Common Mistakes

Statistics · AP · Sampling Distributions

Focus

Sampling Distributions for Sample Means

This topic is assessed on the AP Exam.

Frequent mistakes

### 1. Parameter vs statistic

What it looks/sounds like: p̂ is described as ‘the population proportion’.

Why it happens: Notation for parameter and statistic is swapped.

How to fix: Use p, μ for parameters; p̂, x̄ for statistics.

### 2. Sampling distribution confusion

What it looks/sounds like: One sample histogram is called the sampling distribution.

Why it happens: Population, sample, and sampling distribution are conflated.

How to fix: Ask: many samples of statistics vs one sample’s data.

### 3. Correct work, wrong question

What it looks/sounds like: The algebra is fine but answers a different quantity than the stem asks for.

Why it happens: Attention locks onto the first operation instead of the final ask.

How to fix: Underline the final question; after solving, verify the boxed answer matches it.

### 4. Notation and justification gaps

What it looks/sounds like: Missing units, limit language, or ‘because’ statements AP graders expect.

Why it happens: Notation is treated as decoration rather than part of the score.

How to fix: Add one justification phrase per major step (definition, theorem, or rule).

How to avoid them

1. State conditions for Normal/Large Counts models. 2. Describe how sample size affects standard error. 3. Name the parameter of interest.

Quick self-check

• [ ] Can distinguish parameter and statistic
• [ ] Can state CLT conditions in context
• [ ] Can describe sampling distribution shape