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.
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.
Answer:
| 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 |
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.
Answer: 42