Stratified Sampling

## Stratified Sampling

To avoid bias in sampling, a population may be divided into recognisable groups. These divisions create a stratified sample.

The first step is to identify the strata (or layers) that make up the population. This must be done to reflect any bias that may influence the survey.

Then identify how many will be sampled from the population as a whole.

The number of people or items selected from each layer should be in proportion to the size of the strata in the population. Use a fraction text(strata size)/text(population) to obtain the number to be selected from each group.

## Example 1

A survey of people going to a tennis tournament is being undertaken. The survey calls for 200 people to be interviewed in a stratified sample based on age.

How many people should be interviewed in each strata?

Age range (y) Number
0 < y ≤ 12 254
12 < y ≤ 18 264
18 < y ≤ 25 249
25 < y ≤ 60 233
60 < y 214

The fraction to be used for each class is frac([text(strata size)/text(population)]).

Note that the results must be rounded to the nearest integer as you cannot interview part of a person. The rounded values do not add up to 200. Consider the values that are close to being rounded and adjust them up or down to suit.

Age range (y) Number text(strata size)/text(population) x sample Stratified sample
0 < y ≤ 12 254 frac(254)(1214) x 200 = 41.85 42
12 < y ≤ 18 264 frac(264)(1214) x 200 = 43.49 44
18 < y ≤ 25 249 frac(249)(1214) x 200 = 41.02 41
25 < y ≤ 60 233 frac(233)(1214) x 200 = 38.38 38
60 < y 214 frac(214)(1214) x 200 = 35.25 35
TOTALS 1214 200

## Example 2

A school is conducting a survey about homework. The number of of students in each year is as follows:

Year Group Students
Y7 293
Y8 265
Y9 255
Y10 212
Y11 242

It is intended to survey 250 students using stratified sampling. How many Year 10s should be included in the survey?

The total number of students at the school is 1267.

The fraction to be used is frac(text(strata size))(text(total population)).

The number of Year 10s to be surveyed is

frac(212)(1267)` x 250

= 41.83, which is 42 students.