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Module 5 · L02 of 8 ~30 min MST-12-S2-08 ⚡ +70 XP available

Describing Correlation

Cricket Australia analysts use correlation to find which batting statistics best predict match wins, not always the obvious ones. To use correlation like this, you need to describe both direction (positive/negative) and strength (strong/moderate/weak) precisely.

Think first, A scatterplot shows that taller people tend to earn more. Is this a strong or weak relationship? Is it positive or negative?
0/5QUESTS
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Orient to correlation

Connect direction, strength and the language of association.

Worksheets

Practise this lesson

Three printable worksheets that build from foundations to mastery, or build your own from any module’s questions.

Build Foundations & guided practice Apply Application practice Master Mastery challenge Build custom Build your own from any module question
01
Think First, recall from memory
+5 XP warm-up

A scatterplot shows that taller people tend to earn more. Before reading on, decide: is this relationship strong or weak? Is it positive or negative? How would you describe it in a complete sentence?

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02
The big idea, direction and strength together
+5 XP to read

Correlation describes the relationship between two variables in a scatterplot. It has two components you must always state together.

Direction: positive (both variables increase together), negative (as one increases the other decreases), or no correlation.

Strength: strong (points close to a line), moderate, or weak (widely scattered).

Full description = direction + strength + "linear correlation"
e.g. "strong positive linear correlation"
Direction first
Is the overall pattern going up (positive) or down (negative)? Or is there no clear direction?
Strength second
How close are the points to a straight line? Tight = strong; a broad band = moderate; random scatter = weak or none.
Use both words
Always state both direction AND strength. "Positive correlation" alone is incomplete, add "strong," "moderate," or "weak."
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What you will learn
Know

Key facts

  • The three possible directions: positive, negative, none
  • The three possible strengths: strong, moderate, weak
  • The correct language for a full correlation description
Understand

Concepts

  • What "direction" means visually on a scatterplot
  • What "strength" means in terms of how close points are to a line
  • Why both components are needed to describe correlation
Can do

Skills

  • Identify direction and strength from a scatterplot description
  • Write a complete correlation description using correct vocabulary
  • Match a description to one of several scatterplot patterns
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Key terms, correlation
CorrelationA measure of the relationship between two variables, described by direction and strength.
Positive correlationAs the x variable increases, the y variable tends to increase, points rise from lower-left to upper-right.
Negative correlationAs the x variable increases, the y variable tends to decrease, points fall from upper-left to lower-right.
No correlationNo consistent pattern between the two variables, points appear randomly scattered with no clear direction.
Strong correlationPoints are clustered closely around a straight line, the relationship is clear and consistent.
LinearDescribes a relationship that follows an approximately straight-line pattern (as opposed to curved).
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Identify direction

Distinguish positive, negative and no correlation from the pattern of points.

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Direction, positive, negative, or none
MST-12-S2-08 core

The direction of correlation describes whether the two variables move in the same direction or opposite directions as you move along the x-axis.

  • Positive: Higher x tends to pair with higher y. The points slope upward from left to right. Example: hours studied and exam score, more study tends to give higher scores.
  • Negative: Higher x tends to pair with lower y. The points slope downward from left to right. Example: temperature and hot coffee sales, hotter days mean fewer hot drinks sold.
  • No correlation: No consistent pattern. Example: shoe size and IQ score, no systematic relationship.
Visual check: Imagine a line through the cloud of points. Does it slope up? Down? Or is there no line that fits? That tells you the direction.

Correlation direction: positive means both variables increase together; negative means one increases as the other decreases; no correlation means there is no consistent linear trend between the variables.

Pause, copy the three correlation directions: positive (points rise left to right), negative (points fall left to right), and no correlation (points show no consistent direction) with a one-line description of each into your book.

Quick check: A scatterplot shows that as daily temperature increases, the number of umbrellas sold decreases. What direction is this correlation?

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Judge strength

Use the closeness of points to a line to classify strength.

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Strength, strong, moderate, or weak
MST-12-S2-08 core

Direction tells you whether the pattern goes up, down, or nowhere, but two scatterplots can both be positive and look completely different. Strength captures how tightly the points cluster around an imaginary straight line: strong means points are close to the line, moderate means some scatter, and weak means points are widely spread with only a vague trend.

The strength of correlation describes how closely the points follow a straight line.

  • Strong: Points are tightly clustered along a line, you can predict y from x with high accuracy. The trend is obvious at a glance.
  • Moderate: Points follow a general trend but with noticeable scatter, you can predict the direction of y but not its exact value.
  • Weak: Points are widely scattered, there is barely a pattern, and x is a poor predictor of y.

Think of strength as "how close together are the dots?", the tighter the band of points around a straight line, the stronger the correlation.

Remember: Even a weak correlation has a direction (unless there is truly no correlation). Always state both, e.g. "weak positive" or "strong negative."

Correlation strength describes how tightly the points cluster around a linear trend: strong (tight cluster), moderate (visible trend with scatter), or weak (barely discernible trend). Strength and direction are reported together.

