What is Systematic Sampling?

S7-SA3-0121

Grade Level:

Class 12

AI/ML, Physics, Biotechnology, FinTech, EVs, Space Technology, Climate Science, Blockchain, Medicine, Engineering, Law, Economics

Definition

What is it?

Systematic sampling is a way to pick a sample from a larger group by selecting items at regular intervals. Imagine you have a long list, and you decide to pick every 5th item; that's systematic sampling. It's an easy and structured method to get a representative subset.

Simple Example

Quick Example

Suppose your school wants to survey students about their favorite lunch item. Instead of asking everyone, the principal decides to pick every 10th student from the school's attendance register. If the register has 1000 students, they'd pick student #10, #20, #30, and so on, until student #1000.

Worked Example

Step-by-Step

Let's say a mobile company wants to test the quality of their new smartphone battery. They produce 500 phones in a batch and want to test 50 of them using systematic sampling.

Step 1: Determine the total population size (N). Here, N = 500 phones.
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Step 2: Determine the desired sample size (n). Here, n = 50 phones.
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Step 3: Calculate the sampling interval (k) by dividing N by n. k = N / n = 500 / 50 = 10.
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Step 4: Choose a random starting point between 1 and k (inclusive). Let's say we randomly pick '7' as our starting point.
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Step 5: Select the sample. Our first sample will be the 7th phone. Then, we add 'k' to find the next phone. So, 7 + 10 = 17 (2nd phone), 17 + 10 = 27 (3rd phone), and so on.
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Step 6: Continue this process until you have 50 phones. The selected phones would be #7, #17, #27, #37, #47, #57, ..., up to #497.

Answer: The sample consists of phones #7, #17, #27, ..., #497.

Why It Matters

Systematic sampling helps researchers quickly and efficiently gather data for big studies, like checking product quality in manufacturing (EVs, Biotechnology) or understanding customer preferences in FinTech. It's used by data scientists and statisticians to make important decisions, ensuring fairness and saving time in fields like AI/ML and Climate Science.

Common Mistakes

MISTAKE: Not calculating the sampling interval correctly, or just picking a random number to add each time. | CORRECTION: The sampling interval (k) must be calculated as Total Population / Sample Size and remain constant throughout the selection process.

MISTAKE: Choosing a starting point outside the range of 1 to k. For example, if k=10, starting at 12. | CORRECTION: The first element for the sample must be chosen randomly from within the first interval (1 to k).

MISTAKE: Using systematic sampling when there's a hidden pattern or cycle in the data that matches the sampling interval. | CORRECTION: Always check if the population list has a repeating pattern. If it does, systematic sampling might pick only one type of item, making the sample biased. In such cases, other sampling methods might be better.

Practice Questions

Try It Yourself

QUESTION: A library has 300 books and wants to inspect 30 of them for damage. If they use systematic sampling, what is the sampling interval? | ANSWER: Sampling interval (k) = Total books / Sample size = 300 / 30 = 10.

QUESTION: A factory produces 1000 light bulbs daily. They want to check 50 bulbs using systematic sampling. If their random starting point is the 12th bulb, list the first three bulbs they will inspect. | ANSWER: Sampling interval (k) = 1000 / 50 = 20. Starting point = 12. First bulb: 12. Second bulb: 12 + 20 = 32. Third bulb: 32 + 20 = 52. So, 12th, 32nd, and 52nd bulbs.

QUESTION: A market researcher wants to survey 100 people from a list of 2500 shoppers. They use systematic sampling. If the random starting number is 15, what will be the 5th person they survey? | ANSWER: Sampling interval (k) = 2500 / 100 = 25. Starting point = 15. The 1st person is 15. The 2nd is 15+25=40. The 3rd is 40+25=65. The 4th is 65+25=90. The 5th person is 90+25=115. So, the 115th person.

MCQ

Quick Quiz

Which of the following is a key characteristic of systematic sampling?

Every item in the population has an equal chance of being selected randomly.

Items are selected from the population at regular, predetermined intervals.

The population is divided into smaller groups, and then some groups are randomly selected.

Only volunteers are included in the sample.

The Correct Answer Is:

Systematic sampling specifically involves selecting items at fixed, regular intervals after a random start. Option A describes simple random sampling, Option C describes cluster sampling, and Option D is convenience sampling.

Real World Connection

In the Real World

Imagine a food delivery app like Zomato or Swiggy wanting to check if their delivery partners are following hygiene rules. They might use systematic sampling to pick every 20th delivery partner from their daily active list for a quick check-up. This helps them maintain quality and ensure customer satisfaction across India.

Key Vocabulary

Key Terms

POPULATION: The entire group you want to study | SAMPLE: A smaller group chosen from the population | SAMPLING INTERVAL: The fixed gap between selected items | RANDOM START: The first item picked by chance | BIAS: When a sample does not truly represent the population

What's Next

What to Learn Next

Now that you understand systematic sampling, explore 'Stratified Sampling'. It's another powerful method where you divide the population into important subgroups before sampling, which can give even more precise results! Keep building your data skills!