AP Stats

Mean

average of all data values. Add them up and divide by how many there are.

Median

The middle value when data are ordered from least to greatest.

Mode

The value that appears most often.

Range

The difference between the maximum and minimum values.

5-Number Summary

Minimum, Q1, Median, Q3, Maximum. Used to make a boxplot

IQR (Interquartile Range):

Q3 – Q1. Measures the spread of the middle 50% of the data.

Variance

The average squared distance from the mean.

Standard Deviation

The typical distance a data point is from the mean.

Z-Score

Tells how many standard deviations a value is from the mean. Formula: (x - mean)/s

Residual

The difference between actual and predicted values. Actual - Predicted = ?

Outlier (1.5 × IQR Rule)

Smaller than Q1 - (1.5×IQR) or larger than Q3 + (1.5×IQR)

Undercoverage Bias 

Some groups in the population are left out.

Nonresponse Bias

People chosen for the sample don’t respond.

Response Bias

People give inaccurate answers (lying, wording, etc.).

Wording Bias

Question wording influences responses

Voluntary Response Bias

People choose to respond, usually with strong opinions.

Convenience Sample

Sample chosen because it’s easy to reach.

Population

The entire group we want to study

Sample

The part of the population actually observed or surveyed

Parameter

A number that describes the population

Statistic

A number that describes a sample

Simple Random Sample (SRS)

Every individual has an equal chance of being selected.

Stratified Random Sample

Divide population into groups and take random samples from each.

Cluster Sample

Divide population into clusters, randomly choose a few clusters, and sample everyone in those.

Systematic Sample

Select every nth individual after a random start

Observational Study

Observes individuals but does not impose treatments

Experiment

Imposes a treatment to measure cause and effect

Confounding Variable

A hidden variable that affects both explanatory and response variables.

DUFS

Direction, Unusual Features, Form, Strength — used to describe scatterplots.

Correlation (r)

Measures direction and strength of a linear relationship (–1 ≤ r ≤ +1)

Coefficient of Determination (r²)

Percent of variation in y explained by the regression line.

Least Squares Regression Line (LSRL)

Line that minimizes the sum of squared residuals. ŷ = a + bx

Slope Interpretation

For each 1-unit increase in x, predicted y changes by b units

Y-Intercept Interpretation

Predicted value of y when x = 0.

Experiment

A study where the researcher actively imposes a treatment on subjects to measure cause and effect.

Observational Study

A study that observes individuals and records data without influencing the responses. no treatment imposed

Explanatory Variable (Input)

The variable that is changed or controlled to see if it causes an effect on the response variable.

Response Variable (Output)

The variable that measures the result or outcome of the study.

Treatment

A specific condition applied to individuals in an experiment, often a combination of explanatory variable levels.

Experimental Units

The individuals or objects on which treatments are imposed (called subjects if they’re people).

Placebo

A fake treatment that looks real but has no active ingredient; used to measure the effect of expectation.

Placebo Effect

When subjects show a response to a fake treatment simply because they believe it’s real.

Double-Blind Experiment

Neither the subjects nor the researchers who interact with them know which treatment each subject receives — helps prevent bias.

Blocks (Blocking)

Grouping experimental units that are similar in some important way before assigning treatments to reduce variation.

Matched Pairs Design

A special type of blocking with two very similar units, or one unit measured before and after a treatment.

Block Group

A group of similar experimental units formed to control for outside variables, with random assignment done within each block.

Random Assignment

Using chance to assign treatments to experimental units, helping to balance out unknown variables.

Control Group

The group that does not receive the treatment (or receives a placebo) and is used for comparison.

Randomized block design

a statistical method that groups subjects into blocks based on a shared characteristic to reduce variability and increase experimental precision

Randomized design

an experimental setup in statistics where subjects are randomly assigned to different treatment groups

Statistically significant

a measure that indicates a result is unlikely to have occurred due to random chance, meaning the outcome is likely real. (Less then 5%)