Data Representation & Summary
Visualize and summarize data using five-number summary, box plots, and more
This document explores the essential concepts of data representation and summary as outlined in the Grade 10 Mathematics CAPS curriculum. It focuses on the five-number summary, box and whisker diagrams, methods for representing grouped data, and a summary table of various graph types.
Learning Outcomes
- Calculate the five-number summary (Min, Q1, Median, Q3, Max)
- Construct and interpret box and whisker diagrams
- Identify skewness from box plots (symmetrical, left, right)
- Represent grouped data using histograms and frequency polygons
- Choose appropriate graph types for different data scenarios
- Compare datasets using box plots
1. The Five-Number Summary
Before visualizing data, it is essential to calculate the five-number summary.
Minimum
The smallest value in the ordered dataset.
Q1 (Lower Quartile)
25th percentile; median of lower half.
Median (Q2)
50th percentile; middle value.
Q3 (Upper Quartile)
75th percentile; median of upper half.
Maximum
The largest value in the dataset.
Five-Number Summary Example
2, 5, 7, 8, 12, 15, 18, 20, 22, 25
Quiz 1 - Five-Number Summary
For data: 3, 6, 9, 12, 15, 18, 21, what is the median?
2. Box and Whisker Diagrams
Box plots visually display the five-number summary and show skewness.
Skewness Visualizer
Click on the shapes to see how skewness affects box plots:
Left Skew (Negative)
Tail on left, median > mean
Symmetric
Balanced, mean ≈ median
Right Skew (Positive)
Tail on right, median < mean
Quiz 2 - Box Plot Interpretation
If the right whisker is longer than the left, the data is:
3. Representing Grouped Data
Histograms
Bar-style graphs where bars touch, showing continuous data intervals.
Frequency Polygons
Join midpoints of histogram tops with straight lines.
Pie Charts
Show proportions of categories as sectors of a circle.
4. Summary Table of Graphs
| Graph Type | Best Use Case | Key Feature |
|---|---|---|
| Box Plot | Comparing spreads/skewness | Shows 5-number summary |
| Histogram | Showing frequency of ranges | No gaps between bars |
| Frequency Polygon | Showing trends in grouped data | Line graph through midpoints |
| Scatter Plot | Identifying relationships | Points on Cartesian plane |
| Pie Chart | Showing proportions | Circle sectors |
Quiz 3 - Graph Types
Which graph is best for showing the frequency of continuous data ranges?
Practice & Assess
Test your knowledge with these interactive games.
Match - Graph to Use Case
Fill - Five-Number Summary
Min, Q1, Median, Q3, ___
Arrange - Quartiles in Order
Click the boxes in ascending order:
Practice Questions
Find five-number summary: 4, 8, 12, 16, 20, 24, 28, 32
What does a longer left whisker indicate?
Which graph has bars that touch?
