Many companies and organisations collect data to improve their information and products. Skills in collecting data make this process more efficient and reliable.
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.
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 |
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) |
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.
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 |
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.