1. College Entrance You are responsible for admitting new students to the college. You have six places available. Who do you admit?

2. Exam Scores UNSCALED SCORES: Ranking made by total raw score ABCDEFGH Total Alan 10030477240753047441 Bart 9038436020654870434 Charlie 6136404541556280420 Derek 6332519030704735418 Edgar 5655418245404941409 Frank 8045496465453820406 George 2347455560803260402 Harry 4035527056206065398 Ian 8540604028515530389 John 7254501025356675387 Kyle 4857553470603610370 Lars 1060592035307058342

3. College Entrance The same scores are now scaled to give each exam marks from 0 (lowest) to 100 (highest), with intermediate scores scaled accordingly. Now who do you admit to the college?

4. Exam Scores SCALED SCORES: High score = 100 and low score = 0. Scale others ABCDEFGH Total Lars 01009512301710069423 Kyle 4290753010067150419 John 698050010259093417 Ian 8334100386526229414 Harry 331760757207579411 George 1457255680100571408 Frank 7850456890422014407 Edgar 518359050334844404 Derek 5975510020834336403 Charlie 5720044425880100401 Bart 892715630754586400 Alan 100035774092053397

5. College Entrance Rather than going on raw scores or on scaled scores, someone suggests ranking. So, with students ranked for each test (1 for highest, through to 12 for lowest), who do you now admit?

6. Exam Scores POSITION RANKED SCORES: High score rank 1, low score rank 12 ABCDEFGH Total Frank 46752891152 Kyle 9231015 1252 Charlie 79128663152 Harry 10 444124452 Ian 37191075 52 Edgar 83112596852 Derek 61151938952 George 1159731 552 Bart 281061247352 Alan 1128372 752 John 5461211102252 Lars 1212118 1652

7. 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.

8. 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.

9. Faulty Comparisons 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.

10. 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.

11. Improper sampling The Literary Digest, in 1936, predicted, on the basis of a massive telephone survey, an election victory for Republican candidate, Landon.

12. Improper sampling In the event, the Democratic candidate, Roosevelt, won a landslide victory. Why? The people who voted for Roosevelt were poor, and had no telephones!

13. Misleading Presentation Look at the graph opposite. On the basis of this graph, would you invest in this company?

14. Misleading Presentation How about this view of the data? On the basis of this graph, would you invest in this company?

15. Biased Perspective Deaths on the road rises by 100% in April. or Only 1 more road fatality this month than in March. Deaths on the road MarchApril 12

16. Invalid Argument

17. Biased Perspective Rate of rise of inflation falls to just 1%. or Inflation now stands at over 40%. Rate of Inflation 20032004 40.040.4

18. “There are Lies, Damn Lies, and Statistics” Quote attributed to Benjamin Disraeli, British Prime Minister 1868, and 1874-1880 Reference: How to Lie with Statistics By Darrell Huff