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Classifying Data, SM-Bank 016 MC

The following question was asked in a survey.

'What month were you born?'

How would the responses be classified?

  1. Categorical, ordinal
  2. Categorical, nominal
  3. Numerical, discrete
  4. Numerical, continuous
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\(A\)

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\(\text{Months are names and so categorical data and}\)

\(\text{they are ordered}\)

\(\longrightarrow\ \text{Categorical, ordinal.}\) 

\(\Rightarrow A\)

Classifying Data, SM-Bank 014 MC

Which of the following is an example of categorical nominal data?

  1. Gold, Silver, Bronze medals
  2. Small, Medium, Large
  3. French Bulldog, Poodle, Cavoodle
  4. First place, Second place
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\(C\)

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\(\text{French Bulldog, Poodle and Cavoodle are types of dogs (order not important) }\)

\(\longrightarrow\ \text{categorical nominal}\)

\(\Rightarrow C\)

Classifying Data, SM-Bank 013

Which of the following is an example of categorical ordinal data?

  1. Pink, Blue, Mauve
  2. Small, Medium, Large
  3. Apple, Pear, Orange
  4. Labrador, Beagle, Poodle
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\(B\)

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\(\text{Small, Medium, Large are categories with an order }\longrightarrow\ \text{categorical ordinal}\)

\(\Rightarrow B\)

Classifying Data, SM-Bank 010

State whether the following categorical data is nominal or ordinal.

  1. Rating exam questions as easy or hard.  (1 mark)

  2. Listing the colours of cars passing the bus stop during period 3.  (1 mark)

  3. Recording dietary preferences such as vegan, gluten-free, vegetarian.  (1 mark)

  4. Receiving an A, B, C, D or E on a report card.  (1 mark)

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a.    \(\text{Ordinal}\)

b.    \(\text{Nominal}\)

c.    \(\text{Nominal}\)

d.    \(\text{Ordinal}\)

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a.    \(\text{The data is ranked}\ \longrightarrow\ \text{Ordinal}\)

b.    \(\text{Colours are the names assigned}\ \longrightarrow\ \text{Nominal}\)

c.    \(\text{Preferences are the names assigned}\ \longrightarrow\ \text{Nominal}\)

d.    \(\text{Grades rank the data}\ \longrightarrow\ \text{Ordinal}\)

Classifying Data, SM-Bank 009

State whether the following data is categorical or numerical.  If numerical, state whether discrete or continuous.

  1. The distance thrown by the 15 years javelin champion.  (1 mark)

  2. The types of fruit used in a fruit salad.  (1 mark)

  3. The number of students travelling to the Year 7 camp by bus.  (1 mark)

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a.    \(\text{Numerical continuous}\)

b.    \(\text{Categorical}\)

c.    \(\text{Numerical discrete}\)

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a.    \(\text{Data is a measurement}\ \longrightarrow\ \text{Numerical continuous}\)

b.    \(\text{Fruit is grouped into categories or types}\ \longrightarrow\ \text{Categorical}\)

c.    \(\text{Students can be counted}\ \longrightarrow\ \text{Numerical discrete}\)

Classifying Data, SM-Bank 008

Match each variable with its classification on the right.  (2 marks)

\begin{array} {ll} \text{A.  Hair colour of students in Year 7} &\text{1.  Numerical discrete} \\\text{B.  Heights of players in the Boomers basketball team} & \text{2.  Categorical ordinal} \\\text{C.  The number of people living in each household in NSW}\  & \text{3.  Numerical continous}\\\text{D.  A, B, C, D, E grades on a report card}  & \text{4.  Categorical nominal}\end{array}

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\(\text{A}\longrightarrow 4,\ \text{B}\longrightarrow 3,\ \text{C}\longrightarrow 1,\ \text{D}\longrightarrow 2\)

Show Worked Solution

\(\text{A. Hair colour is data grouped in categories with no order}\)

\(\therefore\ \text{4. Categorical nominal}\)

\(\text{B. Heights are measurements which are numerical and continuous}\)

\(\therefore\ \text{3. Numerical continous}\)

\(\text{C. The people living in each household are counted}\)

\(\therefore\ \text{1. Numerical discrete}\)

\(\text{D. Grades on a report card are categorical but the order is important}\)

\(\therefore\ \text{2. Categorical ordinal}\)

Classifying Data, SM-Bank 007

Classify the following as either categorical or numerical data. 

