﻿ One thing that most UKCAT candidates get wrong 09 Nov 2012 Print One thing that most UKCAT candidates get wrong

I was looking through some results of UKCAT test questions the other day and I came across one question that had a surprisingly high rate of incorrect answers. So I thought I’d write a few words here to try and clarify things a little: which mistake should UKCAT candidates really avoid?

Some context first

Before answering this question, let’s put some context in place. A picture, they say, is worth a thousand words (although who ‘they’ are, is never made clear) and so is an example problem.

Suppose we had the following table of data and associated question: Q. What is the percentage of left-handed people across France and Germany?

On the face of it this looks like a very easy question, almost too easy. Surely it is simply the sum of all the percentages (9.7+13.9=23.6) divided by the number of items we are averaging
(2) and we get the simple calculation:

23.6 / 2 = 11.8

Right? Wrong!

Hands up everybody who made this mistake. I’m sorry, I meant ‘hands up in the air everybody who made this mistake’ otherwise it will just make your eyes water.

The problem here is that simply taking the average of the percentages will only work in the rare cases when the populations are equal and both countries’ contribution is of equal weight.

So what methodology should we use?

Since that isn’t the case here, Germany contributes 824.59 to the overall average for every 1% of left-handed people whereas France only contributes 610.13. This weighting needs to be accounted for when calculating the overall average.

The solution is to calculate the total number of left-handed people in France and Germany individually and add them together. Then we must divide this number by the total population of the two countries combined.

The total number of left-handed people in a country is the population of the country multiplied by the prevalence of left-handed people in that country. So, for France this is:

61013*9.7=591826.1

Similarly, for Germany it is:

82459*13.9=1146180.1

The total number of left-handed people across both countries, therefore, is:

591826.1+1146180.1=1738006.2

The total population across the two countries is:

61013+82459=143472

We can now calculate the percentage of left-handed people across France and Germany combined which is:

1738006.2/143472=12.1%

A piece of good advice

Note that I took one or two shortcuts during this calculation by not dividing by 100 for the percentages or accounting for the thousands in the population figures. This was because I knew I was going to reverse the percentages in the later calculation and everything would cancel out in the end. There’s no point doing unnecessary work and taking up extra time.

So what is the take-away here? Well, some things are more complex than they seem and always be suspicious if a question has an overly simply solution to it. Moreover, when you are dealing with percentages and averages, keep in mind that you may not shortcut your calculation because that very often leads to wrong results.

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