AP Statistics Formula Sheet Cheat Sheet

Key Facts

• The sample mean is $\bar{x}=\frac{\sum x_i}{n}$, and it measures the average value in a sample.
• The sample standard deviation is $s=\sqrt{\frac{\sum (x_i-\bar{x})^2}{n-1}}$, and it measures typical distance from the sample mean.
• For independent events, $P(A \cap B)=P(A)P(B)$, and for conditional probability, $P(A\mid B)=\frac{P(A \cap B)}{P(B)}$.
• For a binomial random variable, $\mu_X=np$ and $\sigma_X=\sqrt{np(1-p)}$ when there are $n$ independent trials with success probability $p$.
• For a sampling distribution of a sample proportion, $\mu_{\hat{p}}=p$ and $\sigma_{\hat{p}}=\sqrt{\frac{p(1-p)}{n}}$ when the independence and large counts conditions are met.
• A one-sample confidence interval has the general form $\text{statistic} \pm \text{critical value}\times \text{standard error}$.
• A common one-sample $z$ interval for a proportion is $\hat{p}\pm z^*\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$.
• The least-squares regression line is $\hat{y}=a+bx$, where $b=r\frac{s_y}{s_x}$ and $a=\bar{y}-b\bar{x}$.

Vocabulary

Parameter

A parameter is a number that describes an entire population, such as $\mu$, $p$, or $\sigma$.

Statistic

A statistic is a number calculated from sample data, such as $\bar{x}$, $\hat{p}$, or $s$.

Sampling Distribution

A sampling distribution is the distribution of a statistic over many random samples of the same size.

Standard Error

A standard error is an estimated standard deviation of a statistic, often used in confidence intervals and hypothesis tests.

P-value

A $P$-value is the probability, assuming the null hypothesis is true, of getting a result at least as extreme as the observed result.

Correlation

Correlation $r$ measures the strength and direction of a linear relationship between two quantitative variables.