Question

Systematic Sampling Technique is used to select 5 numbers between 1 and 200. The first selected number is 12. What should be next four numbers?

Answer 1

Answer:  52, 92 , 132, 172

Step-by-step explanation:

• A systematic random sampling is a random sampling technique in which a sample from a large population are chosen according to a random beginning point and a fixed periodic interval (k).

Given : Systematic Sampling Technique is used to select 5 numbers between 1 and 200.

⇒ Population size : N=200

Required Sample size  : n=5

Since , Sampling interval is given by :-

$k=\dfrac{N}{n}$

⇒ [tex]k=\dfrac{200}{5}[=40/tex]

If the first selected number is 12, then the next four numbers would be :

(12+K) , (12+2k) , (12+3k) , (12+4k)

Put value of k , we get

(12+40) , (12+2(40)) , (12+3(40)) , (12+4(40)) =(52, 92 , 132, 172)

Hence, the  next four numbers are : 52, 92 , 132, 172