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)

Plot each (x ; y) pair on a set of axes with clearly labelled scales
Describe the correlation: direction (positive/negative) and strength (strong/moderate/weak)
Positive r: y increases as x increases. Negative r: y decreases as x increases
r close to 1 or −1: strong. r close to 0: weak

Grade 12Paper 2Level 1, Knowledge

A scatter plot is drawn for the height (in cm) and service speed (in km/h) of 10 tennis players. Three values of r are given: r = 0,93 ; r = −0,42 and r = 0,52. 2.2.1 Which ONE of the values of r best represents the data in the scatter plot?

Source: DBE Mathematics Paper 2, November 2018, Question 2.2.1

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)

Use a calculator to find a and b: on a scientific calculator, enter stat mode, input paired data, then read off â and b̂
Write the equation: ŷ = a + bx
To predict: substitute the x-value and calculate ŷ
Only predict within the data range (interpolation), extrapolating beyond the data is unreliable

Grade 12Paper 2Level 2, Routine Procedures

The table below shows the monthly income (in rands) of 6 different people and the amount (in rands) that each person spends on the monthly repayment of a motor vehicle. MONTHLY INCOME: 9 000 ; 13 500 ; 15 000 ; 16 500 ; 17 000 ; 20 000 MONTHLY REPAYMENT: 2 000 ; 3 000 ; 3 500 ; 5 200 ; 5 500 ; 6 000 1.1 Determine the equation of the least squares regression line for the data. 1.2 If a person earns R14 000 per month, predict the monthly repayment that the person could make towards a motor vehicle.

Source: DBE Mathematics Paper 2, November 2019, Question 1.1–1.2

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.