Mətn anlaşılması: rəqəmsal cədvəlin təhlili
Read this short report and answer the questions that follow. A university library surveyed 200 students about their study habits. Of the respondents, 120 said they study in the morning, 90 said they study in the evening, and 30 said they study at both times. The report also states: "Students who study at both times reported the highest satisfaction, although the difference was small." The library plans to extend opening hours either in the morning or in the evening, but not both, because of a limited budget. The librarian argues that morning extension is the better choice because 120 students study in the morning, which is more than the 90 who study in the evening.
1. How many students study only in the morning, only in the evening, and neither? Show your calculation and explain why the librarian's comparison of 120 and 90 is misleading.
Read the worked answer
Given. Total = 200; morning = 120; evening = 90; both = 30.
Only morning. 120 − 30 = 90. Only evening. 90 − 30 = 60. Morning or evening (union). 90 + 60 + 30 = 180. Neither. 200 − 180 = 20.
Check. 90 + 60 + 30 + 20 = 200. Correct.
Why the librarian is misleading. The figures 120 and 90 include the 30 students who study at both times. Those 30 students would benefit from an extension at either time, so they are counted in both groups. Comparing the raw totals therefore double-counts the overlap and exaggerates the morning advantage.
Fair comparison. Among students who study at only one time, 90 study only in the morning and 60 only in the evening, a ratio of 3:2 rather than 4:3. The morning group is still larger, so the librarian's conclusion may still hold - but the margin is bigger than the raw numbers suggest, and the 30 flexible students would be served by either option. A correct argument must state which group is being compared.
2. The report says students who study at both times had the highest satisfaction, "although the difference was small." What can and cannot be concluded from this, and how should it affect the decision?
Read the worked answer
What can be concluded. The both-times group (30 students) reported the highest satisfaction. That is a descriptive statement about a small subgroup.
What cannot be concluded.
- Causation. We do not know whether studying at both times caused higher satisfaction or whether already-satisfied students simply choose to study more. The report gives no design that would separate these.
- Size. The phrase "the difference was small" means the effect may be within noise. With only 30 students in the key group, a small difference is weak evidence.
- Generalisability. Satisfaction is not the same as usage. A student may be satisfied but still not use extended hours.
Effect on the decision. The satisfaction finding should not drive the choice between morning and evening, because it does not distinguish between the two options - the both-times group benefits either way. The decision should rest on the usage counts, and even there the correct comparison is 90 only-morning versus 60 only-evening, not 120 versus 90.
Recommended framing. Morning extension serves 90 exclusive users plus 30 flexible users (120 total); evening extension serves 60 exclusive users plus the same 30 flexible users (90 total). Morning still wins on reach, but the honest margin is 30 students, not 30 in raw terms alone - and the report should say so.