“There are Lies, Damn Lies, and Statistics�
Quote attributed to Benjamin Disraeli, British Prime Minister 1868, and 1874-1880
College Entrance
You are responsible for admitting new students to the college.
You have six places available.
Who do you admit?
Exam Scores UNSCALED SCORES: Ranking made by total raw score A
B
C
D
E
F
G
H
Total
Alan
100
30
47
72
40
75
30
47
441
Bart
90
38
43
60
20
65
48
70
434
Charlie
61
36
40
45
41
55
62
80
420
Derek
63
32
51
90
30
70
47
35
418
Edgar
56
55
41
82
45
40
49
41
409
Frank
80
45
49
64
65
45
38
20
406
George
23
47
45
55
60
80
32
60
402
Harry
40
35
52
70
56
20
60
65
398
Ian
85
40
60
40
28
51
55
30
389
John
72
54
50
10
25
35
66
75
387
Kyle
48
57
55
34
70
60
36
10
370
Lars
10
60
59
20
35
30
70
58
342
College Entrance ď ľ
The same scores are now scaled to give each exam marks from 0 (lowest) to 100 (highest), with intermediate scores scaled accordingly.
ď ľ
Now who do you admit to the college?
Exam Scores SCALED SCORES: High score = 100 and low score = 0. Scale others A
B
C
D
E
F
G
H
Total
Lars
0
100
95
12
30
17
100
69
423
Kyle
42
90
75
30
100
67
15
0
419
John
69
80
50
0
10
25
90
93
417
Ian
83
34
100
38
6
52
62
29
414
Harry
33
17
60
75
72
0
75
79
411
George
14
57
25
56
80
100
5
71
408
Frank
78
50
45
68
90
42
20
14
407
Edgar
51
83
5
90
50
33
48
44
404
Derek
59
7
55
100
20
83
43
36
403
Charlie
57
20
0
44
42
58
80
100
401
Bart
89
27
15
63
0
75
45
86
400
Alan
100
0
35
77
40
92
0
53
397
College Entrance ď ľ
Rather than going on raw scores or on scaled scores, someone suggests ranking.
ď ľ
So, with students ranked for each test (1 for highest, through to 12 for lowest), who do you now admit?
Exam Scores POSITION RANKED SCORES: High score rank 1, low score rank 12 A
B
C
D
E
F
G
H
Total
Frank
4
6
7
5
2
8
9
11
52
Kyle
9
2
3
10
1
5
10
12
52
Charlie
7
9
12
8
6
6
3
1
52
Harry
10
10
4
4
4
12
4
4
52
Ian
3
7
1
9
10
7
5
10
52
Edgar
8
3
11
2
5
9
6
8
52
Derek
6
11
5
1
9
3
8
9
52
George
11
5
9
7
3
1
11
5
52
Bart
2
8
10
6
12
4
7
3
52
Alan
1
12
8
3
7
2
12
7
52
John
5
4
6
12
11
10
2
2
52
Lars
12
1
2
11
8
11
1
6
52
What do you mean, mean?
The average (or mean) value is often quoted as the most sensible measure to give to determine the centre of the data.
In Britain in the 50s, the figure of 3.6 was obtained for the average family size.
This accounts for why so many 3-bedroom housed were built.
However, there were more families with 2 people or 5 people, than either 3 or 4.
Averages of averages
One commonly made mistake is to think there is anything valid about an average of a set of averages
Teachers do this all the time --- how do you think we get your end of year grade?
There is an activity, “Average of Averages”, which should highlight this danger.
Faulty Comparisons ď ľ
The largest proportion of car accidents are caused by people in the 20 to 29 age range. By the same token the age range of 90 to 99 is one of the safest groups.
Faulty Comparisons
“Flying has become more dangerous” is shown by the fact that more people were killed in plane crashes in 1998 than in 1910.
Improper sampling
ď ľ
The Literary Digest, in 1936, predicted, on the basis of a massive telephone survey, an election victory for Republican candidate, Landon.
Improper sampling
ď ľ
ď ľ
In the event, the Democratic candidate, Roosevelt, won a landslide victory. Why? The people who voted for Roosevelt were poor, and had no telephones!
Misleading Presentation Look at the graph opposite. On the basis of this graph, would you invest in this company?
Price of Company X Shares 250 200 Share price
ď ľ
150 100 50 0 1992
1994
1996
1998
2000
Year
2002
2004
2006
Misleading Presentation How about this view of the data? On the basis of this graph, would you invest in this company?
Price of Company X Shares 184 183.5 183 182.5 Share price
ď ľ
182 181.5 181 180.5 180 179.5 179 1996
1997 Year
1998
Biased Perspective ď ľ
Deaths on the road rises by 100% in April. Deaths on the road
or ď ľ
Only 1 more road fatality this month than in March.
March
April
1
2
Biased Perspective
Rate of rise of inflation falls to just 1%. Rate of Inflation
or
Inflation now stands at over 40%.
2003
2004
40.0
40.4
Invalid Argument