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Statistics, STD1 S1 2025 HSC 1 MC

Which of the following could be classified as discrete data?

  1. Colour of a car
  2. Time taken to swim 200 m
  3. Temperature of an ice block
  4. Number of children in a class
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\(D\)

Show Worked Solution

\(\text{Discrete data refers to individual and countable items that can be listed.}\)

\(\text{Consider Options:}\)

\(\text{A. Colour → categorical}\)

\(\text{B. Time → measurement → continuous}\)

\(\text{C. Temperature → measurement → continuous}\)

\(\text{D. Number of children → countable → discrete}\)

\(\Rightarrow D\)


♦♦♦ Mean mark 29%.

Statistics, STD2 S1 2024 GEN1 2 MC

Freddie organised a function at work. He surveyed the staff about their preferences.

He asked them about their payment preference (cash or electronic payment) and their budget preference (less than $50 or more than $50).

The variables in this survey, payment preference and budget preference, are

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

Show Worked Solution

\(\text{Payment preference is categorical.}\)

\(\text{Budget preference contains numbers, however, it cannot be}\)

\(\text{quantified, therefore it is also categorical.}\)

\(\Rightarrow A\)

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`

Show Worked Solution

`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 EQ-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`

Show Worked Solution

`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 2018 HSC 3 MC

A survey asked the following question.

'How many brothers do you have?'

How would the responses be classified?

  1. Categorical, ordinal
  2. Categorical, nominal
  3. Numerical, discrete
  4. Numerical, continuous
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`text(C)`

Show Worked Solution

`text(The number of brothers a person has is)`

`text(an exact whole number.)`

`:.\ text(Classification is numerical, discrete.)`

`=>\ text(C)`

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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\(A\)

Show Worked Solution

\(\text{Categorical data is qualitative (eliminate C and D)}\)

♦♦ Mean mark 26%.

\(\text{Nominal data not ordered (eliminate B)}\)

`=> 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`

Show Worked Solution

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

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

`⇒ A`

Statistics, STD2 S1 2011 HSC 25a

A study on the mobile phone usage of NSW high school students is to be conducted.

Data is to be gathered using a questionnaire.

The questionnaire begins with the three questions shown.

2UG 2011 25a

  1. Classify the type of data that will be collected in Q2 of the questionnaire.   (1 mark)

  2. Write a suitable question for this questionnaire that would provide discrete ordinal data.   (1 mark)

  3. An initial study is to be conducted using a stratified sample.

     

    Describe a method that could be used to obtain a representative stratified sample.   (1 mark)

  4. Who should be surveyed if it is decided to use a census for the study?   (1 mark)

Show Answers Only
  1. `text(Categorical)`
  2. `text(See Worked Solutions)`
  3. `text(See Worked Solutions)`
  4. `text(A census would involve all high school students in NSW.)`
Show Worked Solution

a.    `text(Categorical)`
 

b.    `text(How many outgoing calls do you make per day?)`

`text{(Ensure it can be answered with a numerical score.)}`
 

c.  `text(The method could be to work out how many)`

♦♦♦ Mean mark 7%.
COMMENT: Know random, systematic and stratified sampling definitions.

`text{students are in each year and ask 10% of the}`

`text{students in each year. (Note the sample of}`

`text{students in each year must be  proportional to}`

`text{their percentage in the population).}`

 

♦♦♦ Mean mark 18%.
MARKER’S COMMENT: A specific population is required here.

d.  `text(A census would involve all high school)`

`text(students in NSW.)`

 

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`

Show Worked Solution

`text(Eye colour is categorical data)`

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

`=>  C`