Practice question · Fill in the blanks
Complete the statement of the Central Limit Theorem.
The Central Limit Theorem says that for a large enough sample, the distribution of ______ is approximately normal.
Word bank: the sample mean · the raw data values · the population · the population standard deviation
Hints
- The theorem is about a sampling distribution, not about the data themselves.
- Which quantity is recomputed afresh for every new sample?
Show the answer
The Central Limit Theorem says that for a large enough sample, the distribution of the sample mean is approximately normal.
Why
It is the distribution of the statistic that turns normal, regardless of the population's own shape. The data stay as skewed as they always were; it is their averages that become bell-shaped.
Practise Sampling and the Central Limit Theorem
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