What is Stratified Sampling?

S8-SA1-0067

Grade Level:

Class 5

AI/ML, Data Science, Research, Journalism, Law, any domain requiring critical thinking

Definition

What is it?

Stratified sampling is a smart way to pick a sample from a large group (population) to make sure your sample looks exactly like the big group. You divide the big group into smaller, similar subgroups (like dividing students by class) and then pick some from each subgroup. This helps get a fair and accurate picture.

Simple Example

Quick Example

Imagine your school has 100 students: 50 in Class 5, 30 in Class 6, and 20 in Class 7. If you want to pick a sample of 10 students to ask about their favourite snack, you wouldn't just pick any 10. Using stratified sampling, you'd pick 5 students from Class 5, 3 from Class 6, and 2 from Class 7. This way, your sample of 10 truly represents the proportion of students in each class.

Worked Example

Step-by-Step

Let's say a mobile company wants to understand how satisfied its customers are in a city. There are 10,000 customers in total.

They know their customers are divided into three groups based on their data plan: Basic (6,000 customers), Standard (3,000 customers), and Premium (1,000 customers).

The company wants to survey a sample of 500 customers.

STEP 1: Calculate the proportion of each group in the total customer base.
Basic: 6,000 / 10,000 = 0.6 (or 60%)
Standard: 3,000 / 10,000 = 0.3 (or 30%)
Premium: 1,000 / 10,000 = 0.1 (or 10%)

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STEP 2: Multiply these proportions by the desired sample size (500) to find out how many customers to pick from each group.
Basic: 0.6 * 500 = 300 customers
Standard: 0.3 * 500 = 150 customers
Premium: 0.1 * 500 = 50 customers

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STEP 3: Pick 300 customers randomly from the Basic group, 150 from the Standard group, and 50 from the Premium group.

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Answer: The company should survey 300 Basic, 150 Standard, and 50 Premium customers to get a representative sample of 500.

Why It Matters

Stratified sampling is super important in fields like Data Science and Research because it helps collect data that is fair and accurate, avoiding wrong conclusions. Journalists use it to conduct reliable surveys, and even in Law, it can ensure fair representation in studies. It helps people make better decisions based on good data.

Common Mistakes

MISTAKE: Not dividing the population into groups before sampling. | CORRECTION: Always identify the different important subgroups (strata) in your population first, like age groups or income levels, before picking anyone.

MISTAKE: Picking an unequal number of people from each group without considering their size in the original population. | CORRECTION: Ensure the number of samples you pick from each group is proportional to that group's size in the overall population. If Class 5 is bigger, more students should be picked from Class 5.

MISTAKE: Not picking randomly within each subgroup. | CORRECTION: Once you decide how many to pick from each subgroup, make sure to pick those individuals randomly from within that subgroup to avoid bias.

Practice Questions

Try It Yourself

QUESTION: A library wants to know what type of books students prefer. There are 200 primary school students, 300 middle school students, and 500 high school students. If they want a sample of 100 students, how many should they pick from each group using stratified sampling? | ANSWER: Primary: 20, Middle: 30, High: 50

QUESTION: A local election has 10,000 voters. 4,000 are male, and 6,000 are female. If a survey needs a sample of 200 voters, how many males and females should be included to represent the voter population accurately? | ANSWER: Males: 80, Females: 120

QUESTION: A video game company has 1,000 users. 50% are casual gamers, 30% are regular gamers, and 20% are pro gamers. If they want to survey 150 users about a new game feature, how many should they select from each category? After selecting, if 10% of the casual gamers, 20% of the regular gamers, and 30% of the pro gamers in the sample respond, how many total responses did they get? | ANSWER: Casual: 75, Regular: 45, Pro: 30. Total responses: 7.5 + 9 + 9 = 25.5 (or 26 if rounded up)

MCQ

Quick Quiz

Why is stratified sampling often preferred over simple random sampling when a population has distinct subgroups?

It is always easier to implement.

It guarantees that all subgroups are represented proportionally in the sample.

It allows picking only from the largest subgroup.

It requires no prior information about the population.

The Correct Answer Is:

Stratified sampling ensures that important subgroups within a population are included in the sample in their correct proportions, leading to a more representative and accurate survey. Simple random sampling might accidentally miss some subgroups.

Real World Connection

In the Real World

When a company like Zomato or Swiggy wants to understand customer satisfaction across different cities or delivery zones, they might use stratified sampling. They'd divide customers by city or zone (strata) and then survey a proportional number from each to get a fair view of satisfaction across their entire service area in India.

Key Vocabulary

Key Terms

POPULATION: The entire group you are interested in studying | SAMPLE: A smaller, representative part of the population that you actually study | SUBGROUP (STRATA): A distinct, similar group within a larger population, like 'boys' and 'girls' | PROPORTION: The fraction or percentage that one part makes up of the whole | REPRESENTATIVE: A sample that accurately reflects the characteristics of the larger population

What's Next

What to Learn Next

Now that you understand stratified sampling, you can explore other sampling methods like 'cluster sampling' and 'systematic sampling'. Each method has its own benefits and is used in different situations, building on your understanding of how to collect good data.