MYP 2 Mathematics · Data and Probability

Types of data — census, sample, frequency distribution

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What Is Data?

Before we can analyse anything in science, we need data — the raw facts and figures we collect through observation, measurement, or questioning.

Data

Information collected through observations, measurements, surveys, or experiments that can be organised and analysed.

Think about it: every time you measure the temperature outside, count the number of birds in a tree, or record how tall your classmates are, you're collecting data. But not all data is the same, and how we collect it matters just as much as what we collect.

Types of Data

Before we dive into how to collect data, we need to understand what kind of data we're dealing with. There are two main types:

Qualitative Data

Data that describes categories or qualities — it cannot be measured with numbers. Also called categorical data. Examples: eye colour, favourite sport, type of rock.

Quantitative Data

Data that is measured or counted using numbers. Examples: height in cm, number of pets, temperature in °C.

Quantitative data can be further split into two subtypes:

Discrete Data

Quantitative data that can only take specific, separate values (usually whole numbers). You count discrete data. Example: number of siblings (you can have 2 or 3, but not 2.5!).

Continuous Data

Quantitative data that can take any value within a range, including decimals. You measure continuous data. Example: height (a person could be 162.4 cm or 162.37 cm).

Exam Tip

Quick test: Ask yourself — can the data be counted (discrete), measured (continuous), or does it describe a category (qualitative)? Getting this right helps you choose the correct graph and analysis method later!

In this subtopic, we'll explore:

  • The difference between a census and a sample
  • How to organise data using frequency distributions
  • Why choosing the right method of data collection is critical in science

Census — Collecting Data from Everyone

Census

A method of data collection where information is gathered from every single member of a population or group being studied.

Imagine your teacher wants to know the favourite sport of every student in your class. If she asks every single student, that's a census — no one is left out.

Real-world example: Many countries conduct a national census, usually every 10 years (though some countries, like Canada, do it every 5 years). In a national census, the government tries to collect information from every household in the country — things like how many people live there, their ages, languages spoken, and more.

Advantages of a census:

  • Gives a complete and accurate picture of the whole group
  • No risk of missing important information
  • Results are fully reliable for the group studied

Disadvantages of a census:

  • Can be very time-consuming and expensive, especially for large populations
  • Difficult to carry out if the population is very large or hard to reach
  • By the time data is collected, some information may already be outdated
Analogy

A census is like checking every single apple in a crate for bruises. You'll know exactly how many are damaged, but it takes a long time if the crate is huge!

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