Verbal - An advertisement that uses the word 'every'
A training institute's advertisement reads: "Every graduate of our six-month program who passes the final assessment receives a job offer within 90 days." An auditor checks the 200 people who graduated last year. Of these, 150 passed the assessment, and 96 of those 150 had a written job offer dated within 90 days of graduating. Among the 50 who failed the assessment, 12 did receive offers within 90 days and 30 were still without an offer when the audit closed. The institute's director objects that the audit is unfair, because "most of our graduates did end up with offers" and because some graduates never report their outcomes. The auditor has to write two sentences: one stating what the data prove, one stating what they do not.
1. Read literally, is the advertisement true or false on these data? Identify the smallest piece of evidence needed to settle it, and say whether the 12 offer-holders who failed the assessment are relevant.
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The sentence is a universal claim: for every graduate who passes, an offer exists within 90 days. A universal claim is refuted by one counterexample, and the audit supplies 150 − 96 = 54 of them - graduates who passed the assessment and had no documented offer within 90 days.
So the advertisement is false as written, and the arithmetic needed is a single subtraction, not a percentage.
The 12 are a distraction. They show that offers are not exclusive to people who passed, which is interesting about the job market but irrelevant to the sentence, because the sentence says nothing about graduates who failed. A reader who cites the 12 as the refutation has answered a different question. The refutation is the 54.
What the data do not show is that the program is worthless: 64% of passers had a verified offer, which may be a good outcome. The failure is one of wording, not necessarily of substance.
2. Rewrite the institute's claim as a defensible statistical statement, and explain how the choice of denominator changes what the sentence means.
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Defensible version: "Of the 150 graduates who passed the final assessment last year, 96 - 64% - had a written job offer dated within 90 days of graduating. This was verified by the audit."
Denominator matters:
- 150 (passers): answers "what happens to people who pass?" - 64%. This is the fair replacement for the advertisement, because the original promise was made to passers.
- 200 (all graduates): answers "what happens to someone who enrols?" - 96/200 = 48%. Lower, and arguably the number a prospective student actually needs, since not everyone passes.
- 96 (offer-holders): answers nothing useful. Expressing the figure as "96 graduates got jobs" hides how many did not.
A good rewrite therefore names the denominator out loud. It also replaces "receives" (a guarantee) with "had a written offer dated within 90 days" (an observed, checkable event) and drops "every", which no sample of 150 can support.
3. The director argues that unreported outcomes could make the picture better. What is the strongest version of the institute's position that survives, and what evidence would move the figure above 64%?
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The strongest surviving position: 64% is a documented rate, not necessarily the true rate. Some of the 54 may have received offers within 90 days and simply never sent the letter to the institute. If even half of them did, the real rate among passers would be (96 + 27)/150 = 82%.
But this argument cannot rescue the advertisement, for a structural reason: "every" is a claim about all 150, and the missing paperwork is exactly the evidence that would be needed to verify it. A guarantee cannot rest on documents nobody has seen.
Evidence that would move the number: dated offer letters or employer confirmations for specific individuals among the 54, collected by a method that does not depend on graduates volunteering good news. That last point matters - if only successful graduates reply, the 64% is biased downward, but if the institute only counts replies it receives, the corrected figure is biased upward. A short, mandatory follow-up survey with employer verification would give a number the institute could print without quotation marks around it.