Question

Explain in detail about systematic random sampling with example

Answer 1

Systematic sampling:

In systematic sampling, randomly select the first sample from the first k units.

Then every kth member, starting with the first selected sample, is included in the sample.

Systematic sampling is a commonly used technique if the complete and up-to-date list of the sampling units is available.

We can arrange the items in numerical, alphabetical, geographical or in any other order.

The procedure of selecting the samples starts with selecting the first sample at random, the rest being automatically selected according to some pre-determined pattern.

A systematic sample is formed by selecting every item from the population, where k refers to the sample interval.

The sampling interval can be determined by dividing the size of the population by the size of the sample to be chosen.

That is k = `"N"/"n", where k is an integer.

k = Sampling interval

N = Size of the population

n = Sample size.

Procedure for selection of samples by systematic sampling method

(i) If we want to select a sample of 10 students from a class of 100 students, the sampling interval is calculated as k = `"N"/"n" = 100/"n"` = 10

Thus sampling interval = 10 denotes that for every 10 samples one sample has to be selected.

(ii) The first sample is selected from the first 10 (sampling interval) samples through random selection procedures.

(iii) If the selected first random sample is 5, then the rest of the samples are automatically selected by incrementing the value of the sampling interval (k = 10)

i.e., 5, 15, 25, 35, 45, 55, 65, 75, 85, 95.

Example: Suppose we have to select 20 items out of 6,000.

The procedure is to number all the 6,000 items from 1 to 6,000.

The sampling interval is calculated as k = `"N"/"n" = 6000/20` = 300

Thus sampling interval = 300 denotes that for every 300 samples one sample has to be selected.

The first sample is selected from the first 300 (sampling interval) samples through random selection procedures.

If the selected first random sample is 50, then the rest of the samples are automatically selected by incrementing the value of the sampling interval (k = 300) ie,50, 350, 650, 950, 1250, 1550, 1850, 2150, 2450, 2750, 3050, 3350, 3650, 3950, 4250, 4550, 4850, 5150, 5450, 5750.

Items bearing those numbers will be selected as samples from the population.