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Grade 12 Statistics — How to Identify the Question Type

Grade 12 statistics introduces bivariate data analysis — scatter plots, the regression line (line of best fit), and the correlation coefficient. Questions also test interpretation: what does the r-value mean, and how does the regression line allow prediction?

Type 1: Scatter plots and correlation

Trigger words: "Draw a scatter plot", "describe the correlation", "positive correlation", "r ="

Trigger structure: Two variables (x and y) are given as paired data. The question asks you to draw or interpret the scatter plot.

Do not confuse with: Regression line — the scatter plot shows the data points; the regression line is a separate calculation.

Method (no numbers — just the steps)

  1. Plot each (x ; y) pair on a set of axes with clearly labelled scales
  2. Describe the correlation: direction (positive/negative) and strength (strong/moderate/weak)
  3. Positive r: y increases as x increases. Negative r: y decreases as x increases
  4. r close to 1 or −1: strong. r close to 0: weak
Grade 12Paper 2Level 1 — Knowledge
2.1 The correlation coefficient for a data set is r = −0.87. Describe the correlation between the two variables.

Source: DBE Mathematics Paper 2, November 2022, Question 2.1

See the progression — same type, increasing difficulty

Easy
A data set has r = 0.95. What does this tell you about the relationship between x and y?

Practice question — not sourced from a past paper.

Medium
Data points are (1 ; 3), (2 ; 5), (3 ; 4), (4 ; 7), (5 ; 8). Draw a scatter plot and describe the correlation.

Practice question — not sourced from a past paper.

Hard
r = 0.02 for a data set. A student says 'there is no relationship between the variables'. Evaluate this claim.

Practice question — not sourced from a past paper.

Type 2: Regression line (line of best fit)

Trigger words: "Least squares regression line", "ŷ = a + bx", "equation of the regression line"

Trigger structure: A bivariate data set is given. The question asks you to determine or use the regression line equation.

Do not confuse with: Drawing a line by eye — the regression line is calculated, not estimated visually.

Method (no numbers — just the steps)

  1. Use a calculator to find a and b: on a scientific calculator, enter stat mode, input paired data, then read off â and b̂
  2. Write the equation: ŷ = a + bx
  3. To predict: substitute the x-value and calculate ŷ
  4. Only predict within the data range (interpolation) — extrapolating beyond the data is unreliable
Grade 12Paper 2Level 2 — Routine Procedures
2.3 The regression line for a data set is ŷ = 3.2 + 1.8x. 2.3.1 Write down the gradient. 2.3.2 Predict y when x = 5.

Source: DBE Mathematics Paper 2, November 2023, Question 2.3

Common mistake

Confusing a and b — b is the gradient (how much y changes per unit of x) and a is the y-intercept.

See the progression — same type, increasing difficulty

Easy
The regression line is ŷ = 10 − 2x. What does the gradient tell you about the data?

Practice question — not sourced from a past paper.

Medium
The data set has mean x̄ = 4 and ȳ = 10, and the regression gradient b = 1.5. Find the y-intercept of the regression line.

Practice question — not sourced from a past paper.

Hard
r = 0.92 and the regression line is ŷ = 5 + 2.3x. A student predicts y = 51 when x = 20. Evaluate the reliability of this prediction.

Practice question — not sourced from a past paper.

Words like determine and hence appear throughout this topic — see the instruction word glossary for full definitions.