What is covered in Grade 10 Mathematics Statistics?

Measures of central tendency and spread for ungrouped and grouped data. Five-number summary, box-and-whisker plots. Histograms. Analyse and comment in context.

Is Grade 10 Statistics tested in Paper 1 or Paper 2?

Grade 10 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 10 Mathematics?

Statistics is taught in Term 3 of Grade 10 according to the CAPS Annual Teaching Plan (ATP) for Mathematics in South Africa.

Is Grade 10 Mathematics Statistics on the CAPS curriculum?

Yes. Statistics is part of the official CAPS Mathematics curriculum for Grade 10, 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 10 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 10 Mathematics

Grade 10 · Term 3Mathematics

Statistics

We collect, organise and summarise univariate data using measures of central tendency (mean, median, mode) and measures of spread (range, quartiles, IQR). We draw and interpret box-and-whisker plots and histograms, and work with both ungrouped and grouped data.

8.1 Measures of Central Tendency & Spread 8.2 Grouped Data & Histograms

Week 6

8.1 Measures of Central Tendency & Spread

Calculate mean, median, mode for ungrouped data; estimate mean for grouped data
Calculate range, quartiles (Q1, Q2, Q3), IQR and semi-IQR
Construct a five-number summary and box-and-whisker plot
Identify and interpret percentiles

🌍

Real-World Connection

When newspapers report the 'average salary', they typically mean the mean — which is pulled upward by a few very high earners. The median is usually more representative of what most workers earn. Knowing the difference between these two measures helps you read any statistical report critically.

Mean (ungrouped)

\bar{x} = \frac{\sum x_i}{n}

$\sum x_i$ = sum of all values; $n$ = number of data values

Definition

Mode

The value that appears most frequently in a data set. A data set may be unimodal (one mode), bimodal (two modes), or have no mode if all values appear equally often.

\text{Mode = value(s) with the highest frequency}

Definition

Median

The middle value when data is arranged in ascending order. With n odd: median is the $\left(\frac{n+1}{2}\right)$ th value. With n even: median is the average of the $\frac{n}{2}$ th and $\left(\frac{n}{2}+1\right)$ th values.

\tilde{x} = \text{middle value of ordered data}

Interquartile Range

\text{IQR} = Q_3 - Q_1

$Q_1$ = lower quartile (median of lower half); $Q_3$ = upper quartile (median of upper half)

Definition

Five-Number Summary

A data summary using five values: Minimum, Q1, Median (Q2), Q3, Maximum. These five values define the box-and-whisker plot.

\{\text{Min};\;Q_1;\;Q_2;\;Q_3;\;\text{Max}\}

💡 Tip

Semi-IQR = IQR/2. The p-th percentile is the value below which p% of the data falls. Q1 = 25th percentile, Q2 = 50th percentile (median), Q3 = 75th percentile.

Worked Examples

Worked Example

Find mode and compare with mean and median

Problem

Shoe sizes sold in a store on one day: 5, 7, 8, 7, 9, 6, 7, 8, 5, 7. Find the mode, mean and median.

Worked Example

Five-number summary and box plot

Problem

Data: 12, 8, 15, 22, 9, 17, 14, 8, 25, 11. Find the five-number summary and IQR.

Worked Example

Effect of an outlier on mean vs median

Problem

Salaries (in R1000s): 18, 21, 19, 22, 20, 95. Find the mean and median. Which is more representative?

Activity — 8 Questions

CAPS Cognitive Level Distribution

L1 · Knowledge2 Q

L2 · Routine Procedures2 Q

L3 · Complex Procedures2 Q

L4 · Problem Solving2 Q

L1 · Knowledge1 mark

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

L1 · Knowledge2 marks

Find the median of: 3, 7, 1, 9, 5, 2.

L2 · Routine Procedures3 marks

Data: 2, 5, 7, 9, 11, 14, 18. Find Q1, Q3 and IQR.

L2 · Routine Procedures3 marks

A dataset has Q1 = 15 and Q3 = 27. Is the value 50 an outlier (using the 1.5 × IQR rule)?

L3 · Complex Procedures4 marks

Six scores: 65, 72, 78, 81, 85, 90. A 7th score raises the mean to 79. Find the 7th score.

L3 · Complex Procedures4 marks

Box plot: Min=10, Q1=18, Median=25, Q3=35, Max=60. Calculate IQR and semi-IQR, and describe the skewness.

L4 · Problem Solving4 marks

A class of 30 has mean 62. Five new students join with mean 80. Find the new class mean.

L4 · Problem Solving4 marks

A dataset of 10 values has mean 15 and the value 25 is removed. Find the new mean.

Week 7

8.2 Grouped Data & Histograms

Estimate the mean of grouped data using midpoints of class intervals
Identify the modal class interval and the class interval containing the median
Draw and interpret histograms (no gaps between bars; frequency on y-axis)
Use statistical summaries to analyse data and make comments in context

🌍

Real-World Connection

National exam results for millions of students are always reported as grouped data — marks in bands like 0–29%, 30–39%, etc. A histogram reveals at a glance whether most students passed or failed, and where performance clusters. Every education policy decision is guided by reading histograms like these.

Estimated mean of grouped data

\bar{x} \approx \frac{\sum f_i m_i}{\sum f_i}

$f_i$ = frequency of class $i$; $m_i$ = midpoint of class interval $i$

Definition

Modal class

The class interval with the highest frequency. We cannot identify the exact mode in grouped data.

\text{Modal class = interval with greatest } f_i

Definition

Median class

The class interval that contains the $\frac{n}{2}$ th value (cumulative frequency crosses 50%). We cannot find the exact median from grouped data — only the interval.

\text{Median class: interval where cumulative freq first exceeds } \frac{n}{2}

ℹ️ Note

In a histogram, each bar represents a class interval. The bars touch (no gaps). The area of each bar is proportional to the frequency. When class widths are equal, frequency is proportional to bar height.

Worked Examples

Worked Example

Estimate mean from a frequency table

Problem

Estimate the mean for the following grouped data: [10-20): f=3; [20-30): f=7; [30-40): f=12; [40-50): f=6; [50-60): f=2

Worked Example

Find modal class and median class

Problem

Using the data from the worked example above, find the modal class and the class interval containing the median.

Activity — 8 Questions

CAPS Cognitive Level Distribution

L1 · Knowledge2 Q

L2 · Routine Procedures2 Q

L3 · Complex Procedures2 Q

L4 · Problem Solving2 Q

L1 · Knowledge1 mark

In a grouped frequency table, what is the midpoint of the class interval [40; 50)?

L1 · Knowledge1 mark

A histogram has bars for [0;10), [10;20), [20;30) with frequencies 4, 9, 6. Which is the modal class?

L2 · Routine Procedures4 marks

Estimate the mean: [0;10): f=5; [10;20): f=8; [20;30): f=7.

L2 · Routine Procedures3 marks

A frequency table has n = 40. In which position(s) does the median lie, and how would you identify the median class?

L3 · Complex Procedures6 marks

Scores (out of 50) grouped as: [0;10): 2; [10;20): 5; [20;30): 11; [30;40): 8; [40;50]: 4. Find the estimated mean, modal class and median class.

L3 · Complex Procedures3 marks

Describe the difference between a histogram and a bar chart.

L4 · Problem Solving4 marks

A learner says the mean of grouped data is exact. Explain why this is incorrect and describe the effect of using wider class intervals.

L4 · Problem Solving4 marks

Two classes wrote the same test. Class A: mean=64, IQR=8. Class B: mean=64, IQR=25. Write a detailed comparison of the two classes' performance.

Analytical Geometry

Probability