Misleading Graphs

Statistical Literacy — When Numbers Lie Without Lying

"There are three kinds of lies: lies, damned lies, and statistics." — attributed to Mark Twain. A graph can contain only true numbers and still be deeply misleading. Here is how to spot it.

Six Ways Graphs Mislead

1. Truncated Y-axis
Starting the Y-axis at a value other than zero makes small differences look enormous. A graph of house prices from $900k to $920k looks dramatic; the same data from $0 to $1M looks flat.

2. Cherry-picked time range
Choosing a start or end date that flatters your argument. "Crime has dropped 30% since 2019" might ignore that 2019 was a historic high — zoom out and the trend may be flat.

3. Confusing correlation with causation
Two things that move together do not necessarily cause each other. Ice cream sales and drowning rates both peak in summer — but ice cream does not cause drowning.

4. Percentage vs absolute numbers
"A 100% increase" sounds alarming. "From 1 case to 2 cases" sounds trivial. These are the same statistic. Context determines meaning.

5. Missing denominator
"400 people were affected" — out of 400? Out of 4 million? Without the denominator, the number is meaningless. This is common in health and crime reporting.

6. Inappropriate comparison
Comparing different groups, time periods, or methods as if they are equivalent. "Our school's test scores improved" — compared to last year, or compared to other schools?

NZ Examples to Analyse

Read each scenario. Identify which misleading technique is being used and explain why it is deceptive:

Scenario A: A political party releases a graph showing unemployment. The Y-axis runs from 4.0% to 5.5%. The line appears to show unemployment nearly doubling. The actual change is from 4.2% to 5.1%.

Technique used: ______________ Why it's deceptive: _________________________________

Scenario B: A headline reads: "Māori crime rate 300% higher than Pākehā." The statistic is technically correct for arrests, but does not account for differences in police patrol intensity by area, rates of pre-trial detention, or the fact that most crime goes unreported.

Technique used: ______________ Why it's deceptive: _________________________________

Scenario C: A council report claims "recycling has increased by 200% over five years." On closer inspection, the council only started measuring recycling properly two years ago and the baseline was a single pilot suburb.

Technique used: ______________ Why it's deceptive: _________________________________

Critical Questions

1. When you see a graph in a news article, what are three questions you should ask before accepting what it appears to show?

2. Scenario B involves Māori crime statistics. Why is the absence of context in that statistic particularly harmful, beyond just being misleading?

3. Create your own: Find or invent a real NZ statistic (e.g., school attendance, water quality, house prices). Write two descriptions of the same statistic — one that makes it sound alarming, and one that makes it sound reassuring. Then explain which is more honest and why.

4. Argue (PEEL): Is it ever ethical to present statistics in a way that is technically true but designed to mislead? Consider cases like public health campaigns, political advertising, or advocacy for social causes.

Whakaaro Hōhonu — Reflection

Statistics about Māori health, incarceration, and poverty are frequently reported without context in NZ media. What responsibility do journalists, readers, and educators have when working with these numbers?

NZC Curriculum Alignment

Mathematics and Statistics — Statistical Literacy: Evaluate statistical claims, identify misuse of data, and understand the relationship between data representation and interpretation.
English — Reading / Viewing: Critically evaluate the purpose and effect of visual information, including graphs and infographics, used in non-fiction texts.

🌿 Te Ao Māori Lens

Statistics about Māori are often used to describe deficits — what Māori lack, where Māori fall behind. This framing treats the mainstream as the norm and Māori experience as deviation. An alternative approach is to centre Māori voices, Māori explanations, and Māori solutions — asking not "what's wrong with Māori outcomes?" but "what systems produce these outcomes, and what would look different if Māori communities had more control?" Kaupapa Māori research methodology starts from a position of Māori normalcy, not deficit.