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 ABCDEFGH Total Alan Bart Charlie Derek Edgar Frank George Harry Ian John Kyle Lars

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?

Exam Scores SCALED SCORES: High score = 100 and low score = 0. Scale others ABCDEFGH Total Lars Kyle John Ian Harry George Frank Edgar Derek Charlie Bart Alan

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?

Exam Scores POSITION RANKED SCORES: High score rank 1, low score rank 12 ABCDEFGH Total Frank Kyle Charlie Harry Ian Edgar Derek George Bart Alan John Lars

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

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!

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

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

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

Invalid Argument

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

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