Dividing by the wrong total
"What share is X?" means X ÷ (the relevant total). The classic miss: dividing by a subtotal, by everything-except-X, or by a total from the wrong row — the division is right, the denominator isn't.
Why your brain does this
Questions deliberately offer several candidate totals (column totals, row totals, grand totals), and 'hidden total' variants don't print the total at all — you must build it. Under pressure, any sum that's visible feels like THE total.
The fix
Name the population before dividing: "share of WHAT?" If the total isn't printed, compute it first as its own step and write it down. Check the result direction: a share of a grand total must be smaller than the same value's share of any subtotal.
See the trap in a real question
| Channel | £000 |
|---|---|
| Digital | 60 |
| TV | 130 |
| 110 | |
| Radio | 70 |
| Total | 370 |
What percentage of the £370,000 total is the Print channel?
Share = part ÷ total × 100, using the overall total as the denominator. The correct answer is 29.7%. Traps to avoid: 18.9% comes from the "wrong slice" error; 14.9% comes from the "wrong total" error; 16.2% comes from the "wrong slice" error; 42.3% comes from the "divided by others" error.
Where it strikes
This trap appears in 54 of our questions, across: Share of total · Probability from a table · Share of hidden total · Revenue share.
Do you make this mistake?
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