Why a Random Sample Matters
Written by Studio AM.
Your result
- Words per minute
- Score
- Pace
Words per minute mean something only with the score beside them. They describe this passage on this read. With fewer than 3 right, try the next slower pace.
Choose a pace and select Start. The passage is paced and timed, then the questions check what you understood. How pace mode works
Reading time 0:00
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 simple random sample uses a process that gives each book an equal 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. Larger random samples generally reduce chance fluctuations in the estimated proportion of damaged books.
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 include information about method and uncertainty. Readers need to know how books were chosen, how damage was defined, and how much sampling variation remains plausible. Readers can judge the estimate better when its selection and measurement rules are clear.
The passage is hidden while you answer. It comes back with your result.
Questions
Choose an answer. The explanation appears after you answer.
-
Question 1 of 4
Which statement best expresses the main idea?
The answer is D: 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.
-
Question 2 of 4
Why might the shelf nearest the desk give a distorted estimate?
The answer is A: 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.
-
Question 3 of 4
What does “fluctuations” mean in the second paragraph?
The answer is B: 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.
-
Question 4 of 4
What three kinds of information should accompany the estimate?
The answer is C: 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.
Score: none answered yet.