Question
Select all possible systematic samples of size $3$ from a population of size $12.$
✓
Answer
Here population size $(N)$ is $12$ and sample size $(n) = 3$.
So the sample interval $k = N/n = 12/3 = 4.$
Now, every 4th unit will be selected after randomly selecting the first unit from $1$ to $4.$ Thus we will get $4$ possible samples.
Thus, possible samples are:
Sample $I : 1, 5, 9$
Sample $II : 2, 6, 10$
Sample $III : 3, 7, 11$
Sample $IV : 4, 8, 12$
So the sample interval $k = N/n = 12/3 = 4.$
Now, every 4th unit will be selected after randomly selecting the first unit from $1$ to $4.$ Thus we will get $4$ possible samples.
Thus, possible samples are:
Sample $I : 1, 5, 9$
Sample $II : 2, 6, 10$
Sample $III : 3, 7, 11$
Sample $IV : 4, 8, 12$
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