#40
Top 50 Mistake
Averaging the values column instead of using frequencies
"The Frequency Forgetter"
The Mistake in Action
Score: 1, 2, 3, 4, 5 Frequency: 3, 7, 5, 4, 1
Student writes: "Mean = (1+2+3+4+5) ÷ 5 = 3"
Why It Happens
Students see a column of values and instinctively average them, completely ignoring the frequency column. They treat it like a simple list.
The Fix
The frequency tells you how many times each value appears. You must:
- Multiply each value by its frequency (the fx column)
- Add up all the fx values
- Divide by the TOTAL frequency (not how many rows)
Correct working:
| Score | f | fx |
|---|---|---|
| 1 | 3 | 3 |
| 2 | 7 | 14 |
| 3 | 5 | 15 |
| 4 | 4 | 16 |
| 5 | 1 | 5 |
| Total | 20 | 53 |
Mean = $\frac{53}{20} = 2.65$
Spot the Mistake
Can you identify where this student went wrong?
Score × Frequency:
Mean = (1 + 2 + 3 + 4 + 5) ÷ 5
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: