Home › AP Statistics › Statistics › The Central Limit Theorem › The standard deviation of the sampling distribut…
The standard deviation of the sampling distribution is the population standard deviation divided by:
AThe square root of n
BThe value of n itself
CThe square of n
DTwice the value of n
Answer & Solution
Correct answer: A. The square root of n
1. Averages vary less than individual observations do.
2. Standard deviation is the square root of variance.
3. The standard deviation of the sampling distribution is the standard deviation of the original distribution divided by the square root of n.
4. That shrinking spread is exactly why bigger samples give tighter estimates.
_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: