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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
Show Answers Only

\(D\)

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.
Show Answers Only

\(A\)

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, STD2 S1 2024 HSC 3 MC

Shoppers are invited to complete an online survey.

What type of sampling is this?

  1. Self-selecting
  2. Simple random
  3. Stratified
  4. Systematic
Show Answers Only

\(A\)

Show Worked Solution

\(\text{By elimination}\)

\(\text{Option A: Individuals voluntarily choose to participate.}\ \checkmark\)

\(\text{Option B: Simple random sampling requires every individual in the population}\)

\(\text{to have an equal chance of being selected.}\ \cross \)

\(\text{Options C and D: Both options refer to a systematic process for those included}\)

\(\text{in the survey.}\ \cross \)

\(\Rightarrow A\)

♦ Mean mark 42%.

Statistics, STD1 S1 2022 HSC 13

Kim wants to investigate what students think about the food that is sold at the school's canteen. Kim decides to use a survey to interview a sample group of students to find out their opinions on a number of different issues.

  1. As part of the survey, Kim is thinking about using one of the options listed below.
     

     
    Name ONE advantage for each option.  (2 marks)

  2. After collecting data, Kim drew the following graph to summarise the opinions related to the price of the food.
     
             
     
    What TWO features of the graph make it misleading?  (2 marks)

Show Answers Only

a.   Advantages

Option A → This option would be very easy to collate as there are only 2 choices.

Option B → This option gives a more detailed idea of the students’ thoughts about the food as they can grade their choice from 1 – 10.

 

b.   Misleading features:

→ The scale on the vertical axis is not equal. This makes the “Too Expensive” column (at 50) appear to have more than twice the number of responses as “Okay Prices” (~30) and “Cheap Prices” (~30) which is incorrect.

→ The varying column widths are also misleading as the wider column could be interpreted as being having more weight than the other 2.

Show Worked Solution

a.   Advantages

Option A → This option would be very easy to collate as there are only 2 choices.

Option B → This option gives a more detailed idea of the students’ thoughts about the food as they can grade their choice from 1 – 10.
 

b.   Misleading features:

    • The scale on the vertical axis is not equal. This makes the “Too Expensive” column (at 50) appear to have more than twice the number of responses as “Okay Prices” (~30) and “Cheap Prices” (~30) which is incorrect.
    • The varying column widths are also misleading as the wider column could be interpreted as being having more weight than the other 2.

♦♦ Mean mark 32%.

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
Show Answers Only

`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 21

A survey question is shown.

Give TWO reasons why this survey may be considered to be poorly designed.   (2 marks)

Show Answers Only

\(\text{Examples of poor design:}\)

\(\text{Only 3 choices of many colours are given.}\)

\(\text{Two colours might be someone’s equal favourite colours.}\)

Show Worked Solution

\(\text{Examples of poor design:}\)

\(\text{Only 3 choices of many colours are given.}\)

\(\text{Two colours might be someone’s equal favourite colours.}\)

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
Show Answers Only

`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
Show Answers Only

`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 2017 HSC 4 MC

A factory’s quality control department has tested every 50th item produced for possible defects.

What type of sampling has been used?

A.     Random

B.     Stratified

C.     Systematic

D.     Numerical

Show Answers Only

`C`

Show Worked Solution

`text(A systematic sample divides a population)`

`text(into equal sample sizes and then selects)`

`text(equally among them.)`

`=> 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 
Show Answers Only

\(A\)

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
Show Answers Only

`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 2006 HSC 23c

Vicki wants to investigate the number of hours spent on homework by students at her high school.

  1. Briefly describe a valid method of randomly selecting 200 students for a sample.  (1 mark)

  2. Vicki chooses her sample and asks each student how many hours (to the nearest hour) they usually spend on homework during one week.

     

    The responses are shown in the frequency table.
     
         2UG-2006-23c

    What is the mean amount of time spent on homework?  (2 marks)

Show Answers Only
  1. `text(A valid method would be using a stratified sample.)`

     

    `text(The number of students sampled in each year is)`

     

    `text(proportional to the size of each year.)`

  2. `text(7.275 hours)`
Show Worked Solution

a.   `text(A valid method would be using a stratified sample.)`

`text(The number of students sampled in each year is)`

`text(proportional to the size of each year.)`

MARKER’S COMMENT: This “routine” exercise of finding a mean from grouped data was incorrectly answered by most students! The best responses copied the table and inserted a class-centre column (see solution).

