Question

Explain in detail the systematic random sampling. According to the following information, define the sample elements

• No. of elements in population: 17024

• No. of desired sample: 19

• The first random number of samples: 112

Answer 1

Solution :

Systematic sampling :

In this systematic sampling method we number all the elements in population starting from 1 to N. Then we obtain a constant k such that k = N/n. Where n is the sample size and N is population size. Then we randomly select a starting point and the chosen starting point will be our first sampling element. After that we select every kth sampling elements untill desired.

We have, N = 17024, n = 19

Hence, k = 17024/19 = 896

First random number of the samples is 112. It means our first sample element will be the element corresponding to 112th number.

Afetr 112th unit being the first sampling unit we shall selecte every 896th unit of the population as our sample elements.

Hence, our sample elements would be corresponding to following numbers.

Serial No.	Sample Elements
1	112th
2	112 + 896 = 1108th
3	1008 + 896 = 1904th
4	1904 + 896 = 2800th
5	2800 + 896 = 3696th
6	3696 + 896 = 4592th
7	4592+ 896 = 5488th
8	5488 + 896 = 6384th
9	6384 + 896 = 7280th
10	7280 + 896 = 8176th
11	8176 + 896 = 9072th
12	9072 + 896 = 9968th
13	9968 + 896 = 10864th
14	10864 + 896 = 11760th
15	11760 + 896 = 12656th
16	12656 + 896 = 13552th
17	13552 + 896 = 14448th
18	14448 + 896 = 15344th
19	15344 + 896 = 16240th