4.1 Sampling, data quality and outliersIB Maths: Applications and Interpretation HL: Subtopic test

1. 1
   A council wants to find out how its residents travel to work. A researcher stands outside the main railway station one morning and questions the first 80 people who walk past. The council has 12 000 residents on its electoral register.

   (a)

   Which sampling technique has the researcher used?

   [1 mark]

   • ASimple random sampling
   • BConvenience sampling
   • CSystematic sampling
   • DQuota sampling

   (b)

   Which statement best explains why the sample may be biased?

   [1 mark]

   • AThe sample size of 80 is too small to calculate a mean
   • BCommuting times are continuous data, which cannot be sampled
   • CResidents who do not use the station, such as those who drive or cycle, have no chance of being selected
   • DQuestioning the first 80 people gives every resident an equal chance of selection

   (c)

   Describe how the council could take a simple random sample of 80 residents from the electoral register.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A sports club has 600 members: 240 juniors, 210 adults and 150 seniors. The club takes a stratified sample of 80 members for a survey about its facilities.

   (a)

   How many juniors should be in the sample?

   [1 mark]

   • A32
   • B40
   • C24
   • D16

   (b)

   How many adults should be in the sample?

   [1 mark]

   • A21
   • B27
   • C35
   • D28

   (c)

   Explain why a stratified sample is more suitable than a simple random sample for this survey.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Eleven students record the time, in minutes, they take to finish a puzzle: 12, 14, 15, 15, 17, 18, 19, 21, 22, 24, 41. The student who took 41 minutes says she forgot to stop her timer. Use your GDC to find quartiles.

   (a)

   Find the interquartile range (IQR) of the times.

   [3 marks]

   (b)

   Show that $41$ is an outlier, and comment on whether it should be kept in the data.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A company has 2400 employees listed in a database. The HR manager takes a systematic sample of 60 employees for a questionnaire about hours worked. Of the 60 questionnaires sent out, 52 are returned. One returned questionnaire states 400 hours worked last week.

   (a)

   The first employee selected is number $17$ in the list.
   (i) Find the sampling interval.
   (ii) Find the position in the list of the fifth employee selected.
   (iii) Find the position in the list of the last employee selected.

   [6 marks]

   (b)

   (i) Explain why the 8 missing questionnaires may bias the results.
   (ii) Suggest one way of dealing with the missing data.
   (iii) Explain how the reply of 400 hours should be treated.

   [6 marks]

   Total for question 4: 12 marks

End of questions