Stock market foundationsModule 6, lesson 29 of 29
Misleading numbers and charts
How cherry-picked dates, truncated chart axes, averages, base rates, survivorship and relative risk are used to make numbers say more than they should.
In this lesson
- Spot a return figure that depends on a carefully chosen start or end date.
- Read a chart's axes before reacting to the shape of its line.
- Ask for the base rate before being impressed by a success rate.
- Recognise survivorship bias and small samples in performance claims.
- Tell relative changes from absolute ones.
Builds on
- Correlation and causationMisleading statistics often rely on chance patterns and small samples, introduced there.
On this page
In simple terms
Numbers and charts can be completely accurate and still leave you with the wrong impression. Most misleading statistics do not involve false data. They involve choosing which data to show, how to frame it, and what to leave out.
This lesson collects the techniques you will meet most often, in fund advertisements, social media "results", news headlines and tip groups, with a question to ask for each.
Choosing the start and end dates
A return figure depends on the dates it covers, and those can be chosen to tell almost any story.
Worked example: One fund, three true claims
A made-up fund's unit price was ₹100 in January 2020, fell to ₹62 in a crash in March 2020, recovered to ₹99 by March 2021 and reached ₹120 by January 2023.
| "Up 60% in a year!" March 2020 to March 2021 | +59.7% |
|---|---|
| "Flat over a year" January 2020 to March 2021 | −1.0% |
| Three years, January 2020 to January 2023, as a CAGR | about 6.3% a year |
All three are accurate. The advertisement will usually choose the first. Ask for returns over several standard periods, such as one, three, five and ten years, and for the worst period as well as the best.
Reading a chart's axes
A chart whose vertical axis starts at 98 rather than zero can make a move from 98 to 102, about 4%, fill the whole height of the picture and look like a soaring rise. Before reacting to the shape of a line, read the numbers on the axes, check the time span, and see whether the scale is linear or logarithmic. Two charts of the same data can look completely different.
Averages that hide the spread
As the averages and volatility lesson showed, a mean can be dragged up by one extreme value, and an average yearly return can overstate how much money actually grew. When you see an average, ask whether it is a mean or a median, and whether a return average is simple or compound.
Success rates without base rates
A base rate is how often something happens in general. Without it, a success rate cannot be judged.
- "9 out of 10 of our picks went up last year" means little if 85% of all shares went up.
- "Our signal predicted the last three crashes" means little if it also "predicted" ten crashes that never came.
Always ask: compared with what?
Only the survivors
Survivorship bias happens when only the successes remain visible. Funds that performed badly are often closed or merged, so the funds still around look better than funds as a whole did. A tip group may have started ten channels with different tips and kept only the one that happened to do well, as the stock tip groups lesson describes. Ask what happened to the ones you are not being shown.
Small samples
Three good trades, one strong quarter or a single lucky year prove very little. As the correlation and causation lesson showed, striking patterns appear by chance in small samples. Ask how many results the claim is based on, over how long, and whether they included bad conditions.
Relative and absolute numbers
"Risk doubles" sounds alarming, and "returns up 100%" sounds impressive. Both can come from tiny absolute changes: a risk going from 1% to 2%, or a profit going from ₹1 lakh to ₹2 lakh. The percentages lesson covers percentage points and base effects. Ask for the actual numbers behind the percentage.
A checklist for any claim
- Who is making the claim, and what do they gain if you believe it?
- Over what period, and why that period?
- Compared with what: an index, a base rate, doing nothing?
- How many results, and what happened to the ones not shown?
- Is the average a mean or a median, simple or compound?
- What do the chart's axes actually say?
- Is it a relative change or an absolute one?
Why it matters
Misleading numbers are the main tool of investment scams and aggressive marketing, and they also creep into honest news reporting. A small set of questions catches most of them, and asking them becomes a habit that protects every later decision you make, from choosing a fund to judging a company's results.
Limitations
- These questions help you spot weak evidence; they do not tell you what the truth is. Sometimes a striking claim is also correct.
- Good-faith analysts make these errors too, so a misleading statistic is not always a sign of dishonesty.
- Some claims cannot be checked from public data at all, which is itself a reason for caution.
Common mistakes
- Reacting to a chart's shape before reading its axes.
- Accepting a return figure without asking about the period.
- Being impressed by success rates without a base rate.
- Forgetting the failures that were never shown.
- Treating a relative change as if it were large in absolute terms.
Try it yourself
- Find an advertisement or social media post that quotes a return. Apply the checklist above and note which questions it fails to answer.
- Look up the price of an index on several dates and calculate the return for three different start dates ending today. How different are the results?
- Find a chart in a news report and check where its vertical axis starts.
Key takeaways
- A return can be made to look good or bad by choosing where it starts and ends. Ask for several periods, including the worst ones.
- Check a chart's axes before its shape. A cut-off vertical axis turns a small move into a dramatic one.
- A success rate means little without the base rate. "Nine out of ten of our picks rose" is unimpressive in a year when most shares rose.
- Performance claims often show only the survivors. Ask what happened to the funds, tips or traders you are not being shown.
- A risk that has "doubled" may have gone from 1% to 2%. Ask for absolute numbers, not just relative ones.
Check your understanding
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Terms used in this lesson
- Base rate
- How often something happens in general. A success rate means little until it is compared with the base rate.
- Survivorship bias
- The error of judging something by the examples that survived or succeeded, while ignoring the many that failed and dropped out of view.
- Cherry-picking
- Choosing the data, dates or examples that support a claim while leaving out the ones that do not.
- Mean and median
- Two kinds of average. The mean adds values and divides by the count; the median is the middle value when they are put in order.
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This lesson is general education, not investment advice. Examples use made-up or clearly dated figures to explain ideas; they are not recommendations. Read the disclaimer.