 

b.    2UG-2006-23c Answer

 

`text(Mean)` `= text(Sum of Scores) / text(Total scores)`
  `= 1455/200`
  `= 7.275\ text(hours)`

Statistics, STD2 S1 2007 HSC 17 MC

Ms Wigginson decided to survey a sample of 10% of the students at her school.

The school enrolment is shown in the table. 
 


 

She surveyed the same number of students in each year group.

How would the numbers of students surveyed in Year 10 and Year 11 have changed if Ms Wigginson had chosen to use a stratified sample based on year groups? 

  1.    Increased in both Year 10 and Year 11
  2.    Decreased in both Year 10 and Year 11
  3.    Increased in Year 10 and decreased in Year 11
  4.    Decreased in Year 10 and increased in Year 11
Show Answers Only

`C`

Show Worked Solution

`text(Total students surveyed)`

`= text(10%) xx 1200`

`= 120`

`text(Students surveyed per year group)`

`= 120/6`

`= 20`

 

`text(A stratified sample would have sampled 10%)`

`text(of each year group.)`

`text(In Year 10, 10%) xx 230 = 23`

`text(In Year 11, 10%) xx 150 = 15`

`:.\ text(More students sampled in Year 10 and)`

`text(less in Year 11.)`

`=>  C`

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 24c

The Australian Bureau of Statistics provides the NSW government with data on the age of residents living in different areas across the state. After analysing this data, the government makes decisions relating to the provision of services or facilities.

Give an example of a possible decision the government might make and describe how the data might justify this decision.     (2 marks)

Show Answers Only

`text(The data might show that a large number of retirees live in a)`

`text(particular area. The government could decide to increase)`

`text(public transport in the area as the older retirees get, the more)`

`text(they rely on public transport.)`

Show Worked Solution

`text{One example (of many):}`

`text(The data might show that a large number of retirees live in a)`

`text(particular area. The government could decide to increase)`

`text(public transport in the area as the older retirees get, the more)`

`text(they rely on public transport.)`

Statistics, STD2 S3 2009 HSC 5 MC

Jamie wants to know how many songs were downloaded legally from the internet in the last 12 months by people aged 18–25 years. He has decided to conduct a statistical inquiry.

After he collects the data, which of the following shows the best order for the steps he should take with the data to complete his inquiry?

  1.    Display, organise, conclude, analyse
  2.    Organise, display, conclude, analyse
  3.    Display, organise, analyse, conclude
  4.    Organise, display, analyse, conclude
Show Answers Only

`D`

Show Worked Solution

`text(Process of statistical enquiry requirements)`

`=>  D`

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
Show Answers Only

`C`

Show Worked Solution

`text(Eye colour is categorical data)`

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

`=>  C`

Statistics, STD2 S1 2012 HSC 26d

Greg needs to conduct a statistical inquiry into how much time people aged 18–25 years have spent accessing social media websites in the last two weeks. He has decided to survey a sample of students from his university.

The process of statistical inquiry includes the following steps, which are NOT in order.
 

2012 26d 

  1. Using the letters A, B, C, D, E and F, list the steps in the most appropriate order for Greg to conduct his statistical inquiry.   (2 marks)

  2. Greg conducts his statistical inquiry.

     

    At which step in the process would he have drawn this graph?    (1 mark) 

2012 26d2

Show Answers Only
  1. `text(B, E, C, F, D, A)`
  2. `text(F)`
Show Worked Solution

a.   `text(B, E, C, F, D, A)`

b.   `text(F)`

Statistics, STD2 S1 2012 HSC 2 MC

Handmade chocolates are checked for size and shape. Every 30th chocolate is sampled.

Which term best describes this type of sampling? 

  1.   Census
  2.   Random
  3.   Stratified
  4.   Systematic
Show Answers Only

`D`

Show Worked Solution

`text(Systematic Sampling)`

`=>  D`

Statistics, STD2 S1 2013 HSC 8 MC

A high school has 100 students in each year group, Year 7 to Year 12. A survey is to be conducted to determine the average number of text messages sent per month by students at the school.

Which of the following would provide the most representative sample for this survey?

  1. All Year 7 students
  2. All physics students in Year 11 and 12
  3. 20 students chosen at random from each year group
  4. 120 students chosen at random from the school roll
Show Answers Only

`C`

Show Worked Solution

`text(The best sample would have an equal amount)`

`text(of people in each year randomly selected.)`

`=>\ C`