Teaching mathematics
Teaching mathematics

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Teaching mathematics

1.2 Population and sampling

The population of a survey is everyone who can be questioned in relation to that survey. For example, if a learner wanted to find out the most popular meal in their school canteen, the population of the survey would be all of the students, and possibly also the teachers, in the school.

A sample is a small selection of the population, for example just one class in a school.

There are advantages and disadvantages to using entire populations and samples.

Table 1 Advantages and disadvantages of sampling

AdvantagesDisadvantages
Population

Every opinion is included

Representative and therefore reliable

Time consuming

Expensive

Sample

Quick

More cost effective

Only some opinions

Selection method could cause bias

Activity 1 Reflecting

Timing: Allow 5 minutes

How could a selection method mean that the results of a sample could cause bias?

Discussion

When data is collected from the entire population, all opinions are taken into consideration. When data is collected from a sample of the population, it is important that the sample is representative of the population.

For example: Joe wants to find out whether motorbikes or cars are more popular, so he has asked 20 people at a motor bike convention which they prefer.

Comment: Joe’s data selection method is clearly flawed as he is much more likely to find that people prefer motorbikes within this sample of the population.Thus they are unlikely to be representative of the wider population.

Considering potential bias when sampling data is part of having data sense.

Sampling

When collecting data from a sample of the population, decisions have to be made about how the sample is chosen. It is important to think about how to ensure the sample is representative of the wider population.

There are many different sampling methods. Here are a few examples.

Convenience sampling is the most simple and straightforward way to collect a sample of data since participants are chosen in the most convenient way and are often asked to volunteer. Statistical investigations carried out by young learners are likely to use this form of sampling, for example when investigating favourite pets earlier in this section, the learners used their own classmates for convenience.

Random sampling can be done by assigning a number to each member of the population and then using a random number generator to select the required number of individuals.

Systematic sampling involves choosing individuals at regular intervals. For instance, if a sample of 20 is needed from a population of 100, every 5th individual would be used in the sample. This sample will obviously vary depending on how the population is ordered. This is a convenient and simple way to collect a sample but may result in some bias as some smaller groups within the population could be omitted from the sample.

A stratified sample takes into consideration different groups and their proportions within the overall population, using the same proportions in the sample. For example, if a school has more students in year 7 and fewer students in year 11, the sample would take a greater number of participants from year 7 and fewer from year 11. This is done using percentages.

A quota sample does not take into consideration the proportion of each group in the population. Instead, a quota sample may require there to be 20 male and 20 female participants in the sample, regardless of whether there are many more of either gender in the wider population.

Sampling methods are not generally covered in the middle school curriculum. But it is important for learners to be aware that their sampling choices will affect the reliability of their findings when conducting statistical investigations.

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