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In statistics, we use two key words: variable and observation. It is important to understand the difference in their meanings. A variable is a characteristic or an attribute that can have different values; an observation is the value of a variable that has actually been counted, measured or observed. Some variables are shown below, with a list of possible observations next to each one.

Glossary

variable A variable is a factor that can change in quality, quantity, or size, which you have to take into account in a situation.

characteristic The characteristics of a person or thing are the qualities or features that belong to them and make them recognizable.

attribute An attribute is a quality or feature that someone or something has.

Variable	Observations
favourite colour	purple, blue, orange
number of pets	3, 1, 0
time spent reading	2 hours, 1 hour
number of children in a family	1, 5, 2
eye colour	brown, blue
number of letters in a name	10, 4, 8

The observations for a variable can be described as quantitative or qualitative, depending on what the information is about. Quantitative data is something which can be measured or counted using a number. Qualitative data represents a characteristic that uses words to describe it but does not use any numbers.

Examples of quantitative variables are:

time taken to complete a test

the number of books in a library

the highest temperature in a month

Examples of qualitative variables are:

the nationality of people in a cinema

the favourite sport of children in a school

the colours of balloons at a party

Exercise 6

Match the words on the left to their definitions on the right.

1 A variable	a Data which can be measured or counted using a number.
2 An observation	b The value of a variable that has actually been counted, measured or observed.
3 Quantitative	c Data representing a characteristic that uses words to describe it but does not use any numbers.
4 Qualitative	d A characteristic or an attribute that can have different values.

Exercise 7

State whether each of the following variables is quantitative or qualitative:

1 number of pages in a book

2 names of students in a class

3 hair colour

4 weight of apples in a bag

5 height of trees in a park

Exercise 8

Answer these questions.

1 Explain the difference between a quantitative and a qualitative variable.

2 Give an example of each type of variable.

3 Explain why:

‘type of tree’ is a qualitative variable

‘number of pupils in a class’ is a quantitative variable

Exercise 9

Without looking back at the section ‘What is statistics?’, put these statistical stages into the correct order.

1 organize data

2 present data

3 collect data

4 interpret data

Exercise 10

Use the words in the box to complete these questions about the stages above.

data features patterns sets of data

display method present technique

1 What type of ________are we interested in?

2 Which data collection ________shall we use?

3 What ________shall I use to summarize my data?

4 What interesting ________or ________can I see?

5 What questions do my ________answer?

6 What is the clearest way to ________and ________my data?

Exercise 11

Match the questions in Exercise 10 to the stages in Exercise 9.