Thinking Skills: Critical Thinking and Problem Solving

5.4 Data analysis and inference 225

We saw in Chapter 3.8 that problems
involving making inferences from data or
suggesting reasons for the nature of the data
may appear in either the critical thinking or
the problem-solving sections of thinking
skills examinations. In this type of question
for thinking skills examinations at AS Level
and those using short questions, the nature
of the data is usually presented explicitly and
little analysis is required. This chapter deals
with longer questions which may appear in
Cambridge A2 examinations, BMAT Paper 1
and AQA Unit 2.
Data analysis may be carried out for a
number of reasons and using a wide variety of
methods. Some data is collected to investigate
a hypothesis or to make decisions on a course
of action (for example, will reducing a speed
limit reduce road accidents?). Other data is
collected as routine and analysis may be much
more open-ended, to try to discover patterns
and trends.
Examination questions normally use several
of the skills introduced in Unit 3. Data
selection and processing are obvious, but
searching and suggesting hypotheses for
variation are also central to this analysis. This
type of question does not cover statistical
significance finding, but the search for
patterns in complex data is an important part
of problem solving. The following
introductory example uses relatively simple
data to illustrate some of the techniques used.

5.4 Data analysis and inference

The table below shows class sizes in publicly

funded elementary schools.

Percentage of pupils by

class size

Average

class size

Year <19

pupils

19–25

pupils

>25

pupils

2006 12.7 50.7 36.6 23.6

2007 15.3 58.9 25.8 22.8

2008 15.5 62.6 21.9 22.6

2009 16.1 62.9 21.0 22.5

2010 21.6 53.6 24.8 22.4

2011 20.2 56.7 23.2 22.5

Summary Statistics for Schools in Scotland 2011

1    Draw a graph showing how the percentage

of pupils in each class size has varied over

the period shown. Express what is shown

by this graph in a few short sentences.

2    The table shows the percentage of pupils

in classes of the size shown. If we assume

that the average class size of classes with

less than 19 pupils is 10 and the average

for classes over 25 is 30, what are the

percentages of actual classes for the three

sizes in 2011?

3    The average class sizes have remained

constant over the period shown but there

have been significant changes in the

proportions of pupils in the various sizes

of class. How is this possible?

Activity