SHS Maths | shsmaths.com Populations and Sampling Stats GCSE Chapter 1

Populations vs Samples The ‘population’ in an investigation is everyone who could be involved in that investigation.  A school wants to investigate GCSE performance of its Y11 students. The population is everyone in Y11 in that school.  If we investigate everyone in the population we call this a census.  Every 10 years there is a UK Government census – loads of questions to the whole adult population. Takes years to process. Sometimes we can’t investigate the whole population. In this case, we take a sample.  Population could be too large.  Census could be too expensive.  Testing could be destructive – eg battery factory.

Populations vs Samples AdvantageDisadvantage Census Unbiased Accurate Includes everyone Takes time Expensive Too much data? Have we included everyone? Sample Cheaper Quicker Less data Doesn’t use whole population (if testing is destructive) Open to bias Non-representative

Sampling The ‘Sampling Units’ are the people or things to be sampled  A school wants to investigate GCSE performance of its Y11 students. Sampling unit = a child in Y11. The ‘Sampling Frame’ is the list of people who could be part of the sample  Sampling Frame = list of current students in Y11  Sampling Frame should be same as the population, but this may not always be practical. Eg – a general election. Whenever we sample we are trying to avoid bias – we are trying to get a good representation of the population.  Bias can occur with: unrepresentative sample / misleading questions / wrong population…

Sampling Methods 1. Random Sampling  Simple random sampling: you just chose a random selection of people from the population: Random number generator / table of random numbers / pull numbers out of a hat.  Stratified random sampling: the population is divided into ‘strata’ – eg male/female etc., and a random sample is taken from each strata. The size of each sample must be in proportion to the relative size of the strata.

Example of Stratified Sampling The head of a school of 1000 students wants to take a sample of 60 students for a survey. How many students should she include from each year? Year 7Year 8Year 9Year 10Year Year 7 and 8: Year 9: Year 10 and 11:

Other Forms of Sampling Cluster Sampling  This is when the population falls into natural clusters (like people in a town or village) and a sample of these clusters is taken.  Eg: ‘What should we do about the Post Office in the UK?’ Ask everyone in a number of villages. Quota Sampling  This is used a lot in opinion polls. An interviewer might be asked to go out an find 20 men over 35 who wear glasses, and 18 women over 40 who are left-handed. Systematic Sampling  This might be used in a factory: we take every 100 th item a machine produces and test it. It might not be representative!