How can summary statistics from a sample be used to say something about the whole population?

As long as the sample is representative , the population's statistics can be taken to be approximately the same as the sample's. So the population mean is assumed to be about equal to the sample mean, and the same goes for the median, the range and the quartiles.

True or False? A statistic worked out from a sample is unlikely to be exactly the same as the population's.

True. A sample is only a selection of the members rather than all of them, so it cannot capture the population exactly. Two different samples drawn from the same population will usually not even agree with each other.

How could the reliability of an estimate made from a sample be improved?

By using a larger sample . A bigger sample is more likely to reflect the whole population, so the statistics worked out from it come closer to the population's own.

GCSEStatisticsAQAFoundationFlashcardsProcessing, Representing & Analysing DataQuality Assurance & Estimation

Quality Assurance & Estimation (AQA GCSE Statistics: Foundation): Flashcards

Exam code: 8382

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FrontEstimation from Statistical Data
How can summary statistics from a sample be used to say something about the whole population?

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How can summary statistics from a sample be used to say something about the whole population?
As long as the sample is representative, the population's statistics can be taken to be approximately the same as the sample's.
So the population mean is assumed to be about equal to the sample mean, and the same goes for the median, the range and the quartiles.
True or False?
A statistic worked out from a sample is unlikely to be exactly the same as the population's.
True.
A sample is only a selection of the members rather than all of them, so it cannot capture the population exactly.
Two different samples drawn from the same population will usually not even agree with each other.
Complete the prediction that can be made from a sample median.
About $______$ per cent of the population will lie above the sample median, and about the same proportion will lie $______$ it.
The completed prediction is:
About 50 per cent of the population will lie above the sample median, and about the same proportion will lie below it.
A sample of rabbits has a lower quartile weight of 1.2 kg and an upper quartile of 2.1 kg. Roughly how many of the 600 rabbits weigh between those values?
About 300, because half of the values in a data set lie between the two quartiles.
Half of 600 is $\frac{1}{2} \times 600 = 300$ rabbits, on the assumption that the sample represents the population well.
A sample of 50 rabbits has a total weight of 82.5 kg. What is the estimate for the mean weight of a rabbit in the population?
Work out the sample mean by dividing the total by the number in the sample, $\frac{82.5}{50} = 1.65$ kilograms.
The population mean is then estimated to be about the same, so roughly 1.65 kg per rabbit.
How could the reliability of an estimate made from a sample be improved?
By using a larger sample.
A bigger sample is more likely to reflect the whole population, so the statistics worked out from it come closer to the population's own.

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