A categorical data

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Chapter 9E
Types of data
It is vital that we understand the various types of data that we are able to gather (shown
below)
Nominal
Categorical
(qualitative)
Ordinal
DATA
Numerical
(quantitative)
Discrete
Continuous
Categorical data are observations that fit some qualitative category. Data of this type do not
involve numbers or measurements
Numerical data, on the other hand, involve quantitative amounts. Contrasting categorical,
numerical data engages with numbers and measurements, such as, number of pets, school
pencils and handbags or how high can a plane fly, the daily temperature etc
** Here is a worked example to help you with the process of finding particular data
assigned to specific questions
WORKED EXAMPLE (1)
page 327
State whether the following pieces of data are categorical or numerical
a) The value of sales recorded at each branch of a fast – food outlet
b) The breeds of dog that appear at a dog show
THINK
WRITE
a) The value of sales at each branch can
be measured
a) The breeds of dog at a show cannot
be measured
The value of sales are numerical data
The breeds of dog are categorical data
Both data’s, numerical and categorical, have two categories attached
The numerical data that we use falls into two categories
1. Discrete
2. Continuous
Discrete data are responses, observations or records that can take only a certain, set
values.
Examples of discrete data would include, for example: the number of children
in a family, the number of marks obtained in a test or the number of students in a
class (you cannot have half a student)
Continuous data may take any value within the range of the data.
For example: a person’s height (within the range of human heights) not certain
fixed heights, time in a race (measure it to fractions of a second), a dog’s weight or
the length of a leaf
However, the categorical data is divided into
1. Nominal
2. Ordinal data
Keep in mind, that if there is no order associated with the categories formed by the data,
then there are termed nominal data
For example: answers to questions about a student’s hair colour or method of
transport used to travel to school
When the data categories are aligned or some qualitative scale, they are termed ordinal data
A response to a question on a scale, for example: strongly disagree to strongly
agree, would constitute ordinal data (that is, some order is implied)
**Worked example 2 clearly identifies between what is discrete or continuous data
WORKED EXAMPLE (2)
page 328
State whether each of the following records of numerical data is discrete or continuous
a) The number of people in each car that passes through a tollgate
b) The mass of a baby at birth
THINK
WRITE
a) 1. The number of people in the car
must be a whole number (you cannot
count half a person)
2. Give a written answer
b) 1. A baby’s mass can be measured to
various degrees of accuracy
2. Give a written answer
The data are numerical and discrete
because the answer to this observation is a
set value (number of people in the car)
The data are numerical and continuous
because the mass of the baby is within the
range of data (how much the baby weighs, in
kilograms)
Now that I hope you have a fair understanding of what chapter 9E is about, test
yourself 
Question 1 (similar to worked example 1)
State whether the data collected in each of the following situations would be
categorical or numerical
a) The number of matches in each box is counted for a large sample of boxes
b) The sex of respondents to a questionnaire is recorded as either M or F
c) A fisheries inspector records the lengths of 40 cod
d) The occurrence of hot, warm, mild and cool weather for each day in January is
recorded
Question 2
For each of the following, state if the data are categorical or numerical. If numerical,
state if the data are discrete or continuous
a)
b)
c)
d)
The number of students in each of your multiple dance classes
The teams people support at a soccer match
The brands of chocolate sold at your Woolies
The heights of people in your mini golf club
Question 3 – multiple choice
The number of people who are using a particular bus service are counted over a 2 –
week period. The data formed by this survey would best be described as:
A
categorical data
B
numerical and discrete data
C
numerical and continuous data
D
quantitative data
Question 4
The graph at right shows a boy’s shoe size each year for 10 years. Describe the data
in this example
Answers!!!
1. a) Numerical
b) Categorical
c) Numerical
d) Categorical
2. a) Numerical and discrete
b) Categorical
c) Categorical
d) Numerical and continuous
3. B
4.
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