From the Exploring Data website - http://curriculum.qed.qld.gov.au/kla/eda/
© Education Queensland, 1997
The Barramundi Dataset
This dataset contains 1000 integers having a normal distribution with mean = 55 and sigma = 12. The
data fit nicely onto both sides of an A4 sheet of paper. I have used this data to simulate a population
of barramundi in the Fitzroy river, but you of course can make up your own scenario. By having
students 'catch' samples of size 2, size 8 and size 32, the effect of increasing the sample size on the
interval estimate of the population mean can be observed. Here is how I do it:
Every student selects a sample of two 'barra' at random and calculates the mean length. This is their point
estimate of the average length of a barramundi in the Fitzroy River. The student calls out the mean, which is
typed into a statistics program datasheet (e.g. NCSS Jr). This set of data illustrates a sample distribution for a
sample of size 2.
Use your statistics program to calculate the mean and standard deviation of this set of sample means
and construct a histogram. Discuss what the summary statistics and the histogram are telling us. It is
important to stress that this 'sample distribution of the mean' doesn't actually exist, as in reality just a
single sample is taken rather than a large number of samples. Cut and paste the histogram into a word
processing document for later use.
Repeat the above procedure, but with each student selecting a random sample of size 8. Paste the
histogram into the same document.
Repeat with each student selecting a sample of size 32. Students may want to work in pairs as it is
probably more efficient.
As a class (or in groups) look at the three histograms, the three sample means and the three sample
standard deviations. What is the effect of selecting a larger sample? How do the means of the sample
distributions compare? How do the standard deviations of the sample distributions compare? Why do
large samples give you better information than small samples?
From the Exploring Data website - http://curriculum.qed.qld.gov.au/kla/eda/
© Education Queensland, 1997
Barramundi Length
A
50
68
36
65
39
76
78
32
71
51
B
41
48
58
37
52
46
64
50
22
44
C
38
59
44
54
65
54
68
57
38
30
D
68
46
44
35
77
67
59
53
60
69
E
43
54
54
54
55
50
45
58
64
56
F
66
56
39
54
67
50
40
70
57
53
G
49
43
27
35
67
39
68
43
31
56
H
56
46
53
61
49
57
83
55
60
74
I
58
35
47
54
51
66
61
55
73
72
J
45
49
31
42
63
66
45
67
66
69
49
41
77
37
56
55
56
53
71
55
70
48
66
68
70
55
41
37
44
46
54
52
69
59
63
61
57
49
61
40
55
69
49
56
72
46
42
74
31
37
38
60
52
47
54
52
69
50
59
31
47
68
41
54
43
52
55
69
45
46
67
47
31
68
49
58
58
46
62
52
39
58
65
73
74
54
50
52
78
63
70
69
53
54
26
55
54
73
64
53
41
72
55
32
32
50
57
62
32
59
55
40
38
61
46
58
54
77
49
61
54
53
62
46
45
36
61
51
70
57
62
56
77
61
63
42
53
63
63
39
47
61
45
60
48
54
51
43
44
60
55
64
72
51
30
60
66
55
49
42
51
30
54
39
83
68
33
41
58
59
52
46
40
36
51
62
72
57
75
59
72
73
67
39
45
32
51
69
56
65
43
63
61
51
25
64
54
43
65
70
63
66
75
30
55
34
69
55
57
40
52
52
73
43
86
53
73
46
43
38
59
60
53
52
47
42
42
51
48
71
49
46
66
52
35
66
66
47
57
68
56
61
44
31
29
61
46
47
38
49
51
69
72
40
49
62
51
65
43
70
71
48
63
67
43
80
42
65
24
52
62
52
62
54
38
84
42
42
60
65
69
55
76
45
68
42
46
54
41
46
42
75
65
52
57
66
67
49
27
62
54
41
61
52
46
66
63
61
56
35
35
57
75
59
50
61
52
52
72
18
51
76
71
42
49
51
50
42
62
33
47
43
50
81
66
69
41
42
43
63
57
45
61
76
74
24
50
54
68
46
71
42
73
64
75
37
63
74
42
55
54
57
52
42
69
67
54
50
71
49
37
78
56
40
65
56
59
67
51
45
72
44
52
64
89
32
55
31
68
78
50
53
65
52
54
44
43
63
66
39
46
57
67
54
48
63
71
63
59
69
From the Exploring Data website - http://curriculum.qed.qld.gov.au/kla/eda/
© Education Queensland, 1997
Barramundi Length
K
58
38
53
40
52
74
40
74
70
50
L
53
53
67
54
45
57
55
62
62
56
M
61
44
58
69
63
51
59
75
55
61
N
68
35
83
73
43
49
58
67
54
72
O
51
62
73
51
37
43
61
43
47
42
P
40
58
63
37
41
64
66
57
61
65
Q
40
60
60
61
41
51
38
81
42
38
R
67
64
67
68
62
31
45
50
53
69
S
62
67
58
59
68
14
48
50
45
63
T
37
47
43
42
55
48
62
59
73
55
67
31
60
73
40
86
47
54
61
62
39
46
50
75
46
68
62
42
54
56
46
33
38
56
70
45
54
51
39
58
65
48
41
47
76
52
69
39
44
64
34
72
52
49
61
66
63
62
58
30
66
51
43
63
66
48
54
27
38
48
67
52
28
61
67
69
49
34
54
52
54
42
61
49
67
81
57
58
47
61
69
58
44
80
64
73
64
75
70
20
53
61
46
58
70
43
56
63
39
50
48
59
55
41
41
46
56
59
38
25
56
62
70
68
70
76
71
47
43
55
43
75
46
66
58
54
42
81
64
63
32
61
58
75
43
44
81
55
42
59
39
40
60
41
49
86
36
43
59
65
55
57
51
41
54
57
47
67
50
53
50
60
41
56
48
63
74
32
66
59
67
54
54
58
38
74
56
50
29
45
62
69
56
48
68
57
47
38
58
62
49
48
53
48
56
45
55
50
50
47
38
52
59
81
71
62
31
44
60
57
69
79
25
47
76
68
58
56
53
39
58
38
56
64
36
61
72
50
51
58
45
64
53
64
48
37
55
50
68
43
61
69
31
64
42
45
54
62
59
55
56
36
46
31
47
51
57
38
64
49
93
55
64
59
43
44
47
45
62
68
44
81
37
71
31
68
66
57
55
53
50
60
70
62
55
66
53
65
58
63
57
51
61
41
61
60
44
66
51
56
61
54
65
54
49
58
35
57
63
62
49
56
50
54
61
46
43
57
56
59
50
42
50
66
74
46
67
65
53
56
58
69
65
45
56
41
47
53
58
50
57
40
51
52
34
59
56
34
51
62
40
68
65
54
76
66
59
46
68
55
50
54
47
69
47
36
44
67
41
61
70
57
62
47
52
54
59
55
58
67
47
46
43
40
55
63
37
66
59
66
55
73
46
54
60
70
52
55
28
47