One of the following is true for relation between sample mean \((\bar{x})\) and population mean \((\mu)\).
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(|\bar{x} - \mu|\) decreases when increase the size of samples
The spread of the sample mean about the population mean is measured by the standard error:
\( \displaystyle SE(\bar{x}) = \frac{\sigma}{\sqrt{n}} \)
As the sample size n increases, \(\sqrt{n}\) increases and the standard error decreases. So the sample mean comes closer to \(\mu\): the difference \(|\bar{x} - \mu|\) decreases as the sample size increases (in the usual sense, on average over samples).
A sample mean need not equal \(\mu\) for every sample, so \(\bar{x} = \mu\) for all sample sizes is not true, and the difference neither grows nor stays fixed as n grows.
CBSE Applied Mathematics (Class XII):
Sampling Errors
