CoStudy

HomeCertificationsHS Statistics › Designing Studies: Sampling and Experimental Design

Designing Studies: Sampling and Experimental Design — HS Statistics practice questions

11 multiple-choice questions and 33 flashcards on Designing Studies: Sampling and Experimental Design, about 7% of the HS Statistics bank. Every one carries a written rationale.

Written and maintained by Nick Burton · last updated 2026-08-22 · how we write and review questions

What this chapter covers

Designing Studies: Sampling and Experimental Design is one of 7 chapters in CoStudy's HS Statistics bank, and it holds 11 of the bank's 150 multiple-choice questions — roughly 7% of the total. That proportion is not arbitrary: chapters follow the certifying body's published exam outline, and the number of questions in each is set by that domain's published weight, so the share of your practice time this chapter takes matches the share of the real exam it accounts for.

Studying by chapter is worth doing once you have a diagnostic score. A single overall percentage tells you whether you are close; it does not tell you which domain is dragging. Working a weak chapter in isolation, and re-testing it in isolation, is the fastest way to move a score that has stalled — and it is why the mock exams in CoStudy report by domain rather than as one number.

Free Designing Studies: Sampling and Experimental Design practice questions

8 questions drawn from this chapter, with the full rationale shown — the controlling principle behind the right answer, and why each wrong option tempts and fails.

Data is described as POSITIVELY SKEWED when:

  1. Symmetric
  2. No tail
  3. Tail to left
  4. Tail extends to the right (high values); mean > median; typical of income data
  5. Bimodal

Answer: D — Tail extends to the right (high values); mean > median; typical of income data

Right (positive) skew: tail to right, mean pulled up by extreme values (mean > median). Left (negative) skew: tail to left (mean < median). Symmetric: mean ≈ median. Income/wealth typically right-skewed.

Which sampling method gives every member EQUAL chance of being selected?

  1. Convenience sampling
  2. Stratified
  3. Voluntary response
  4. Simple random sampling (each individual equally likely)
  5. Snowball

Answer: D — Simple random sampling (each individual equally likely)

Simple random sample (SRS): each member has equal probability, every sample size n equally likely. Gold standard. Stratified divides population then samples within. Cluster samples whole groups. Convenience/voluntary biased.

Variance is defined as the:

  1. Square root of standard deviation
  2. Average of the raw data
  3. Median of the data
  4. Square of the standard deviation

Answer: D — Square of the standard deviation

D) Variance = (SD)²; equivalently SD = √variance. A) Reversed the relationship. B) Confused variance with mean. C) Confused with a central tendency measure.

A study finds that ice cream sales and drowning deaths are correlated. What likely explains this?

  1. Confounding variable (warm weather causes both); correlation does not imply causation
  2. Ice cream causes drowning
  3. Drowning causes ice cream sales
  4. Random coincidence
  5. Direct causation

Answer: A — Confounding variable (warm weather causes both); correlation does not imply causation

Classic confounding: warm weather → both more ice cream AND more swimming/drowning. Lurking/confounding variable. CRITICAL principle: correlation ≠ causation. Always seek causal mechanism and consider alternative explanations.

What is the INTERQUARTILE RANGE (IQR)?

  1. Mean - median
  2. Mode count
  3. Max - min
  4. Standard deviation
  5. Q3 - Q1 (75th percentile minus 25th percentile; middle 50% of data spread)

Answer: E — Q3 - Q1 (75th percentile minus 25th percentile; middle 50% of data spread)

IQR = Q3 - Q1. Measures spread of middle 50% of data. Less affected by outliers than range. Outlier rule: below Q1 - 1.5·IQR or above Q3 + 1.5·IQR. Used in box plots.

If the standard deviation of a data set equals 0, then:

  1. The mean equals 0
  2. All data values are equal
  3. The distribution is normal
  4. The mean equals the median

Answer: B — All data values are equal

B) SD measures spread around the mean; SD = 0 means no spread, so every value matches the mean. A) SD = 0 says nothing about the mean's value. C) Normality is unrelated. D) Mean and median agreeing does not require SD = 0.

What is a HISTOGRAM used for?

  1. Categorical data
  2. Showing means only
  3. Time series
  4. Visualizing distribution of NUMERICAL data — bars represent frequency in intervals (bins)
  5. Single value display

Answer: D — Visualizing distribution of NUMERICAL data — bars represent frequency in intervals (bins)

Histogram: numerical (quantitative) data distribution. X-axis: intervals/bins. Y-axis: frequency/density. Reveals shape (skewed, symmetric, bimodal). Categorical data: bar chart (distinct categories).

The range of {3, 7, 9, 12, 18} is:

  1. 9
  2. 12
  3. 15
  4. 6

Answer: C — 15

C) Range = max − min = 18 − 3 = 15. A) Used a middle value. B) Used the second-largest. D) Difference of two arbitrary values.

Designing Studies: Sampling and Experimental Design flashcards

4 cards from the 33 in this chapter.

Ethical issues in research?

Informed consent, privacy, no harm, IRB approval.

Sum of probabilities?

Must equal 1.

Common stats error: small sample assuming representative?

Small samples have high variability. Inference unreliable.

Geometric distribution?

Number of trials until first success. p constant.

Practise the full chapter

These are a sample. The full Designing Studies: Sampling and Experimental Design chapter runs 44 items with per-chapter progress tracking, on the web and in the iOS app.

Open HS Statistics in CoStudy →

Other HS Statistics chapters

All HS Statistics practice questions →