Page 153 - DMGT209_QUANTITATIVE_TECHNIQUES_II

Quantitative Techniques-II

Notes

Notes Reason for Stratified Sampling

Sometimes, marketing professionals want information about the component part of the
population. Assume there are three stores. Each store forms a strata and the sampling
from within each strata is being selected. The resultant might be used to plan different
promotional activities for each store strata.
Suppose a researcher wishes to study the retail sales of products, such as tea in a universe
of 1,000 grocery stores (Kirana shops included). The researcher can first divide this universe
into three strata based on the size of the store. This benchmark for size could be only one
of the following (a) floor space (b) volume of sales (c) variety displayed etc.
Size of stores No. of stores Percentage of stores
Large stores 2,000 20
Medium stores 3,000 30
Small stores 5,000 50
10,000 100

Suppose we need 12 stores, then choose four from each strata, at random. If there was no
stratification, simple random sampling from the population would be expected to choose
two large stores (20% of 12) about four medium stores (30% of 12) and about six small
stores (50% of 12).
As can be seen, each store can be studied separately using the stratified sample.

Stratified sampling can be carried out with:
1. Same proportion across the strata proportionate stratified sample.
2. Varying proportion across the strata disproportionate stratified sample.

Example:

No. of Sample Sample
Size of stores
stores(Population) Proportionate Disproportionate
Large 2,000 20 25
Medium 3,000 30 35
Small 5,000 50 40

Estimation of universe mean with a stratified sample.

Example:

Size of stores Sample Mean Sales per store No. of stores Percent of stores
Large 200 2000 20
Medium 80 3000 30
Small 40 5000 50
10,000 100

The population mean of monthly sales is calculated by multiplying the sample mean by
its relative weight.

200 × 0.2 + 80 × 0.3+40 × 0.5 = 84

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