Stratified Sampling
1. The problem involves selecting a sample of employees from an organisation with 5 departments, each having a different number of employees.
2. Since the HR manager has a list of all employees and departments vary in size, a stratified sampling method is appropriate. This ensures each department is proportionally represented.
3. The formula for the sample size from each department is:
$$ n_i = \frac{N_i}{N} \times n $$
where $n_i$ is the sample size from department $i$, $N_i$ is the number of employees in department $i$, $N$ is the total number of employees, and $n$ is the total sample size desired.
4. Important rules:
- The sum of all $n_i$ must equal $n$.
- Each $n_i$ should be rounded appropriately to ensure whole employees are selected.
5. Steps to apply:
- Calculate total employees $N = \sum_{i=1}^5 N_i$.
- Decide total sample size $n$.
- Calculate each $n_i$ using the formula.
- Select $n_i$ employees randomly from each department.
This method ensures fair representation of all departments in the sample, reflecting the organisation's structure accurately.