What is covered in Grade 12 Mathematics Statistics?

Regression analysis: least squares regression line. Correlation coefficient. Interpret scatter plots and make predictions.

Is Grade 12 Statistics tested in Paper 1 or Paper 2?

Grade 12 Mathematics Statistics is assessed in Paper 2 of the end-of-year examinations, as per the CAPS Mathematics curriculum guidelines.

When is Statistics taught in Grade 12 Mathematics?

Statistics is taught in Term 3 of Grade 12 according to the CAPS Annual Teaching Plan (ATP) for Mathematics in South Africa.

Is Grade 12 Mathematics Statistics on the CAPS curriculum?

Yes. Statistics is part of the official CAPS Mathematics curriculum for Grade 12, Term 3 in South Africa. The content on MathSciBuddy follows the Annual Teaching Plan (ATP) set by the Department of Basic Education.

Is this Grade 12 Mathematics study material free?

Yes. All chapter notes, definitions, formulas, and worked examples on MathSciBuddy are completely free to read. No account or subscription is needed to access CAPS-aligned study notes.

Grade 12 Mathematics

Grade 12 · Term 3Mathematics

Statistics

We study the normal distribution, z-scores, and apply regression and correlation to real data in final-preparation contexts.

Week 5

9.1 Normal Distribution & Regression

Understand the shape and properties of the normal distribution
Calculate and interpret z-scores
Use the 68-95-99.7 rule for normal distributions
Apply regression and correlation for data analysis and prediction

🌍

Real-World Connection

Test scores, heights, and manufacturing tolerances all follow an approximate normal distribution. Quality control engineers use the 68-95-99.7 rule: 95% of products within 2σ of the mean are acceptable; those outside are defects.

Property / Rule

Normal Distribution Properties

Bell-shaped, symmetric about the mean $\mu$ . Mean = Median = Mode. Area under the curve = 1 (total probability). Characterised by $\mu$ and $\sigma$ .

X\sim N(\mu,\sigma^2)

z-score

z = \frac{x-\mu}{\sigma}

$x$ = data value; $\mu$ = mean; $\sigma$ = standard deviation; $z$ = number of standard deviations from mean

Property / Rule

68-95-99.7 Rule (Empirical Rule)

For a normal distribution: approximately 68% of data within 1σ of mean; 95% within 2σ; 99.7% within 3σ.

P(\mu-\sigma<X<\mu+\sigma)\approx0.68

ℹ️ Note

A z-score of $z=2$ means the value is 2 standard deviations above the mean. A negative z-score means the value is below the mean. Comparing z-scores from different distributions allows fair comparison.

Worked Examples

Worked Example

z-score and normal distribution

Problem

\mu=65

Activity — 8 Questions

CAPS Cognitive Level Distribution

L1 · Knowledge2 Q

L2 · Routine Procedures2 Q

L3 · Complex Procedures2 Q

L4 · Problem Solving2 Q

L1 · Knowledge3 marks

Heights are distributed

N(170, 49)

(mean=170,

\sigma^2=49

). Find

P(163<X<177)

L1 · Knowledge1 mark

A data value has

z=-1.5

. Is it above or below the mean?

L2 · Routine Procedures3 marks

N(50, 100)

: find the percentage of data between 30 and 70.

L2 · Routine Procedures4 marks

Student A scores 72 in a class with

\mu=65

\sigma=8

. Student B scores 80 in a class with

\mu=70

\sigma=15

. Who performed relatively better?

L3 · Complex Procedures4 marks

A factory produces bolts with diameter

N(20\text{ mm}, 0.04)

(

\sigma=0.2

mm). Bolts are accepted if diameter is between 19.6 and 20.4 mm. What percentage is rejected?

L3 · Complex Procedures4 marks

Data:

(1,3),(2,5),(3,6),(4,9),(5,11)

. Calculate

\bar{x}

\bar{y}

, and describe the relationship.

L4 · Problem Solving4 marks

For the data in activity 6, the regression line is

\hat{y}=1.9x+1.1

. Predict

y

when

x=7

and comment.

L4 · Problem Solving4 marks

Describe, with examples, the difference between correlation and causation.

Probability