alleryStart learning →The law of large numbers says that as samples get larger, the sample mean gets:
ALarger without any limit
BCloser to the population mean
CFurther from the population mean
DCloser to exactly zero
Answer & Solution
Correct answer: B. Closer to the population mean
1. Averaging more observations makes an estimate steadier.
2. The law of large numbers says that if you take samples of larger and larger size from any population
then the mean of the sample tends to get closer and closer to the population mean.
3. So a big sample gives a more trustworthy estimate of the centre.
4. The estimate settles on the true mean rather than on zero.
_Source: OpenStax Introductory Statistics 2e (CC BY 4.0), Ch 7 'The Central Limit Theorem', sections 7.1-7.3_
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