Which statement best expresses the main idea?

Careful random selection and clear measurement rules make sample estimates more defensible, though uncertainty remains. (The passage distinguishes selection from measurement and says transparent rules improve an estimate without eliminating chance variation.)

Why might the shelf nearest the desk give a distorted estimate?

That shelf may differ systematically from the whole collection in age or use. (The passage offers several ways the convenient shelf could be unusual, so its repair rate may not reflect the full library.)

What does “fluctuations” mean in the second paragraph?

Variations in results that occur from sample to sample (The passage says different samples can contain different amounts of damage by chance, and larger samples generally reduce these changes.)

What three kinds of information should accompany the estimate?

How books were chosen, how damage was defined, and plausible sampling variation (The last paragraph explicitly lists the selection method, the damage definition, and remaining sampling uncertainty.)

Why a Random Sample Matters: Level 4 Reading Comprehension Questions

Suppose a librarian wants to know how many books in a vast collection need repair. Inspecting every volume would take too long, so she examines a sample. If she chooses the shelf nearest her desk, however, convenience may distort the result. That shelf could contain unusually old books, popular books handled every day, or recent books that are nearly untouched.

A random sample uses a selection process that gives each book a known chance of inclusion. Randomness does not promise a miniature copy of the library. One sample may contain more damaged books than the collection as a whole, just through chance. Its advantage is that the selection rule does not knowingly favor the convenient shelf, a certain subject, or books with visible wear. Repeating the process with larger samples generally reduces the size of chance fluctuations.

Selection and measurement solve different problems. A perfectly random list is still unhelpful if inspectors disagree about what counts as damage. Conversely, a precise damage rule cannot rescue a sample drawn only from one unusual room.

The estimate should therefore travel with information about method and uncertainty. Readers need to know how books were chosen, how damage was defined, and how much sampling variation remains plausible. A sample earns trust not by looking representative, but by being selected and assessed through rules that other people can examine.

Comprehension questions