Page 154 - DMGT209_QUANTITATIVE_TECHNIQUES_II

Unit 8: Sampling and Sampling Distribution

Sample Proportionate Notes

If N is the size of the population.
n is the size of the sample.
i represents 1, 2, 3,…………..k [number of strata in the population]
 Proportionate sampling

n n n n
p = 1  2  ................  k 
N 1 N 2 N k N

n 1 n n
N 1 = N  n  N  n 1 and so on
1
n is the sample size to be drawn from stratum 1
1
n + n +………… n = n [Total sample size of the all strata]
1 2 k

Example: A survey is planned to analyse the perception of people towards their own
religious practices. The population consists of various religions, viz., Hindu, Muslim, Christian,
Sikh, Jain, assuming a total of 10,000. Hindu, Muslim, Christian, Sikh and Jains consists of 6,000,
2,000, 1,000, 500 and 500 respectively. Determine the sample size of each stratum by applying
proportionate stratified sampling, if the sample size required is 200.
Solution: Total population, N=10,000

Population in the strata of Hindus N = 6,000
1
Population in the strata of Muslims N = 2,000
2
Population in the strata of Christians N = 1,000
3
Population in the strata of Sikhs N = 500
4
Population in the strata of Jains N = 500
5
Proportionate Stratified Sampling

n n n n n n
P = 1  2  3  4  5 
N 1 N 2 N 3 N 4 N 5 N
 Let us determine the sample size of strata N
1
n n 200
1
=  N   6,000
1
N N 10,000
1
= 20 × 6
= 120
n 200
n =  N   2,000
2
2 N 10,000
= 40

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