Question

A salesperson obtained a systematic sample of size 20 from a list of 500 clients. To do​ so, he randomly selected a number from 1 to 25​, obtaining the number 16. He included in the sample the 16th client on the list and every 25th client thereafter. List the numbers that correspond to the 20 clients selected.

Answer 1

16,41,66,91,116,141,166,191,216,241,266,291,316,341,366,391,416,441,466,491

Explanation:

The numbers that corresponds to 20 clients can be selected through systematic sampling. The samples selected through systematic sampling starting from i and then every kth unit is selected i.e. i,i+k,i+2k,...,i+(n-1)k

Sr.no Samples

1. 16

2. 16+25=41

3. 16+2*25=66

4. 16+3*25=91

5. 16+4*25=116

6. 16+5*25=141

7. 16+6*25=166

8 16+7*25=191

9. 16+8*25=216

10. 16+9*25=241

11. 16+10*25=266

12. 16+11*25=291

13. 16+12*25=316

14. 16+13*25=341

15. 16+14*25=366

16. 16+15*25=391

17. 16+16*25=416

18. 16+17*25=441

19. 16+18*25=466

20. 16+19*25=491

The numbers correspond to 20 clients selected are 16,41,66,91,116,141,166,191,216,241,266,291,316,341,366,391,416,441,466,491.