For a sample to be a representative sample of a population, it is necessary that
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → the selection is random and the sample is large enough
A representative sample must reflect the features of the population without bias. For this, two conditions are needed:
(i) the sampling process must have a component of random selection, and
(ii) the sample size must be large enough to show the variability of the population.
Why the other options are incorrect
Option (1) the sample is taken from the members who are easiest to reach — Incorrect. This is convenience sampling, which gives a biased sample.
Option (2) the members decide for themselves whether to be in the sample — Incorrect. This gives voluntary response bias.
Option (3) the sample is kept as small as possible — Incorrect. A very small sample cannot show the variability of the population; the sample must be large enough.