"Families Are Better Off": Reading an Average
A news item reports: "Average daily family income in Barangay San Isidro rose from ₱500 to ₱560 - a 12% increase - so families are better off." A Grade 10 class runs the same question as a survey of 100 households. Ten households, all along the commercial strip, report ₱5,000–₱20,000 daily; the other 90 report ₱300–₱650. The class computes a mean of ₱1,180 and a median of ₱450. Last year's survey, using the same method, gave a median of ₱420. Rice and fuel in the barangay rose about 8% over the same period. Three households refused to answer. The class must decide what can honestly be said about whether families are better off.
1. Which measure of central tendency should the class report, and why? Address what the mean of ₱1,180 does and does not tell you.
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Report the median (₱450), and report it alongside the distribution - not the mean alone.
Reasoning:
- The distribution is extremely skewed: ten households earn ₱5,000–₱20,000 while ninety earn ₱300–₱650. In a skewed distribution the mean is dragged upward by the extreme values and stops describing a "typical" household.
- The mean of ₱1,180 sits far above the income of 90 of the 100 households. Fewer than 10% of families earn near or above it. As a description of the barangay, it is close to fiction.
- The median of ₱450 is the middle value: half the households earn less, half earn more. It is resistant to the ten very high incomes, which is exactly why it is the honest summary here.
- The two numbers together are informative, not redundant: mean ₱1,180 versus median ₱450 is a compact, quantitative statement of inequality. Report both, plus the range or the share of households below ₱650.
- Any "average" reported without the shape of the distribution is a claim the data cannot support. The news item's ₱500 → ₱560 figures may even be a mean over a different, non-comparable set of households - which is a further reason to check the method, not just the number.
2. Compute the change in real income for (a) the ₱500 → ₱560 family and (b) the median family (₱420 → ₱450), given 8% inflation. What conclusion follows?
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Method: a nominal increase only means a real increase if it outpaces prices. Real change = (1 + nominal growth) ÷ (1 + inflation) − 1.
(a) The ₱500 → ₱560 family
- Nominal growth = (560 − 500)/500 = 0.12, i.e. 12%.
- Real index = 1.12 ÷ 1.08 = 1.0370…
- Real change ≈ +3.7%
- Cross-check: 560 ÷ 1.08 ≈ ₱518.50 in last year's pesos, against ₱500 before - a gain of about ₱18.50, not ₱60.
(b) The median family, ₱420 → ₱450
- Nominal growth = 30/420 ≈ 0.0714, i.e. 7.1%.
- Real index = 1.0714 ÷ 1.08 = 0.9921…
- Real change ≈ −0.8%
- Cross-check: 450 ÷ 1.08 ≈ ₱416.70 in last year's pesos, against ₱420 before - a slight loss in purchasing power.
Conclusion: both statements can be true at once, and that is the point. The family described in the news item is genuinely a little better off in real terms (+3.7%, not 12%). But the median household's income grew more slowly than prices, so the typical family is marginally worse off. The headline's error is not arithmetic; it is using one family's nominal increase, or one skewed mean, to speak for the whole barangay. The defensible sentence is: "Income rose in nominal terms, but after 8% inflation the median household's purchasing power was roughly unchanged to slightly lower."
3. What cautions apply to the three non-respondents and to the survey method, and how should the class phrase its final report?
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Cautions:
Non-response is not random in an income survey. Three households refusing to answer is only 3%, so the effect is small here - but the direction matters. If the refusals cluster among the very poorest (fear of being seen, or of losing eligibility for assistance) or among the wealthiest, the median shifts. The correct move is to report 3/100 non-response and say the direction of the bias is unknown, rather than to silently drop them or to impute a value.
Self-reported income is measured with error. Daily income in an informal economy is irregular; a single visit captures one day, and households may round or under-report. A median of ₱450 from 90 households may be a reasonable estimate, but it is an estimate.
The comparison year must use the same method. The class is comparing its own median (₱450) with "last year's survey, same method" (₱420). If the sampling frame, the question wording, or the season changed, the 7.1% is partly artifact. Plant/harvest season matters enormously in this community - the comparison should say when each survey was taken.
The 8% inflation figure is itself a barangay-level estimate, and different households face different baskets (a rice-heavy household is hit harder than the average). One number understates the burden on the poorest.
Defensible final phrasing: "Median daily income rose from ₱420 to ₱450 (about +7.1%), slightly below the roughly 8% rise in local prices, so the typical household's purchasing power was about the same or slightly lower; mean income was ₱1,180, but the distribution is highly skewed, with 10 of 100 households earning above ₱5,000. Three households did not answer. We therefore cannot say that families in general are better off."
The transferable lesson: ask what the average is an average of, whether the comparison uses the same method, and whether the number is nominal or real.