5 is not the midpoint between 1 and 10?

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

23 March 2008

Here is a simple question: what number lies in the middle of the numbers from 1 (one) to 10 (ten)? Five, isn’t it? Actually, NO! To find out, try this experiment: get 10 small pieces of paper and label them with the numbers from one to ten.

Now arrange the papers with the numbers in numerical order. Next, place one hand on the paper labeled “5” and then count the number of papers on either side. Are they equal? No! One side has four and the other has five. Thus the number 5 does not lie in the middle of one and ten!

But how can that be while everybody knows that 10 divided by two equals five? Well, the catch is that if want to know the number in the middle, you don’t divide by two. The correct method is to find the average value (strictly speaking, the “mean”). That entails adding all the numbers from one to ten and dividing the answer by ten. The result is 5.5. And if you place you hand somewhere between the paper labeled “5” and the one marked “6”, you will count the same number of papers on either side – five each.

This problem is encountered many times by opinion surveyors when the ask respondents to gauge an issue on a scale of scores. For example, “How do you rate our overall quality of service on a scale of 1 (very bad) to 5 (very good)”

Now that seems like an honest and fair question to ask but there might be a problem with the answers given. Some respondents might feel that the service was slightly above average and indicate a score of 3. In their mind, they are thinking that since a half of 5 is 2.5, a score of 3 is “slightly above average”. However, 3 lies right in the middle of the numbers from one to five. It is the average – add them and divide by five 3.

For this reason, one might feel tempted to widen the scale to go all the way to 10. But still, another problem might arise where a respondent is of the opinion that your service was average and they give you a score of 5. Unfortunately, on that range of choices, 5 is below average! (The average is 5.5, as shown above). In addition, a scale running from one to ten might appear unnecessarily complicated.

One way of overcoming this problem is to start the scale from zero going up to five. That gives respondents six choices with an average value of 2.5. Thus the person who wants to score slightly above average will rightly indicate “3” (without thinking much about it). Those who want to select the middle score will be forced to think whether to go for “2” or “3”. This is good because sometimes you want people to think harder about their responses.