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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, 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

i.  `text(Categorical)`

 

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

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

 

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

♦♦♦ Mean mark 7%. Toughest mark to get in the 2011 exam!
COMMENT: Know and be able to describe random, systematic and stratified sampling!

`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 needed (i.e. high school students).

iv.  `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)

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`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 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

i.   `text(B, E, C, F, D, A)`

ii.   `text(F)`