Introduction: Why Samples Matter

Imagine you want to know if every student in your country likes the taste of a new fizzy drink. It would be impossible to ask millions of people individually! Instead, you might ask a small group of \(100\) students. This small group is called a sample.

In Thinking Skills, assessing the representativeness of a sample means deciding if that small group truly reflects the whole group (the "population"). If the sample is "representative," we can trust the evidence. If it isn't, the conclusion might be a "rash generalization."

Note: This topic is part of the "Evaluating Evidence" section. To see how trustworthy a specific person is, you might also want to look at our notes on Assessing Credibility.

The Three Pillars of Representativeness

According to the 9694 syllabus, there are three main things you must look for when evaluating a sample: Number, Characteristic, and Selectivity. Let’s break these down.

1. Number (Sample Size)

The "Number" refers to how many individuals or items are in the sample. As a general rule: the larger the sample, the more reliable the evidence.

  • Small Samples: If a sample is too small, it might just be a coincidence. If you toss a coin \(2\) times and get "Heads" both times, you wouldn't conclude that the coin always lands on heads. The sample size (\(2\)) is just too small.
  • Large Samples: A larger sample helps to "cancel out" unusual or extreme cases, giving a clearer picture of the average reality.

Quick Tip: In your exam, if you see a very low number (like "A survey of \(5\) doctors..."), this is almost always a weakness in the evidence because the sample size is insufficient to represent a whole profession.

2. Characteristic (Who is in the sample?)

The "Characteristic" refers to the types of people or things in the sample. For a sample to be representative, it must share the same variety of features as the wider population.

Think about these features:

  • Age
  • Gender
  • Location (Urban vs. Rural)
  • Income or Social Class
  • Interests or Jobs

Example: If a researcher wants to know what "the public" thinks about a new tax, but they only interview millionaires, the sample lacks the characteristic of "the public." It misses out on the views of low-income and middle-income earners.

Key Takeaway: Always ask, "Does this small group look like a miniature version of the big group?" If the answer is no, the sample is not representative.

3. Selectivity (How was the sample chosen?)

This is often where bias creeps in. "Selectivity" looks at the method used to pick the participants. If the method favors certain people over others, the sample is "selected" or "biased."

Common issues with selectivity include:

  • Self-Selection: This happens when people choose to take part (like an online poll or a radio call-in). Usually, only people with very strong or angry opinions bother to respond. This does not represent the "quiet majority."
  • Location Bias: If you survey people about exercise habits but you stand outside a gym, your results will be skewed. You have "selected" a group that is already interested in the topic.

"Did you know?"

A sample can be large (high Number) but still fail because of Selectivity. For example, a survey of \(10,000\) people about video games is a large number, but if they were all recruited from a gaming convention, it still won't represent the general population!

How to Write About Representativeness in the Exam

When you are asked to evaluate a source in Paper 2, follow these steps:

  1. Identify the Claim: What is the source trying to prove? (e.g., "Most people prefer cats over dogs.")
  2. Identify the Sample: Who was actually asked? (e.g., "\(20\) people at a Cat Show.")
  3. Apply the Three Pillars:
    • Is the Number big enough? (\(20\) is quite small for a general claim).
    • Are the Characteristics diverse? (No, they are all cat enthusiasts).
    • Is there a Selectivity bias? (Yes, the location—a Cat Show—guarantees a specific result).
  4. Conclusion: State clearly that the sample is unrepresentative and therefore the evidence is weak or the conclusion is unreliable.

Common Mistakes to Avoid

Don't confuse "Representativeness" with "Credibility":

  • Credibility is about whether a source is lying or mistaken (Vested Interest, Expertise, etc.).
  • Representativeness is about whether a small group is a good "snapshot" of a bigger group.

Don't just say "it's too small":
Even a small sample can be useful for a very specific claim. If a claim is only about "students in Class 10A," asking \(15\) out of \(20\) students is actually quite representative! Always check what the target population is before criticizing the sample size.

Summary Checklist

Before you move on, make sure you can answer "Yes" to these questions for any sample you see:

1. Number: Is the group large enough to represent the whole population? (\(n \geq \dots\))
2. Characteristic: Does the group include a variety of different types of people?
3. Selectivity: Was the group picked randomly, or was there a bias in how they were chosen?

Don't worry if this seems tricky at first. The more you practice looking for "who is missing" from a sample, the easier it becomes to spot these flaws in reasoning!