The numbers are usually true. It is the sentence built around them that needs checking.
Judge the claim
A report states: "Learners who own a calculator score 12 points higher in maths, so buying a calculator raises a learner's score." What is wrong with it?
The data may well show the gap, but the word "so" turns an association into a cause. Families who can afford a calculator can usually afford other things too — books, tutoring, reliable electricity — and any of those could be doing the work. D is a fair complaint but not the main one: even with a million learners, the same wrong conclusion would be drawn. Correlation is not causation is the flaw here.
| Ask | Because |
|---|---|
| Who was asked, and how many? | a biased or tiny sample cannot represent anyone |
| Which average was used? | mean, median and mode can tell different stories |
| What does the graph's scale do? | a cut axis exaggerates small differences |
| Is a cause being claimed? | a link is not proof of a cause |
Notice that none of these questions is about arithmetic. A statistical report almost never fails because someone added up wrongly.
"Average salary" is meaningless until you know which average.
| Staff | Monthly salary |
|---|---|
| Owner | ₱300,000 |
| Manager | ₱45,000 |
| Six workers | ₱18,000 each |
total = 300,000 + 45,000 + 108,000
= ₱453,000 over 8 people
mean ≈ ₱56,625
what the advert would quote
median = ₱18,000
what most people earn
Nobody lied. "Average salary ₱56,625" is arithmetically correct and gives an entirely false impression, because one enormous value pulled the mean upwards. With skewed data, the median is the honest choice.
A percentage always hides the number it came from. Ask for the raw count before being impressed by it.
| Problem | Example |
|---|---|
| Self-selected sample | an online poll only strong opinions bother to answer |
| Interested party | a drinks company funding research on its own drink |
| Leading question | "Do you agree the unfair fee should be scrapped?" |
| Wrong population | asking commuters about car ownership |
Funding does not make a study false, and plenty of company research is careful. But it is a reason to read the method rather than the headline.
Two things moving together has at least four explanations.
Only a properly controlled experiment can separate these. A survey, however large, can show that two things travel together and nothing more.
A vitamin trial: 60 of 100 learners who took it got over a cold within a week. Does the vitamin work?
treated group: 60 of 100 = 60%
sounds impressive alone
control group, no vitamin: 58 of 100 = 58%
most colds clear up anyway
difference = 2 percentage points
almost no effect
Without a control group, the 60% is credited to the vitamin even though 58% recover with nothing at all. The evidence is the difference between the groups, not the success rate of one.
A poll of 400 voters: 52% support a candidate, margin of error ±5 percentage points. Is she sure to win a majority?
52 − 5 = 47, 52 + 5 = 57
the plausible range
47% to 57% includes values below 50%
not sure
The margin of error tells how precise an estimate from a sample is. A lead smaller than the margin is not a clear lead.
The same questions, answered with a little arithmetic.
Three averages: weekly allowances of ₱150, ₱150, ₱150, ₱200, ₱250, ₱300, ₱900
mode = ₱150, median = ₱200
most common; middle of seven
mean = 2,100 ÷ 7 = ₱300
pulled up by ₱900
Different: one data set, three honest "averages" — ₱150, ₱200 or ₱300 — so a report must say which.
A cut axis in numbers: bars of 96 and 98, axis starting at 95
drawn heights: 96 − 95 = 1 and 98 − 95 = 3
what the eye compares
looks 3 times as tall; really 98 ÷ 96 ≈ 1.02
about 2% more
Different: we can measure the exaggeration, not just describe it. An axis with no numbers at all is worse still: without a scale we cannot judge the size of the change — a steep line could be a rise of 2 or of 2,000.
A rise then a fall: a ₱20 snack rises 25%, then falls 25%
20 × 1.25 = ₱25
25% of 20 is 5
25 × 0.75 = ₱18.75
25% of 25 is 6.25
Different: the two 25%s have different bases, so "up 25%, down 25%" does not bring the price back to ₱20.
Expect a claim or a graph to judge: a missing sample size, a biased sample, the wrong average, a cut axis, or a cause read into a correlation. The fastest route is to run the four questions — who was asked, which average, what the scale does, is a cause claimed — and stop at the first that fails. The 10-second check: the right choice names a flaw in how the data was gathered or read, not a flaw in the arithmetic.
Choose the honest figure
Eight houses on a street sold for ₱1.2M, ₱1.3M, ₱1.3M, ₱1.4M, ₱1.5M, ₱1.5M, ₱1.6M and ₱14M. Which figure best describes a typical sale price?
The ₱14M sale is an outlier that drags the mean up to ₱3.0M — a figure higher than seven of the eight houses actually sold for. The median of ₱1.45M sits right among the real prices, so it describes a typical sale honestly. C is a measure of spread, not a typical value, and D is the outlier itself.
Hint: check your chosen figure against the actual list. If most of the data sits below the "typical" value, it is not typical.