Pause, copy the three strength categories: strong (points close to a line), moderate (noticeable scatter around the line), and weak (wide scatter, pattern barely visible) into your book.

Which does NOT belong? Descriptions used when classifying correlation:

4

Describe correlation fully

Combine direction, strength, form and variables in a complete statement.

07
Describing correlation using both components together
MST-12-S2-08 core

Direction (positive/negative/none) and strength (strong/moderate/weak) must always appear together in an exam description, writing only one of them earns partial marks at best. Combine them in one sentence using the actual variable names: for example, "there is a strong positive association between hours of study and exam score".

A complete correlation description uses both direction AND strength. The standard HSC format is:

[strength] + [direction] + "linear correlation"

Examples:

  • "There is a strong positive linear correlation between hours of study and exam score."
  • "There is a moderate negative linear correlation between temperature and hot coffee sales."
  • "There is a weak positive linear correlation between age and income." (Note: weak, not strong, because the scatter is large.)
  • "There is no linear correlation between shoe size and reading ability."
Common error
Saying only "positive correlation"
Stating just "positive" or just "negative" without a strength word is incomplete. Full marks require both: "strong positive," "moderate negative," etc.
Common error
Confusing direction with strength
"Strong" and "weak" describe how close the points are to a line, NOT how steep the line is. A steep line can still have weak correlation if the scatter is large.

A complete correlation description uses both direction and strength: e.g., 'strong positive', 'weak negative', or 'no correlation'. In HSC responses, always include both components and relate them to the actual variable names.

Pause, copy the combined description template: "[strong/moderate/weak] [positive/negative] association between [x-variable] and [y-variable]" and write two example sentences using different real variable pairs into your book.

Complete: A scatterplot showing points tightly grouped along a downward-sloping line would be described as a linear correlation.

5

Work correlation examples

Compare complete descriptions across three worked scatterplots.

Worked examples · 3 in a row, reveal as you go

PROBLEM 1 · DESCRIBE FROM A DESCRIPTION

A scatterplot of study hours vs exam score shows points rising from lower-left to upper-right, closely grouped around a straight line. Describe the correlation.

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Direction: points rise from lower-left to upper-right → positive.
As study hours increase, exam scores tend to increase, same direction.
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PROBLEM 2 · IDENTIFY THE MATCHING DESCRIPTION

Four scatterplot descriptions: (A) points slope down, tightly grouped. (B) points slope up, widely scattered. (C) random scatter. (D) points slope up, closely grouped. Which matches "weak positive linear correlation"?

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"Positive" → points slope up. This eliminates (A) and (C).
Positive correlation means both variables increase together, points rise from left to right.
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PROBLEM 3 · DESCRIBE A REAL-WORLD PATTERN

A researcher plots the number of cigarettes smoked per day (x) against resting heart rate (y). The points show a general upward trend but with noticeable scatter. Describe the correlation.

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Direction: upward trend → positive. As smoking increases, heart rate tends to increase.
Both variables go in the same direction.
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6

Apply correlation language

Classify new patterns and revisit the opening prediction.

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Activity, classify and describe

For each situation below, write a full correlation description (strength + direction + "linear correlation"):

  1. Daily temperature (°C) vs hot coffee sales: points slope steeply down, tightly clustered.
  2. Number of absences vs final grade: general downward trend, wide scatter.
  3. Birth month vs favourite colour: no pattern visible.
  4. Height vs weight for adults: clear upward trend, moderate scatter.
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Revisit your thinking

At the start you described the relationship between height and earnings. This relationship, if it exists, would likely be described as a weak positive linear correlation there is an upward trend (taller tends to earn more in some datasets), but the scatter is large because many other factors (education, occupation, experience) affect earnings much more than height does.

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7

Answer correlation questions

Use precise direction-and-strength language in short-answer responses.

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Short answer
ApplyBand 33 marks

Q1. A scatterplot shows the relationship between hours of TV watched per day and academic grade (%). The points cluster loosely around a downward-sloping line. (a) What is the direction of this correlation? (b) What is the strength? (c) Write a complete description of the correlation. (3 marks)

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AnalyseBand 42 marks

Q2. A student says: "The scatterplot shows positive correlation." Explain why this description is incomplete and rewrite it in full. (2 marks)

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Answers (click to reveal)

Activity answers: (1) Strong negative linear correlation. (2) Weak negative linear correlation. (3) No linear correlation. (4) Moderate positive linear correlation.

Q1 (3 marks): (a) Negative, as TV hours increase, grades decrease [1]. (b) Moderate, points cluster loosely (not tightly) around the line [1]. (c) "There is a moderate negative linear correlation between hours of TV watched per day and academic grade" [1].

Q2 (2 marks): The description is incomplete because it states only the direction (positive) but not the strength [1]. A complete description requires both: e.g. "There is a strong positive linear correlation between the two variables" [1].