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The fact that the sampling distribution of the sample mean of a numerical variable becomes closer to the normal distribution as the sample size increases. The sample means are from random samples from some population.
This result applies regardless of the shape of the population distribution of the numerical variable.
The use of ‘central’ in this term is because there is a tendency for values of the sample mean to be closer to the ‘centre’ of the population distribution than individual values are. This tendency strengthens as the sample size increases.
The use of ‘limit’ in this term is because the closeness or approximation to the normal distribution improves as the sample size increases.
Curriculum achievement objectives reference
Statistical investigation: Level 8
