Thinking Skills: Critical Thinking and Problem Solving

104 Unit 3 Problem solving: basic skills

This could, in fact, have been solved without

going to percentages by looking at the relative

sizes of the components in the table for each

country. It would have been quicker to do this,

but would have taken more mental arithmetic.

Commentary

This question is a little more difficult than

some we have seen so far. There are several

ways to approach it. We can note that if we

knew the actual averages for the four colleges

the newspaper did include, it might be possible

to see if these averages disagreed with an

estimated average for the five colleges, and the

direction of the error would give some

indication of which one was forgotten.

Looking at the ‘averages’, the approximate

values (we have to estimate these from the

graph) are 9, 19, 35 and 16 respectively for 1, 2,

3 and 4 A Levels. Multiplying these by^54 (to

correct for the fact that they were divided by 5

instead of being divided by 4), we get

(approximately): 11, 24, 44 and 20.

If we were being very systematic, we could

now compare these with all sets of four

averages, but it would take a long time.

Instead, let us note that the 11 looks a little low

for the average of 1 A Level, as does 24 for the

average of 2. 44 for the average of 3 looks very

low and 20 for the average of 4 looks far too

high. From this, we may suspect that

Danbridge has been missed as it is higher than

the others for 3 A Levels and lower for 4.

We can check this by averaging one of the

columns for the other four colleges (preferably

use 3 or 4 A Levels as they look to have the

biggest discrepancy) and comparing the

results – try this for yourself and see whether

you can confirm that Danbridge is the college

whose results are missing.

The table shows the results of a questionnaire,

asking the five colleges in a town the proportion

of students taking 1–4 A Level subjects.

Percentage of students taking

number of A Levels shown

College 1 2 3 4

Abbey Road 13 25 42 20

Barnfield 5 18 55 22

Colegate 24 36 28 12

Danbridge 16 18 61 5

Eden House 10 14 48 28

The local newspaper (forgetting that there might

be different total numbers of students in the

five colleges) just added the numbers together

and divided by five to produce a percentage

graph for the town as a whole. However, they

forgot to add in the data for one college so their

percentages did not add up to 100.

30

20

10

0

123

Number of A Levels

Percentage of students

4

Which one did they forget?

Activity

Summary

•   We have learned how data may be

represented in more than one way and the

importance of systematic comparisons

between two sets of data in ascertaining

that they are the same.

•   We saw that reading graphs and tables

carefully is necessary in order not to make

errors in identifying similarities.