Stratified sampling

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 group	Number of customers
11-20	12
21-30	34
31-40	48
41-50	21
51+	3

Age group	11-20
Number of customers	12

Age group	21-30
Number of customers	34

Age group	31-40
Number of customers	48

Age group	41-50
Number of customers	21

Age group	51+
Number of customers	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 group	Number 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)

Age group	11-20
Number in sample	(\(\frac{12}{118}\)) x 25 = 2.54 (3 customers)

Age group	21-30
Number in sample	(\(\frac{34}{118}\)) x 25 = 7.20 (7 customers)

Age group	31-40
Number in sample	(\(\frac{48}{118}\)) x 25 = 10.17 (10 customers)

Age group	41-50
Number in sample	(\(\frac{21}{118}\)) x 25 = 4.45 (4 customers)

Age group	51+
Number in sample	(\(\frac{3}{118}\)) x 25 = 0.63 (1 customer)

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?

Country	Number of staff members
Wales	563
England	1408
Scotland	425
Northern Ireland	211

Country	Wales
Number of staff members	563

Country	England
Number of staff members	1408

Country	Scotland
Number of staff members	425

Country	Northern Ireland
Number of staff members	211

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Sampling data - Intermediate & Higher tier - WJECStratified sampling