#41
Top 50 Mistake
Using class boundaries instead of midpoints
"The Boundary Blunder"
The Mistake in Action
Time (t minutes): 0 < t ≤ 10, 10 < t ≤ 20, 20 < t ≤ 30 Frequency: 4, 8, 3
Student uses 10, 20, 30 as the values for calculating mean.
Why It Happens
Students use the upper boundary of each class (the numbers they can see clearly in the inequality) rather than finding the midpoint. Or they use the lower boundary.
The Fix
For grouped data, use the midpoint of each class:
- 0 < t ≤ 10 → midpoint is $\frac{0+10}{2} = 5$
- 10 < t ≤ 20 → midpoint is $\frac{10+20}{2} = 15$
- 20 < t ≤ 30 → midpoint is $\frac{20+30}{2} = 25$
Correct mean: $\frac{(5×4) + (15×8) + (25×3)}{4+8+3} = \frac{20+120+75}{15} = \frac{215}{15} = 14.3$
Spot the Mistake
Can you identify where this student went wrong?
Finding mean for grouped data:
Values: 10, 20, 30 (upper boundaries)
Mean = (10×4 + 20×8 + 30×3) ÷ 15 = 18.7
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: