Before using a number as evidence, ask five questions: when, who or what, compared with what, in which units, and defined how? Missing answers do not make a number false, but they limit what it can support.
Numerical claims appear across sources and credibility and return when you work with charts and tables. This lesson follows separating expertise from agreement. The town and figures below are invented for practice.
What does a number need around it?
A bare figure such as “6,000” is only a start. The surrounding facts decide what it can show.
- Date: the year or period it describes, and when it was published.
- Population or base: whom or what it counts.
- Comparison: what it is measured against, such as an earlier year.
- Unit: people, ringgit, per 1,000, per cent.
- Definition: what counts as a “commuter”, a “visit” or a “user”.
How to check a numerical claim, step by step
- Copy the claim and the figure as given.
- Find the date and the base. If neither is stated, mark them as missing.
- Identify the comparison. Is it a count, a share or a change?
- Recalculate one key number from the raw figures, if both are given.
- Write what the figure can and cannot support.
Worked example (invented figures)
Claim in a campaign leaflet: “Cycling in Rivermouth has risen by 50% since 2015, so cycling is now far more popular.”
Step 1, copy. “Up 50% since 2015.”
Step 2, date and base. The leaflet’s source table gives 2015: 4,000 cyclists; 2023: 6,000 cyclists. It also gives commuters in the town: 100,000 in 2015 and 150,000 in 2023.
Step 3, comparison. The 50% describes a change in a count.
Step 4, recalculate.
- Change in count: (6,000 − 4,000) ÷ 4,000 = 2,000 ÷ 4,000 = 0.5, which is 50%. The arithmetic is correct.
- Share in 2015: 4,000 ÷ 100,000 = 4%.
- Share in 2023: 6,000 ÷ 150,000 = 4%.
Step 5, conclude. The number of cyclists rose by 50%, but so did the number of commuters, so the share stayed at 4%. The figure supports “more people cycle”. It does not support “cycling is more popular” if popularity means share of commuters.
The mistake to watch for
A common slip is to read a rise in a count as a rise in a rate or share.
Mistaken conclusion: “Cycling grew from 4,000 to 6,000, so the share of cyclists must have risen too.”
The student ignored that the base, 100,000 commuters, grew by the same proportion.
The correction is to ask “out of how many?” every time a count is used to claim popularity, success or risk. When the base is missing, say so and avoid conclusions about share.
Check yourself
1. A 2009 survey says “30% of households have a computer”. An article published this year uses it to describe households today. What is the problem?
Show answer
The date. The figure describes 2009 and cannot support a statement about the present. You would look for a more recent source or limit the claim to the past.
2. Shop A sold 80 phones out of 400 customers. Shop B sold 90 phones out of 600 customers. Which had the higher share of customers buying a phone?
Show answer
Shop A: 80 ÷ 400 = 20%. Shop B: 90 ÷ 600 = 15%. Shop B sold more phones, but Shop A had the higher share.
3. A report says “visits to the park doubled”. What two definitions might you need to check?
Show answer
What counts as a “visit” (every entry, or each person once a day) and the period compared (a week, a year, a holiday month). Different definitions can change the result.
Where this leads next
When the context cannot be found, you still have to say something useful. The next lesson, recording uncertainty when evidence cannot be verified, shows how. After that, try the sources and credibility practice set.
If working with percentages and bases slows you down, a teacher in online one-to-one Global Perspectives tuition can slow the steps down with you using examples that are not part of any assessed work.