Bias can be present in any sample collected from a population and may affect the results of a statistical investigation.

Sampling limitations

Maths

Checking understanding of statistical problems

The Statistical Enquiry Cycle

Types of data

Sampling methods

Data collection

Biased questioning

Problem solving with sampling

In this unit, pupils are given the opportunity to assess how valid a sample may be and what the averages might tell us. In the future unit, pupils extend their knowledge of averages to stem and leaf diagrams as well as comparing two data sets.

In the prior unit, pupils considered the mean, median and mode and evaluated their usefulness in a variety of contexts. In this unit, pupils are given the opportunity to consider where the data came from and how it was collected and can therefore start to evaluate how good a representation the sample is of the whole population.

In this unit pupils will learn how to sample, and explore accuracy and limitations with various sampling strategies and data collection techniques.

Sampling

__________ can be present in any sample collected from a population and may affect the results of a statistical investigation.  

Yes, the chance of 3 heads in a row is very low.

No, Laura needs to flip the coin 3 more times to be sure.

No, Laura needs to flip the coin at least 100 more times.

Laura flips a coin three times and it lands heads each time. Laura concludes the coin is biased. Is Laura correct?

Izzy has a biased sample as her friends may like the same music.

Izzy should ask more pupils from year 10.

Izzy should ask some pupils from each year group.

Izzy wants to find out what type of music is most popular among pupils at her school. She asks 5 of her friends who their favourite singer is. Which of these comments are correct?

Jacob and Sofia have both investigated what the favourite subject of the year 10 pupils in their school is. {{}} sample is more likely to be representative of the population.

Jacob had a good sampling method as his sample was more targeted.

Jacob and Sofia have both investigated what the favourite subject of year 10 pupils in their school is. Select the statements that are likely to be true.

Jun shouldn't only ask people at the sports centre

Jun doesn't live in Rowanwood, so shouldn't ask there.

Jun's enthusiasm may influence his results.

Jun wants to find out if the town of Rowanwood needs a new sports centre. Comment on Jun's sampling method.

Capture-recapture is a sampling method which allows you to {{}} the size of a population without counting it fully.

Jacob might have recaptured the same bird twice.

Jacob captures 10 birds and marks each one with some non-toxic dye. Jacob recaptures 10 birds, but finds that none of them have a paper band. Select the possible reasons for this.

The marked animals have mixed into the population so the recapture is random.

Some of new animals will have been born or migrated into the habitat.

Some of the animals will have migrated or died.

Which of these assumptions are made when the method of capture-recapture is used?

As part of a capture-recapture sample, 200 fish from a lake are captured and marked with a white dye. During a recapture of 100 fish, 12 were marked with the white dye. Select the correct statement.

Laura captures 9 deer and marks them by attaching a tag to their legs. Three days later, Laura recaptures 40 deer, and 4 of them have a tag attached. Estimate the total number of deer. 

Jun captures 21 squirrels and marks them by attaching a tag to their legs. Three days later, Jun recaptures 46 squirrels, and 7 of them have a tag attached. Estimate the total number of squirrels. 

Sampling limitations

Lesson outcome