Mathematics • Year 10 • Unit 4 • Lesson 12
Scatter Plots and Correlation — Skill Drill
Build fluency with Lesson 12's two skills: plot pairs of bivariate data on a scatter plot, then describe the correlation in three parts — direction (positive / negative / none), strength (strong / moderate / weak), and shape (linear or not).
1. I do — fully worked example
Read every step. Each one has a short reason on the right so you can see why, not just what.
Problem. The bivariate data below pairs hours studied (x) with test score out of 100 (y) for 5 students:
(1, 50), (2, 58), (3, 68), (4, 75), (5, 85).
(a) Plot the points. (b) Describe the correlation in three parts: direction, strength, shape.
Step 1 — Set up axes.
x-axis: hours studied, 0 → 6. y-axis: test score, 40 → 90.
Reason: pick scales that fit the data with some room around it.
Step 2 — Plot each (x, y) as a single dot. Do NOT join them up.
Reason: a scatter plot shows pairs as points, not a connected line.
Step 3 — Describe direction.
As x increases, y increases → positive direction.
Reason: lesson key term — "positive correlation: as one variable increases, the other tends to increase."
Step 4 — Describe strength + shape, then write a single sentence.
The five points sit very close to a straight line → strong, linear.
Answer: "The scatter plot shows a strong positive linear correlation between hours studied and test score."
2. We do — fill in the missing steps
Same structure as Section 1, but with the working faded. Fill in each blank line. 4 marks
Problem. The data below pairs distance from a heater (m) with measured temperature (°C):
(1, 30), (2, 26), (3, 22), (4, 19), (5, 16).
Step 1 — Axes. x-axis range: ____ to ____; y-axis range: ____ to ____.
Step 2 — Direction.
As distance increases, temperature ____________. This is a __________ correlation.
Step 3 — Strength + shape. Are the points close to a straight line, or scattered?
Comment: ______________________________________________________________________________.
Step 4 — One full sentence describing the correlation.
______________________________________________________________________________________.
3. You do — independent practice
For each scenario, state the correlation (direction + strength + shape) and give a one-line reason. Foundation = pick from the three labels. Standard = plot or interpret. Extension = misconception traps from the lesson.
Foundation — name the correlation
3.1 A scatter plot of (1,2), (2,3), (3,5), (4,7), (5,9). State the direction. 1 mark
3.2 A scatter plot of (1,9), (2,7), (3,5), (4,3), (5,1). State the direction. 1 mark
3.3 A scatter plot of (1,5), (2,3), (3,7), (4,2), (5,6). State the direction. 1 mark
3.4 For each pair of variables, predict positive, negative or none (no plotting needed):
(a) hours of sleep vs reaction time (ms),
(b) outside temperature vs ice-cream sales,
(c) shoe size vs IQ. 1 mark
Standard — plot and interpret
3.5 Plot the data and describe the correlation in one sentence (direction + strength + shape):
(5, 30), (10, 35), (15, 50), (20, 60), (25, 80), (30, 95). 2 marks
|—————————————————————————————————|
0 5 10 15 20 25 30
3.6 The scatter plot of (age in years) vs (running speed in km/h) for 12 people shows a clear downward trend, with points sitting fairly close to a straight line. Write a description in the form "direction + strength + shape". 2 marks
Extension — the lesson's trap variables
3.7 Lesson 12 misconception card says a correlation coefficient of −0.9 is STRONGER than +0.5. Explain why, using the term "absolute value", and write the two coefficients in order from strongest to weakest: 0, +0.3, −0.6, +0.95, −0.8. 3 marks
3.8 A student plots data that follows a perfect parabola (U-shape) and reports "no correlation, r ≈ 0". Use the Lesson 12 misconception card to explain why r can be 0 even though there IS a clear pattern in the data. 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (heater)
Step 1: x 0 → 6 m; y 10 → 35 °C (any sensible range that fits).
Step 2: As distance increases, temperature decreases. This is a NEGATIVE correlation.
Step 3: The five points sit very close to a straight line.
Step 4: "There is a strong negative linear correlation between distance from the heater and measured temperature."
3.1
Positive (y rises as x rises).
3.2
Negative (y falls as x rises).
3.3
No correlation (no clear upward or downward trend).
3.4 — Predict the correlation
(a) Negative: more sleep usually → faster (lower) reaction time.
(b) Positive: hotter weather → more ice cream sold.
(c) No correlation: shoe size has no expected relationship with IQ.
3.5 — Plot and describe
Plot: six points climbing roughly along a straight line from (5, 30) to (30, 95). Description: "Strong positive linear correlation."
3.6 — Age vs running speed
"Strong negative linear correlation" (downward trend, points close to a straight line).
3.7 — Strength ordering
Strength = |r|. So |+0.95| = 0.95, |−0.8| = 0.8, |−0.6| = 0.6, |+0.3| = 0.3, |0| = 0.
Strongest → weakest: +0.95, −0.8, −0.6, +0.3, 0. A correlation of −0.9 is stronger than +0.5 because 0.9 > 0.5 in absolute value.
3.8 — Perfect curve, r ≈ 0
The correlation coefficient r measures the strength of a LINEAR relationship only. A perfect U-shape (parabola) goes down and then up by equal amounts, so a straight line is a terrible fit and r ≈ 0 — but the data still has a very clear (non-linear) pattern. The lesson misconception card is explicit: "Data with a perfect curve can have r = 0 even though there is a clear pattern."