Misleading Data and Critiquing

Being able to spot misleading statistics and evaluate claims is a key skill for Edexcel GCSE Mathematics. Questions on this topic appear across all three papers and require you to think critically about how data is presented.

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Key Vocabulary

Term	Definition
Misleading graph	A graph drawn in a way that gives a false impression of the data
Bias	A systematic error that makes results unrepresentative
Leading question	A question worded to influence the answer
Reliability	Whether results would be similar if the study were repeated
Validity	Whether the study measures what it claims to measure

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Misleading Graphs

Common Tricks

1. Not starting the y-axis at zero (a broken axis)

If the vertical axis starts at, say, 50 instead of 0, small differences look much larger.

Worked Example 1 — Broken y-axis

January sales = 52, February sales = 55. A chart has a y-axis from 50 to 56. Why is this misleading? What would the February bar look like if the axis went from 0 to 60?

Solution:

• With the y-axis from 50 to 56, January's bar is 2 units tall (52 − 50) and February's is 5 units tall (55 − 50). February looks more than twice as tall — implying huge growth.
• With a y-axis from 0 to 60, the bars would be nearly the same height (about 87% vs 92% of the chart), making the small increase visually obvious.
• Conclusion: The broken axis exaggerates a tiny difference of 3 units (about 6%) into something that looks like major growth.

2. Unequal scales or intervals on axes

Spacing years or months unevenly distorts the perceived rate of change.

3. Using area/volume instead of length in pictograms

Doubling the height AND width of a symbol quadruples the area, making one category look four times as big when it is only twice as big.

Worked Example 2 — Area distortion

A newspaper doubles both the height and width of a symbol to show that sales have doubled. Explain why this is misleading.

Solution: When you double both height and width, the area becomes 4 times greater (2 × 2 = 4), not twice. Readers see the larger symbol as 4× bigger, so they overestimate the increase. Pictograms should use the same-size symbol repeated — not a single symbol enlarged.

4. Missing labels or scales; 3D effects on charts; selective data (cherry-picking)

Worked Example 3 — Selective data

A company's profits over 10 years have fluctuated between £5m and £10m. The company advertises: "Record profits this year — £10m!" ignoring that last year they also made £10m and the year before was higher. Why is the headline misleading?

Solution: The headline is factually correct but selective: it omits the context that profits have been similar for several years, and that the trend is not rising. A better presentation would be a line chart of profits over the full 10 years, with the axis starting at zero.

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Critiquing Questionnaires

Edexcel frequently asks you to critique survey questions or methods.

Worked Example 4 — Critiquing a leading question

Critique: "Don't you agree that school lunches are terrible?"

Solution:

• Leading: the phrase "don't you agree" and the word "terrible" push the respondent towards a negative answer.
• No scale / choice: forces a yes/no or agree/disagree response rather than measuring the strength of opinion.
• Better version: "How would you rate school lunches?" with options: Very good / Good / Neutral / Poor / Very poor.

Worked Example 5 — Overlapping options

Critique: "How many hours per week do you exercise? 0–2, 2–4, 4–6."

Solution:

• Overlapping categories: a person who exercises exactly 2 hours could tick two boxes.
• No upper category: someone who exercises 7+ hours has nowhere to go.
• Better version: "0 to less than 2, 2 to less than 4, 4 to less than 6, 6 or more."

Worked Example 6 — Vague time frame and missing options

Critique: "How often do you watch TV? Often / Sometimes / Rarely." Also critique: "How do you travel to school? Car / Bus / Walk."

Solution:

• "Often / Sometimes / Rarely" are vague — one person's "often" is another's "sometimes." Better: "How many hours per week do you watch TV?" with numeric bands.
• The travel question is missing common options (cycle, train, scooter). Always include an "Other (please state)" category.

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Evaluating Statistical Claims

Worked Example 7 — Sample size and representativeness

A TV show says: "90% of viewers say our new series is excellent! (Based on 50 people surveyed outside our studio.)" Critique this claim.

Solution:

1. Sample size is very small (50 people) — results may not be reliable; a repeated survey could give very different figures.
2. Biased sample: people outside the studio have already chosen to attend a recording of the show, so they are likely fans. This does not represent all viewers.
3. Self-selection bias: people who disliked the show would probably not attend, further skewing results.

• A better survey would take a large random sample from the general viewing public using stratified sampling.

Worked Example 8 — Correlation vs causation

"Towns with more fire stations have more fires." Does this mean fire stations cause fires? Explain.

Solution: No. Both are caused by a third factor — town size. Bigger towns have more buildings (more fires) AND more fire stations to cover them. This is a classic confounding variable example.

Worked Example 9 — Averages can mislead

"The mean salary at our company is £85,000." The CEO earns £500,000 and the other 9 employees earn £39,000 each. Calculate the mean, median and comment.

Solution:

• Mean = (500,000 + 9 × 39,000) ÷ 10 = (500,000 + 351,000) ÷ 10 = £85,100.
• Median salary = £39,000 (the middle value when salaries are ordered).
• Comment: The mean is distorted by the CEO's extreme salary. The median (£39,000) is far more representative of what a typical employee earns. Quoting the mean without context misleads the public about typical pay.

Worked Example 10 — Percentages without base numbers

A newspaper headline reads: "Crime up 200%!" The previous year there was 1 crime; this year there are 3 crimes. Comment.

Solution: Mathematically correct (3 − 1)/1 = 200%. But the base rate is tiny — going from 1 to 3 crimes means 2 extra incidents, which is not significant evidence of a crime wave. Always look for the absolute numbers behind percentages, especially when the starting figure is small.

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Worked Exam-Style Example

Worked Example 11 — Full critique

Tom wants to find out how much time students spend on social media. He stands outside the school library at 4 p.m. on a Monday and asks 10 students.

(a) Give two reasons why his sample may be biased. (b) Write a suitable question Tom could use. Include response options. (c) Suggest how Tom could improve his sampling method.

Solution:

(a)

1. He is only surveying students outside the library — these students may be less likely to use social media (they may prefer reading or studying). Not representative.
2. Only 10 students — a very small sample unlikely to represent the whole school.

(b) "On average, how many hours per day do you spend on social media?"

• Less than 1 hour
• 1 to less than 2 hours
• 2 to less than 3 hours
• 3 to less than 4 hours
• 4 hours or more

(c) Tom should use a larger sample (50+). He should use stratified sampling by year group to ensure each year is represented in proportion. He should survey in different locations and times to avoid location/time bias.

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Comparing Data Presentations

You may be shown two ways of presenting the same data and asked which is better. Neither is "wrong" — the best choice depends on the purpose.

• Pie chart: best for showing proportions (fractions of a total).
• Bar chart: best for comparing actual frequencies and reading exact values.
• Line graph: best for data over time.
• Histogram: best for continuous grouped data.

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Limitations of Statistical Measures