One of the following is true relation between sample mean $(\overline{x})$ and population mean $(\mu )$ .

$|\overline {x} - \mu |$ decreases when increases the size of samples

The correct answer is Option (4) → $|\overline {x} - \mu |$ decreases when increases the size of samples

The true relation between the sample mean $(\overline{x})$ and the population mean ($\mu$) is given by the Law of Large Numbers. This law states that as the size of the random sample increases, the sample mean tends to get closer to the population mean.

Mathematically, this implies that the absolute difference between the sample mean and the population mean, $|\overline {x} - \mu |$, tends to decrease as the sample size ($n$) increases.