Strata (Edexcel GCSE Statistics): Revision Notes
Strata
What are strata?
In statistics, a stratum (plural: strata) refers to a distinct group within a population. When we use stratified sampling, we divide the entire population into these separate groups or strata based on certain characteristics like age, gender, class, or any other relevant factor.
The key principle behind using strata is that each group in your sample must have the same proportion as it does in the original population. This means if boys make up 60% of your population, they should also make up 60% of your sample.
Why use strata in sampling?
Stratified sampling with strata gives you a major advantage over simple random sampling. When you use strata, you can guarantee that all important groups in your population are properly represented in your sample. With simple random sampling, you might accidentally miss out certain groups entirely.
For example, if you're studying students in a school and you want to make sure you include students from every year group, using strata ensures each year group appears in your sample in the correct proportion.
Calculating sample sizes for each stratum
When working with stratified sampling, you need to calculate how many people to include from each stratum in your sample. Here's the essential approach:
Formula for Stratified Sampling:
Step-by-step process:
- First, find the proportion of each stratum in the population
- Then multiply this proportion by your desired sample size
- This gives you the number of people needed from each stratum
Worked example: gym membership
Worked Example: Gym Membership Sampling
Let's say a gym has the following membership:
- Males: 120 members
- Females: 80 members
- Total: 200 members
You want to take a stratified sample of 40 gym members. How many males should be in your sample?
Step 1: Calculate the proportion of males in the population
Step 2: Apply this proportion to your sample size
Answer: You need 24 males in your sample of 40 people.
Worked example: school classes
Worked Example: School Class Sampling
A primary school has three classes in Year 6:
- Class A: 34 children
- Class B: 28 children
- Class C: 18 children
- Total: 80 children
The headteacher wants a stratified sample of 20 children. How many should come from each class?
Step 1: Calculate the sample size for each class using the formula
Step 2: Round to whole numbers Since you can't have half a person, you need to round:
- Class A: 8.5 rounds to 9
- Class B: 7 stays as 7
- Class C: 4.5 rounds to 4
Check: ✓
Important points to remember about rounding
When your calculations give you decimal numbers, you must round to whole numbers since you can't sample part of a person.
Rounding Rules for Stratified Sampling:
- Always round to the nearest whole number
- Check that your rounded numbers add up to your target sample size
- If the total is too high after rounding, subtract 1 from the largest stratum
- If the total is too low after rounding, add 1 to the largest stratum
Key Points to Remember:
- A stratum is simply a group within your population based on shared characteristics
- Each stratum in your sample must maintain the same proportion as in the original population
- Use the formula: to calculate how many from each group
- Always round decimal results to whole numbers and check your total adds up correctly
- Stratified sampling ensures all groups are fairly represented, unlike simple random sampling