Collecting and classifying dataIB MYP Maths Extended: Subtopic test

1. 1
   A school survey records four pieces of information about each student: shoe size, the colour of their bag, their height in centimetres and the number of siblings.

   (a)

   Which of the four pieces of information is continuous data?

   [1 mark]

   • AShoe size
   • BColour of bag
   • CHeight
   • DNumber of siblings

   (b)

   What type of data is the colour of a student's bag?

   [1 mark]

   • ADiscrete
   • BContinuous
   • CQuantitative
   • DCategorical

   (c)

   Explain why shoe size is discrete data.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A town council wants to find out how residents travel to work. It has a list of all $8\,000$ residents, of whom $3\,200$ live in the north of the town and $4\,800$ live in the south.

   (a)

   Which method gives a simple random sample of $200$ residents?

   [1 mark]

   • AAsking the first $200$ people to arrive at the railway station
   • BUsing a random number generator to choose $200$ residents from the list
   • CAsking for $200$ volunteers on the council's website
   • DAsking $200$ council employees

   (b)

   A stratified sample of $200$ residents is taken, with the strata being north and south. How many residents should be chosen from the north?

   [1 mark]

   • A$80$
   • B$40$
   • C$100$
   • D$120$

   (c)

   A councillor suggests surveying only people who are at the railway station at 8 am on a weekday. Explain why this sample would be biased.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A student wants to find out how long pupils in her school spend on social media each day. She asks: "You spend too much time on social media, don't you?" The answer boxes are: "A lot", "Some" and "Hardly any".

   (a)

   Identify three faults with the question and the answer boxes.

   [3 marks]

   (b)

   Write an improved question, with answer boxes, that she could use.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A sports centre has $2\,400$ members: $1\,500$ adults, $600$ teenagers and $300$ seniors. The manager wants to survey $120$ members to decide which new activities to offer.

   (a)

   The manager takes a stratified sample of $120$ members.
   (i) Calculate how many members should be chosen from each group.
   (ii) Explain how the manager could choose the members within each group.
   (iii) Explain why a stratified sample is better than asking the first $120$ members who arrive on Saturday morning.

   [6 marks]

   (b)

   The survey includes these questions:
   (i) "How many times did you visit the centre last month?"
   (ii) "How long, in minutes, was your most recent visit?"
   (iii) "Which activity would you most like to see?"
   State whether the data from each question are discrete, continuous or categorical. Only $48$ of the $120$ members chosen replied. Explain how this could affect how reliable the conclusions are, and suggest one way to improve the survey.

   [6 marks]

   Total for question 4: 12 marks

End of questions