2
53.2
57.4
52.5
63.7
57.4
44.1
57.4
46.2
56.7
41.3
53.2
35.7
56
30.8
38.5
45.5
30.1
41.3
56
53.9
55.3
30.8
76.3
40.6
23.1
46.2
38.5
58.1
44.8
50.4
49.7
47.6
37.1
41.3
41.3
42.7
41.3
42
45.5
44.1
48.3
46.2
28.7
32.2
47.6
53.9
51.1
32.9
46.9
42.7
42.7
40.6
56
62.3
47.6
58.1
62.3
49
53.2
59.5
51.1
54.6
60.2
44.8
32.9
48.3
51.8
43.4