Who hates reading about statistical results and knowing that the results are incorrect. I have read many statistical results that say one thing and the following month the numbers are totally the opposite. There are several reasons why numbers can be misleading and I am going to focus on six ways (arithmetical error, false percentage, ficitious precision. misleading presentation, incomplete data, faulty comparison) in which numerical data can be misleading.

The first is arithmetical error. We all tend to have the habit to accept things that are in print as being true, only because we believe that if it was not true they would not print it. The sad truth is that sometimes it is not correct, arithmetic errors occassionally appear in print and if it matters to you, it is best to check the author’s calculations. As stated in the book titled, Practical Statistics, there was an article on the first Kinsey Report, Professor W.A. Wallis pointed out that there were so many arithmetical mistakes that it was not even clear how many men had actually been studied. On one page of the report it stated that the observations were made on a total of 12,214 men, while on another page is a map showing 427 dots, each of which is said to represent 50 men; if so, there were 50 x 427 = 21, 350 all together. Or again, the table shows the number of men 30 years of age or less as being 11,467, while in the very next table the same group total is shown as 11,985. When two such figures differ, it stands to reason that at least one them must be wrong. (Joun. Amer. Statist. Assoc., 1949, pp. 463-84).

We learn about percentage when we are in high school and if we are not careful we can forget little details, which in the present case would leave us to believe some false figures. In the book titled, Practical Statistics it had four scenarios that could lead us to false calculations.

The first is beware of adding percentages, an example they give is: the price of men’s haircuts must be increased. In the past 2 years, wages have risen 10%, combs, brushes, and othe materials have gone up 8%, shop rentals have gone up 10%, and electric light bills have gone up %5 - a total rise of exactly 33%. But this total is wrong. If each of the items making up the cost of each haircut had risen 10%, the total cost would only rise by 10%.

The second is the decreasing percentage. Apples are 100% cheaper than last year. Does this really mean they’re giving apples away free? For 100% less than any quantity is zero.

The third is beware of huge percentages. Sarah earns 1,000% more than Cindy. It sure does sound like Sarah make a great deal more than Cindy. This is actually just saying Sarah earn 11 times more than Cindy.

The fourth one is to beware of percentages unaccompanied by the actual numbers. The example that the book titled, Practical Statistics, used was that in a special experiment, we found that 83^.3% people got relief from Dumpties within 60 seconds. They conveniently forgot to mention that the experiment concerned 6 people, 5 of whom got the stated relief. An if you test enough small groups. sooner or later you’re almost certain to get one group to suit your purpose, purely by chance.

This one is fictitious precision. When you read a statististics and it says something like 1,207 or 111.2 people, make sure that the degree of precision claimed is warranted by the evidence, so just be aware of numbers that are exact to such a degree.

When looking at presentations one must remember that they are trying to make their results look good, so there may be some that suggest a different conclusion from others. Alot of the times, the person who prepared the presentation only wants us to take a single glance, it is when we actually take the time to read the information that units are ommited, values are not shown. So when looking at presentations of data, please take the time to look over the data and make sure it makes sense.

This can be one of the worse ways to mislead in numbers. When there is incomplete data the numerical statistics is distorted. An example used in Practical Statistics, was in Time Magazine (June 12, 1964) it quoted some sober statitistics compiled in recent months by various state authorities; concerning the safety of driving in large cars versus small cars. Three independent reports showed the risk of being killed in a accident was up to 5.5 times greater for person in small cars as compared with large cars. This would make a good advertising point if you were selling large cars, wouldn’t it? But, as Time pointed out, this is only part of the story. For the same official report also showed that small cars don’t get into as many accidents as large cards, so the overall risk is about the same in both.