Stratified sampling - Higher

Stratified sampling is used to select a sample that is representative of different groups. If the groups are of different sizes, the number of items selected from each group will be proportional to the number of items in that group.

Example

Billy wants to survey 25 customers of a restaurant to find out which dessert they prefer. He decides to use a stratified sampling technique to work out how many people of each age group he should select.

The table below shows how many customers attended the restaurant in the last week. This is the total population. The sample size is the number of customers Billy wants to survey, 25 in this example.The strata size is the number of people in each group, 12, 34, 48, 21 and 3 in this example.

Age groupNumber of customers
11-2012
21-3034
31-4048
41-5021
51+3

The total number of customers = 12 + 34 + 48 + 21 + 3 = 118.

He then uses the equation:

Number~selected~from~each~strata~=~(\frac{strata~size}{total~population})~\times~sample~size

Age groupNumber in sample
11-20( \frac{12}{118}) x 25 = 2.54 (3 customers)
21-30( \frac{34}{118}) x 25 = 7.20 (7 customers)
31-40( \frac{48}{118}) x 25 = 10.17 (10 customers)
41-50( \frac{21}{118}) x 25 = 4.45 (4 customers)
51+( \frac{3}{118}) x 25 = 0.63 (1 customer)
curriculum-key-fact
Don’t forget to add all of the items together at the end (3 + 7 + 10 + 4 + 1 = 25) to ensure the correct amount is in the sample.

It is possible to end up with a different number of items than you intended. If this happens you may have to add or take away one item from a specific group. You can select the appropriate group by looking at which calculation has been most affected by rounding.

Question

A toy store has staff from several different countries in the UK (as shown by the table below). The organisation wants to create a focus group of 50 staff to represent the four different countries.

If company bosses decide to use a stratified sampling methodology, how many people from each country should make up the focus group?

CountryNumber of staff members
Wales563
England1408
Scotland425
Northern Ireland211

563 + 1,408 + 425 +211 = 2,607.

( \frac{563}{2607}) × 50 = 10.798 (11 people from Wales)

( \frac{1408}{2607}) × 50 = 27.004 (27 people from England)

( \frac{425}{2607}) × 50 = 8.151 (8 people from Scotland)

( \frac{211}{2607}) × 50 = 4.047 (4 people from Northern Ireland)

Check: 11 + 27 + 8 + 4 = 50.