  1. The colours of the cars entering a shopping centre.  (1 mark)

  2. The temperatures recorded in Brisbane over a 2 week period.  (1 mark)

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a.    \(\text{categorical}\)

b.    \(\text{numerical}\)

Show Worked Solution

a.    \(\text{Colours of cars are words therefore categorical.}\)

b.    \(\text{Temperatures are measurements therefore numerical.}\)

Classifying Data, SM-Bank 004 MC

The variables age (under 55 years, 55 years and over) and preferred travel destination (domestic, international) are

  1. both categorical variables.
  2. both numerical variables.
  3. a numerical variable and a categorical variable respectively.
  4. a categorical variable and a numerical variable respectively.
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\(A\)

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\(\text{Age is a categorical ordinal variable}\)

\(\text{because it is categorical data that can}\)

\(\text{have an order.}\)

\(\text{Preferred travel destination is a categorical}\)

\(\text{nominal value because the data has a name.}\)
 

\(\Rightarrow A\)

Classifying Data, SM-Bank 003

The variables blood pressure (low, normal, high) and age (under 50 years, 50 years or over) are

  1. both nominal variables.
  2. both ordinal variables.
  3. a nominal variable and an ordinal variable respectively.
  4. an ordinal variable and a nominal variable respectively.
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\(B\)

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\(\text{Blood pressure is an ordinal variable}\)

\(\text{because it is categorical data that can}\)

\(\text{have an order.}\)

\(\text{Under 50 and over 50, likewise, is an}\)

\(\text{ordinal variable.}\)
 

\(\Rightarrow B\)

Classifying Data, SM-Bank 002 MC

The variables recovery time after exercise (in minutes) and fitness level (below average, average, above average) are

  1. both numerical.
  2. an ordinal variable and a nominal variable respectively.
  3. a numerical variable and a nominal variable respectively.
  4. a numerical variable and an ordinal variable respectively.
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\(D\)

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\(\text{Recovery time in minutes → numerical variable}\)

\(\text{Fitness level → ordinal (categories that can be ordered)}\)

\(\Rightarrow D\)

Classifying Data, SM-Bank 001 MC

The variables

region (city, urban, rural)

population density (number of people per square kilometre)

  1. are both categorical.
  2. are both numerical. 
  3. are categorical and numerical respectively.
  4. are numerical and categorical respectively.
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\(C\)

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\(\text{Region is a categorical variable and population}\)

\(\text{density is a numerical variable (i.e. it can be}\)

\(\text{represented by countable numbers).}\)

\(\Rightarrow C\)

Statistics, STD1 S1 2021 HSC 2 MC

A survey of which of the following would provide data that are both categorical and
nominal?

  1. Hair colour
  2. Height in centimetres
  3. Number of people present at a concert
  4. Size of coffee cup classified as small, medium or large
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`A`

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`text(By elimination:)`

♦♦ Mean mark 25%.

`text{Qualitative (not quantitative)}`

`text{→ Eliminate B and C}`

`text(Nominal data is not ordered)`

`text{→ Eliminate D}`

`=> A`

Statistics, STD2 S1 SM-Bank 1 MC

A survey asked the following question for students born in Australia:

"Which State or Territory were you born in?"

How would the responses be classified?

  1. Categorical, ordinal
  2. Categorical, nominal
  3. Numerical, discrete
  4. Numerical, continuous
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`B`

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`text{The data is categorical (not numerical) since}`

`text(the name of a State is required.)`

`text(This data cannot be ordered.)`

`=> B`

Statistics, STD2 S1 2016 HSC 7 MC

Which set of data is classified as categorical and nominal?

  1. blue, green, yellow
  2. small, medium, large
  3. 5.2 cm, 6 cm, 7.21 cm
  4. 4 people, 5 people, 9 people 
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`A`

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`text(Categorical and nominal data is)`

♦♦ Mean mark 26%.

`text(qualitative and not ordered.)`

`=> A`

Statistics, STD2 S1 2015 HSC 4 MC

On a school report, a student’s record of completing homework is graded using the following codes.

C = consistently
U = usually
S = sometimes
R = rarely
N = never

What type of data is this?

  1. Categorical, ordinal
  2. Categorical, nominal
  3. Numerical, continuous
  4. Numerical, discrete
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`A`

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`text(The data has been grouped into categories and)`

`text(because each category can be ranked, it is ordinal.)`

`⇒ A`

Statistics, STD2 S1 2009 HSC 3 MC

The eye colours of a sample of children were recorded.

When analysing this data, which of the following could be found?

  1. Mean
  2. Median
  3. Mode
  4. Range
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`C`

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`text(Eye colour is categorical data)`

`:.\ text(Only the mode can be found)`

`=>  C`