Edexcel Mathematics (4XMAH) -Unit 1 - 6.1 Graphical Representation of Data- Study Notes- New Syllabus
Edexcel Mathematics (4XMAH) -Unit 1 – 6.1 Graphical Representation of Data- Study Notes- New syllabus
Edexcel Mathematics (4XMAH) -Unit 1 – 6.1 Graphical Representation of Data- Study Notes -Edexcel iGCSE Mathematics – per latest Syllabus.
Key Concepts:
A construct and interpret histograms (for continuous variables with unequal class intervals)
Edexcel iGCSE Mathematics -Concise Summary Notes- All Topics
Histograms (Unequal Class Intervals)
A histogram is used to represent continuous data grouped into class intervals.
Unlike bar charts, the bars touch each other because the data is continuous.
Important
When class widths are different, we do not use frequency directly. We use frequency density.
\( \mathrm{Frequency\ density}=\dfrac{\mathrm{frequency}}{\mathrm{class\ width}} \)
Class Width
\( \mathrm{Class\ width}=\mathrm{upper\ boundary}-\mathrm{lower\ boundary} \)
Drawing a Histogram
1. Convert classes to continuous boundaries.
2. Calculate class width.
3. Calculate frequency density.
4. Horizontal axis: class boundaries.
5. Vertical axis: frequency density.
Example 1:
The table shows the distribution of the lengths of rods (in cm). Find the Frequency densities
| Length (cm) | Frequency |
|---|---|
| 0 < l ≤ 5 | 6 |
| 5 < l ≤ 10 | 8 |
| 10 < l ≤ 20 | 10 |
| 20 < l ≤ 30 | 12 |
▶️ Answer/Explanation
Class widths
- 0–5 → width = 5
- 5–10 → width = 5
- 10–20 → width = 10
- 20–30 → width = 10
Frequency densities
- 0–5: \( \frac{6}{5} = 1.2 \)
- 5–10: \( \frac{8}{5} = 1.6 \)
- 10–20: \( \frac{10}{10} = 1.0 \)
- 20–30: \( \frac{12}{10} = 1.2 \)
Note: Frequency density helps construct histograms when class widths are unequal.
Example 2:
A class interval is \( 30\text{–}50 \) with frequency 16. Find the frequency density.
▶️ Answer/Explanation
Class width \( =50-30=20 \)
\( \mathrm{Frequency\ density}=16/20=0.8 \)
Conclusion: \( 0.8 \).
Example 3:
A histogram bar has width \( 5 \) and frequency density \( 2.4 \). Find the frequency.
▶️ Answer/Explanation
\( \mathrm{Frequency}=\mathrm{density}\times\mathrm{class\ width} \)
\( =2.4\times5=12 \)
Conclusion: Frequency \( =12 \).