IB MYP 4-5 Maths- Histograms - Study Notes - New Syllabus
IB MYP 4-5 Maths- Histograms – Study Notes
Extended
- Histograms
Histograms
Histograms
A histogram is a graphical representation of grouped data using adjoining rectangles (bars) whose area is proportional to frequency. Unlike bar charts, histograms represent continuous data (intervals have no gaps).
Key Features:
- Used for continuous or grouped data.
- The x-axis represents the class intervals, and the y-axis represents frequency or frequency density.
- Bars are adjacent with no gaps (because data is continuous).
- If intervals are not equal, use frequency density: \( \text{Frequency Density} = \dfrac{\text{Frequency}}{\text{Class Width}} \)
Types of Histograms:
- Histogram for Continuous Fixed Interval Groups: Class widths are equal, so bar height = frequency.
- Histogram for Non-Continuous Interval Groups: Class widths are unequal, so use frequency density.
Histograms for Continuous Fixed Interval Groups
When all class intervals have equal width, the height of each bar is proportional to the frequency. No frequency density adjustment is needed.
Example:
The table shows the marks of 40 students:
| Marks | Frequency |
|---|---|
| 0–10 | 5 |
| 10–20 | 8 |
| 20–30 | 12 |
| 30–40 | 10 |
| 40–50 | 5 |
▶️Answer/Explanation
Step 1: All intervals have equal width (10), so bar height = frequency.
Step 2: Draw histogram with marks on x-axis, frequency on y-axis. Bars: 0–10 → 5, 10–20 → 8, 20–30 → 12, 30–40 → 10, 40–50 → 5.
Observation: Highest frequency = 12 for 20–30 interval.
Example:
The table shows ages of participants in a survey:
| Age (years) | Frequency |
|---|---|
| 0–10 | 4 |
| 10–20 | 6 |
| 20–30 | 10 |
| 30–40 | 8 |
| 40–50 | 2 |
▶️Answer/Explanation
Step 1: Equal width = 10 → Height = frequency.
Step 2: Draw bars with heights: 4, 6, 10, 8, 2.
Observation: Most participants are in 20–30 years group.
Histograms for Non-Continuous Interval Groups
If class widths differ, use frequency density: \( \text{Frequency Density} = \dfrac{\text{Frequency}}{\text{Class Width}} \)
Example:
The table shows weights of students:
| Weight (kg) | Frequency |
|---|---|
| 30–40 | 6 |
| 40–50 | 8 |
| 50–70 | 10 |
| 70–90 | 6 |
▶️Answer/Explanation
Step 1: Calculate width and frequency density:
30–40: width = 10, FD = 6/10 = 0.6
40–50: width = 10, FD = 8/10 = 0.8
50–70: width = 20, FD = 10/20 = 0.5
70–90: width = 20, FD = 6/20 = 0.3
Step 2: Draw bars with heights = FD.
Example:
The table shows time (minutes) spent on social media:
| Time (min) | Frequency |
|---|---|
| 0–10 | 10 |
| 10–30 | 20 |
| 30–60 | 15 |
▶️Answer/Explanation
Step 1: Calculate FD:
0–10: width = 10, FD = 10/10 = 1
10–30: width = 20, FD = 20/20 = 1
30–60: width = 30, FD = 15/30 = 0.5
Step 2: Draw histogram with heights = FD.