MYP 2 Mathematics · Algebra

Dependent and independent variables — graphing patterns

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From One Variable to Two: Introducing Bi-variate Data

So far in your studies, you may have looked at data involving a single measurement — like how many books students read in a month, or the temperature each day. This is called uni-variate data (one variable).

But the real magic happens when we start asking questions like: Does studying more lead to better grades? or Does more rainfall mean more tomatoes? These questions involve two variables at once.

Uni-variate data

Data that involves only one variable. For example: the heights of students in a class.

Bi-variate data

Data that involves two variables, allowing us to explore relationships between them. For example: the relationship between hours of study and exam scores.

Exam Tip

Here's a quick cheat: if a research question asks about a relationship between two things, it is bi-variate data. If it just describes or counts one thing, it's uni-variate.

Example

Decide whether each research question involves uni-variate or bi-variate data:

  • "How many hours of sunlight does a city receive each day in summer?" → Uni-variate (only measuring one thing: hours of sunlight)
  • "Is there a relationship between driving speed and fuel consumed?" → Bi-variate (two variables: speed and fuel)
  • "What is the most popular song in a school survey?" → Uni-variate (one variable: song choice)
  • "What is the relationship between rainfall and number of ripe tomatoes?" → Bi-variate (two variables: rainfall and tomatoes)

The Cartesian Plane: Your Graphing Grid

To graph bi-variate data, we need a special grid called the Cartesian plane. It was invented by the French mathematician René Descartes (1596–1650), who developed a brilliant way to describe the position of any point using just two numbers.

Cartesian plane

A two-dimensional grid formed by two number lines — a horizontal axis (x-axis) and a vertical axis (y-axis) — that cross at a point called the origin. Named after René Descartes.

Here are the key parts of the Cartesian plane:

  • x-axis — the horizontal number line (positive to the right, negative to the left)
  • y-axis — the vertical number line (positive going up, negative going down)
  • Origin — the point where the axes cross, written as
  • Quadrants — the four sections the axes divide the plane into, numbered clockwise starting from the upper right: Quadrant I (upper right), Quadrant II (upper left), Quadrant III (lower left), Quadrant IV (lower right)
Analogy

Think of the Cartesian plane like a map of your city. The x-axis is like streets running East-West, and the y-axis is like avenues running North-South. Every location can be described by how far East/West and how far North/South it is from the centre of the city (the origin).

Note

The word axes is the plural of axis. So one line is an axis; both lines together are the axes.

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