Know Your Stats
Practice Quiz

The key word is "randomly assigns" a treatment. An experiment always involves the researcher actively applying a treatment to subjects. A placebo is the control group — no treatment applied.

No treatment is applied — subjects are simply watched. That is the definition of an observational study. The biologist cannot control wolf behavior.

A sample survey asks a set of questions to a selected group to draw conclusions about a population. No treatment is applied — they are simply asking for opinions/data.

A simple random sample gives every member an equal chance of being chosen. Drawing names from a hat is the classic example — it is equally likely for any name to be picked.

In cluster sampling, the population is split into groups (clusters), entire clusters are randomly selected, and everyone in those clusters is surveyed. Contrast with stratified: in stratified you pick a few people from each group, not whole groups.

Stratified sampling: population → groups by a characteristic → random sample from each group. This ensures each subgroup is represented. Key difference from cluster: you choose people from every group, not whole groups.

A self-selected (voluntary response) sample consists of volunteers who choose to participate. These samples are highly biased because people with strong opinions are more likely to respond, skewing results.

Convenience sampling selects whoever is easy/nearby. It is biased here because early morning coffee shop visitors are NOT representative of the general population — they likely share habits (e.g., working professionals, high caffeine preference).

This is a leading question — it pushes respondents toward agreeing. Phrases like "Don't you agree..." create response bias by influencing how people answer, regardless of their true opinion.

Undercoverage occurs when part of the population is systematically excluded. By only emailing people, those without internet access (a significant group!) are never counted — skewing results toward heavier internet users.

"At least 71" means scores in 71–80, 81–90, and 91–100. Add those bars: \(11 + 8 + 5 = \mathbf{24}\). Do not include 51–60 or 61–70.

The range 76–85 splits across two bars (71–80 and 81–90). We only know how many are in each full bar, not where within the bar they fall. So it is impossible to determine the exact count for 76–85.

In a histogram, bar height = frequency (count). Height 7 on the 181–220 bar means 7 movies had revenues falling within that interval. It does not represent a specific dollar amount.

10 values → positions 5 and 6 are the middle pair. Position 5 = 10, position 6 = 14. Median = \(\frac{10+14}{2} = \frac{24}{2} = \mathbf{12}\). (Many students mistakenly pick 12.5 — double-check your arithmetic!)

Sum = \(4+4+10+10+10+14+15+16+22+25 = 130\). Count = 10. Mean = \(\frac{130}{10} = \mathbf{13}\).

Upper half = {14, 15, 16, 22, 25} (5 values). The middle of this group (position 3) = 16. A common mistake is to answer 18 — that would only be correct if the upper half were {14, 15, 16, 22}, which it is not here.

\(\text{IQR} = Q3 - Q1 = 16 - 10 = \mathbf{6}\). The IQR tells you the range of the middle 50% of your data. Do not confuse it with Range (= Max − Min = 25 − 4 = 21).

By definition, the box in a box plot always contains the middle 50% of the data — from Q1 (25th percentile) to Q3 (75th percentile). Each "section" (whisker, lower box, upper box, whisker) represents 25% of the data.

Plot A: IQR = \(82 - 55 = 27\). Plot B: IQR = \(85 - 50 = 35\). Since \(35 > 27\), Plot B has the greater IQR, meaning its middle 50% is more spread out. Both plots have the same range (Max − Min = 60), but IQR shows internal variability.

Q3 = 85 means 85 is at the 75th percentile — 75% of data is at or below 85, so 25% is above it. Think of it as: Q1 cuts 25% | Median cuts 50% | Q3 cuts 75%. Anything above Q3 is the top 25%.