Check understanding

• Take or are given several random samples of the same size from one population (e.g. draw 20 counters from a bag without looking, record them, return all 20 and mix thoroughly, then draw the next 20 — five times; or five random samples of 20 names from a list), calculate each sample's proportion or mean, and show that the estimates differ
• Explain that equal-sized random samples give different estimates because of chance in which individuals are selected, so a different result does not mean a sample was wrong — and contrast this with a biased method whose estimates are consistently too high or too low
• Use the spread of several sample estimates (e.g. 'the estimates ranged from 25% to 40%') to say how far off a single estimate might be, and explain why one sample cannot make a prediction certain and why larger samples tend to give estimates that vary less
• Distinguish the variation among individual observations within one sample (e.g. pupils' sleep times in one sample range from 6 to 11 hours) from the variation between sample estimates (e.g. the means of five samples of 20 pupils range from 8.6 to 9.3 hours), and explain why sample means usually vary much less than the individual values they are calculated from

“If your child's class takes turns drawing 20 sweets from the same big jar without looking — counting the red ones, then putting all 20 back and giving the jar a good shake before the next person draws — could your child explain why each person gets a slightly different number of reds, and use the spread of everyone's results to say how sure they can be about the fraction of red sweets in the whole jar?”