Q.A population of 1,000 retail outlets is divided into three strata by size — Large: 400 outlets, Medium: 350 outlets, Small: 250 outlets. Using proportional allocation, determine how many outlets should be sampled from each stratum if a total sample of 100 outlets is required.

Proportional allocation keeps each stratum's sample share equal to its share of the total population.

Given: $N = 1{,}000$ (total population), $n = 100$ (required total sample), with strata sizes $N_1 = 400$ (Large), $N_2 = 350$ (Medium), $N_3 = 250$ (Small).

Under proportional allocation, $n_i = n \times \dfrac{N_i}{N}$:

• Large: $n_1 = 100 \times \dfrac{400}{1{,}000} = 40$
• Medium: $n_2 = 100 \times \dfrac{350}{1{,}000} = 35$
• Small: $n_3 = 100 \times \dfrac{250}{1{,}000} = 25$

Verification (independent check): the three stratum populations must add up to the total population, and the three stratum sample sizes must add up to the required total sample. $400 + 350 + 250 = 1{,}000 = N$ ✓, and $40 + 35 + 25 = 100 = n$ ✓ — both checks confirm the allocation is correct.

Allocating an equal sample size to every stratum (e.g., roughly 33-33-34) regardless of stratum size — that is equal allocation, not proportional allocation, and it does not reflect each stratum's true share of the population.