The Density Mapper
Histograms · Frequency Density · Area = Frequency
The Golden Rule
Area = Frequency
FD = F ÷ Class Width
Frequency
40
Class Width
20
FD = Height
2.000
Area ✓
40.0
🎛 Adjust Frequency — Watch FD Change Live
🔑 Histogram Identity
The y-axis shows Frequency Density, not frequency. The area of each bar is the frequency.
⚖️ The Golden Rule
💡 Bar: 10–30
📡 Live Insight
Standard-width class. FD and frequency balance naturally.
All Bars
| Class | F | CW | FD |
|---|---|---|---|
| 10–30 | 40 | 20 | 2.00 |
| 30–45 | 30 | 15 | 2.00 |
| 45–55 | 25 | 10 | 2.50 |
| 55–80 | 50 | 25 | 2.00 |
| 80–100 | 20 | 20 | 1.00 |
| Total | 165 | — | |
📐 Canonical Worked Example
Class: 10 < w ≤ 30 · F = 40
Find Class Width
CW = 30 − 10
CW = 20
Apply FD Formula
FD = 40 ÷ 20
FD = 2
Plot & Verify
Bar: 10 to 30, height 2
Area = 2 × 20 = 40 ✓
🔢 Live Solver
Selected: 10–30 · F = 40
Class Width
CW = 30 − 10
CW = 20
Freq. Density
FD = 40 ÷ 20
FD = 2.0000
Verify Area
2.0000 × 20 = 40.0
Proportionality Check
CW × 2 → FD = 1.000 (halved)
CW ÷ 2 → FD = 4.000 (doubled)
📏 Median Interpolation
Phase 3 · Grade 9 Killer Technique
Median Position
n ÷ 2 = 165 ÷ 2 = 82.5th
Locate Median Bar
Median bar: 45–55
Cum. freq before: 70
Interpolate
45 + (82.5−70) ÷ 25 × 10
≈ 50.00
⚠️ Examiner Note
Show interpolation formula. Never just estimate from the graph without working. Marks require the method.
🌉 Bridge Strategy — Your Progress
Master FD = F ÷ CW. One bar at a time.
Unequal widths. Area always = Frequency.
Estimate the Median. Drag the line.
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