Reading quartiles at wrong cumulative frequency values
"The Quartile Confusion"
The Mistake in Action
There are 80 data values. Find the median from the cumulative frequency curve.
Wrong: Read across from CF = 50 (half of 100)
Why It Happens
Students sometimes read from the wrong value, or confuse the cumulative frequency with a percentage scale.
The Fix
For $n$ data values, read quartiles at these cumulative frequencies:
- LQ: $\frac{n}{4}$ = $\frac{80}{4}$ = 20
- Median: $\frac{n}{2}$ = $\frac{80}{2}$ = 40
- UQ: $\frac{3n}{4}$ = $\frac{3 \times 80}{4}$ = 60
For 80 values, read the median from CF = 40, not 50.
Check: Does $\frac{n}{4} + \frac{n}{2} + \frac{3n}{4}$ make sense? LQ < Median < UQ ✓
Spot the Mistake
Can you identify where this student went wrong?
80 data values, find median
Read from CF = 50
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: