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."