Report A records 400 library visits during one week, counting each entry. Report B records 260 different visitors that week, counting each person once even if they returned.
Which difference explains why the numbers need not conflict?
Answer & why
Answer: One counts entries, while the other counts distinct people.
Returning visitors can produce multiple entries but only one distinct-person count.
An order was placed three days before dispatch. Delivery arrived four days after dispatch. Report A measures four days from dispatch; Report B measures seven days from the order.
Which difference reconciles these reports?
The timing starts at different events.
Neither report includes a starting event.
The package arrived before it was ordered.
The reports use identical start times.
A hint
Before declaring two reports contradictory, compare what each number counts, the denominator, the time interval and the definition used.
Answer & why
Answer: The timing starts at different events.
The extra three days before dispatch are included only when counting from the order.
Of 100 enrolled participants, 80 began a course and 72 finished. Report A describes completion among starters as 90%; Report B describes completion among all enrollees as 72%.
Which difference explains both percentages?
Both percentages divide by 100.
The figures show no one began the course.
The reports divide the same 72 completions by different group totals.
The passage says all 100 people finished.
A hint
Before declaring two reports contradictory, compare what each number counts, the denominator, the time interval and the definition used.
Answer & why
Answer: The reports divide the same 72 completions by different group totals.
72/80 is 90%, whereas 72/100 is 72%. The denominators are different and explicitly stated.
Report A records 400 library visits during one week, counting each entry. Report B records 260 different visitors that week, counting each person once even if they returned.
Which difference explains why the numbers need not conflict?
Both count each person exactly once.
One counts entries, while the other counts distinct people.
A visit and a distinct visitor must always be the same measure.
The reports concern different centuries.
A hint
Before declaring two reports contradictory, compare what each number counts, the denominator, the time interval and the definition used.
Answer & why
Answer: One counts entries, while the other counts distinct people.
Returning visitors can produce multiple entries but only one distinct-person count.
A project began on a Monday and ended fifteen calendar days later. Report A counts all fifteen calendar days. Report B counts only the school days within that interval.
What should a reader compare first?
Which report has the larger title.
Whether all school days are weekends.
Whether days means all calendar days or only school days.
Whether the same interval can contain no calendar days.
A hint
Before declaring two reports contradictory, compare what each number counts, the denominator, the time interval and the definition used.
Answer & why
Answer: Whether days means all calendar days or only school days.
The reports use different definitions of a counted day. A smaller school-day total need not contradict the calendar-day total.
For the same set of journey times, Report A gives the mean as 12 minutes. Report B gives the median as 9 minutes. Each report labels its statistic explicitly.
What is the most useful first distinction?
Both reports state the largest journey time.
A statistic can never describe journey times.
The reports give different statistics, so the values need not be equal.
Mean and median must always have identical values.
A hint
Before declaring two reports contradictory, compare what each number counts, the denominator, the time interval and the definition used.
Answer & why
Answer: The reports give different statistics, so the values need not be equal.
Mean and median summarize a set in different ways; different labeled values are not automatically a contradiction.