What is covered in Grade 11 Mathematics Statistics?

Histograms, frequency polygons, ogives. Variance and standard deviation. Interpret and compare distributions.

Is Grade 11 Statistics tested in Paper 1 or Paper 2?

Grade 11 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 11 Mathematics?

Statistics is taught in Term 4 of Grade 11 according to the CAPS Annual Teaching Plan (ATP) for Mathematics in South Africa.

Is Grade 11 Mathematics Statistics on the CAPS curriculum?

Yes. Statistics is part of the official CAPS Mathematics curriculum for Grade 11, Term 4 in South Africa. The content on MathSciBuddy follows the Annual Teaching Plan (ATP) set by the Department of Basic Education.

Is this Grade 11 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 11 Mathematics

Grade 11 · Term 4Mathematics

Statistics

We extend Grade 10 descriptive statistics to grouped data, variance and standard deviation, and regression (scatter plots and lines of best fit).

Week 1

9.1 Standard Deviation & Regression

Calculate variance and standard deviation for ungrouped data
Interpret standard deviation as a measure of spread
Draw scatter plots and find lines of best fit; calculate the linear regression equation
Interpret correlation coefficient

🌍

Real-World Connection

Standard deviation is used by financial analysts to measure investment risk. A low standard deviation means returns are predictable; high standard deviation means volatile returns. Insurance companies use regression to predict claim costs from historical data.

Variance

\sigma^2 = \frac{\sum(x_i-\bar{x})^2}{n}

Average squared deviation from the mean

Standard Deviation

\sigma = \sqrt{\frac{\sum(x_i-\bar{x})^2}{n}}

Root mean square deviation; same units as data

Definition

Linear Regression

The line of best fit $\hat{y}=a+bx$ minimises the sum of squared vertical distances from the data points to the line. Calculate using: $b=\frac{n\sum xy-\sum x\sum y}{n\sum x^2-(\sum x)^2}$ and $a=\bar{y}-b\bar{x}$ .

\hat{y}=a+bx\quad(\text{least-squares regression line})

Definition

Correlation Coefficient

Pearson's $r$ measures the strength and direction of linear association: $r\in[-1,1]$ . $|r|$ close to 1 = strong linear relationship; $r$ close to 0 = weak or no linear relationship.

-1\leq r\leq 1

ℹ️ Note

Standard deviation measures spread AROUND the mean. If $\sigma$ is small, data is clustered close to the mean. If $\sigma$ is large, data is widely spread.

Worked Examples

Worked Example

Calculate standard deviation

Problem

Data: 4, 6, 8, 10, 12. Find the mean, variance and standard deviation.

Activity — 8 Questions

CAPS Cognitive Level Distribution

L1 · Knowledge2 Q

L2 · Routine Procedures2 Q

L3 · Complex Procedures2 Q

L4 · Problem Solving2 Q

L1 · Knowledge2 marks

State what a small standard deviation tells us about a dataset.

L1 · Knowledge2 marks

Find the mean of: 3, 7, 7, 9, 4.

L2 · Routine Procedures4 marks

Calculate

\sigma

for: 2, 4, 4, 6, 8, 8. (Mean

=5.33

)

L2 · Routine Procedures2 marks

Describe the correlation when

r=-0.92

L3 · Complex Procedures4 marks

Five students' study hours and marks:

(2,45),(3,55),(4,65),(5,70),(6,80)

. Find

\bar{x}

\bar{y}

and describe the pattern.

L3 · Complex Procedures3 marks

Data is shifted by adding 5 to every value. What happens to the mean and standard deviation?

L4 · Problem Solving3 marks

Dataset

A

: mean 50,

\sigma=10

. Dataset

B

: mean 50,

\sigma=2

. Which dataset is more likely to contain the value 65?

L4 · Problem Solving4 marks

Explain why two datasets can have the same mean and range but different standard deviations. Give an example.

Probability