This is a curious question. I know that we want our sample to be both random and representative.
With that said, is it fair to say that:
A sample is random IF AND ONLY IF the sample is representative?
1. No, the statement: ‘A sample is random IF AND ONLY IF the sample is representative?’ is not correct.
Consider this. Here are the spoken languages in the USA
Other Indo-European 3.7%
Asian and Pacific island 3.3%
If I contact 20 of my friends ->
16 English speaking, 2 Spanish speaking, 1 Asian speaking, 1 ‘Other Indo-European’. This is more or less a representative sample. However, it is definitely not random, because all of those 20 people were my friends.
You can claim that: a sample is not representative => it is not random.
That would be true, but the general idea is different – the biggest sampling issues come from the fact that people take representative samples in NON-random manner (intentionally to prove some wrong statement). See example with languages above.
If a sample is not representative, it may be because of lack of knowledge on the person sampling it, causing it to be non-random, too (unintentionally).
Hope this helps!
The 365 Team