Reading the height instead of calculating the area H
"The Reading Error"
The Mistake in Action
From the histogram, find the frequency for the class 20 ≤ x < 50.
The bar for this class has height 4 on the frequency density axis.
Wrong: Frequency = 4
Why It Happens
Students read the height value directly, forgetting that histograms represent frequency through area.
The Fix
In a histogram: Frequency = Area of bar = Width × Height
The bar has:
- Width = $50 - 20 = 30$
- Height (frequency density) = 4
$$\text{Frequency} = 30 \times 4 = 120$$
Always remember: The y-axis shows frequency density, not frequency. You must multiply by the class width to get the actual frequency.
Spot the Mistake
Can you identify where this student went wrong?
Bar height is 4
Frequency = 4
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: