Home › AP Statistics › Statistics › The Central Limit Theorem › The law of large numbers says that as samples ge…
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_
Related questions
The standard error appears in calculator routines as a parameter alongside:Comparing the law of large numbers with the central limit theorem, the law of large numberA population that is already close to normal needs which sample size for the theorem to apRecognising a central limit theorem problem means spotting a question about:Standard deviation is related to variance as its:The mean of the sampling distribution of sample means equals:Doubling the sample size makes the sampling distribution of the mean:The central limit theorem applies to sample means taken from: