AP Stats Unit 1 definition Review

What is statistics?

Collecting, analyzing, interpreting, and communicating data.

What is an individual?

A person or object described by the data.

What is a variable?

A characteristic recorded for each individual.

What is a population?

The entire group we want information about.

What is a sample?

A subset of the population actually studied.

What is a parameter?

A numerical summary of a population.

What is a statistic?

A numerical summary calculated from a sample.

What is a categorical variable?

A variable that places individuals into groups or categories.

What is a quantitative variable?

A numerical variable where arithmetic has meaningful interpretation.

Can a variable with numbers be categorical?

Yes. Jersey numbers are categorical because arithmetic is not meaningful.

What is frequency?

The number of individuals in a category or group.

What is relative frequency?

Frequency divided by the total; often written as a proportion or percent.

What graph is used for one categorical variable?

Bar graph or pie chart.

What graph is used for one quantitative variable?

Dotplot, histogram, stemplot, or boxplot.

Bar graph vs. histogram?

Bar graphs show categories; histograms show quantitative intervals.

What does SOCS stand for?

Shape, Outliers, Center, Spread.

What should you describe first in SOCS?

Shape: symmetric, skewed, uniform, bimodal, or another pattern.

What is right skew?

A distribution with a long tail extending toward larger values.

What is left skew?

A distribution with a long tail extending toward smaller values.

In right skew, how do mean and median usually compare?

Mean is usually greater than the median.

In left skew, how do mean and median usually compare?

Mean is usually less than the median.

What is the mean?

The sum of all values divided by the number of values.

What is the median?

The middle value after observations are ordered.

Which is more resistant: mean or median?

Median; it is less affected by outliers and skewness.

What is range?

Maximum minus minimum.

What is IQR?

Q3 minus Q1; it measures the spread of the middle 50%.

What does standard deviation measure?

The typical distance of observations from the mean.

When is mean and SD usually appropriate?

For roughly symmetric distributions without strong outliers.

When are median and IQR usually appropriate?

For skewed distributions or distributions with outliers.

What is a five-number summary?

Minimum, Q1, median, Q3, and maximum.

What does a boxplot display?

The five-number summary and possible outliers.

What part of a boxplot represents the IQR?

The box from Q1 to Q3.

How do you calculate an outlier fence?

Lower: Q1 − 1.5(IQR); upper: Q3 + 1.5(IQR).

What makes a good distribution comparison?

Compare shape, center, spread, and outliers in context.

How should you interpret a statistic on an FRQ?

State the value and explain what it means in the problem's context.

What is an observational study?

Researchers observe individuals without assigning treatments.

Can an observational study establish causation?

Generally no; it can show association but not establish causation.

What is an experiment?

A study where researchers assign treatments to experimental units.

What can a well-designed randomized experiment provide?

Evidence for a cause-and-effect relationship.

What is an SRS?

A sample where every possible sample of a given size has equal chance of selection.

What is stratified random sampling?

Split into groups, then randomly sample from each group.

What is cluster sampling?

Randomly select entire natural groups and sample everyone in them.

What is a convenience sample?

A sample chosen because individuals are easy to reach.

What is voluntary response bias?

People choose to participate, often attracting those with strong opinions.

What is undercoverage?

Some population members are inadequately represented or excluded.

What is nonresponse bias?

Selected individuals do not respond, potentially making results unrepresentative.

What is response bias?

Responses are systematically inaccurate because of wording or other influences.

What is an experimental unit?

An individual that receives a treatment in an experiment.

What is a subject?

An experimental unit when the individuals are human.

What is a treatment?

A specific condition imposed on experimental units.

What is a control group?

A comparison group that does not receive the experimental treatment.

Why use random assignment?

It helps create comparable treatment groups and reduces confounding.

What is replication in an experiment?

Using enough experimental units in each treatment group.

What is control in experimental design?

Keep conditions similar except for the treatments being compared.

What is blocking?

Group similar subjects first, then randomly assign within each group.

What is confounding?

Effects of two variables are mixed so their individual effects cannot be separated.

What is a completely randomized design?

Randomly assign all subjects directly to treatment groups.

What is a randomized block design?

Form similar blocks, then randomly assign treatments within each block.

What does random sampling help with?

Generalizing results from the sample to the population.

What does random assignment help with?

Establishing cause-and-effect in an experiment.

Random sampling vs. random assignment?

Sampling selects subjects; assignment places subjects into treatments.

What does association mean?

Two variables are related, but the relationship does not prove causation.

What does causation mean?

Changes in one variable produce changes in another.

What is the main AP trap with correlation?

Association alone does not prove that one variable causes another.

If data are strongly skewed, which center is preferred?

Median, because it is resistant to skewness.

If data contain extreme outliers, which spread is preferred?

IQR, because it is resistant to outliers.

What is the formula for relative frequency?

Relative frequency = frequency ÷ total.

What is the formula for IQR?

IQR = Q3 − Q1.

What is the formula for range?

Range = maximum − minimum.

What does Q1 represent?

About 25% of observations are at or below Q1.

What does Q3 represent?

About 75% of observations are at or below Q3.

What percentage lies between Q1 and Q3?

Approximately 50% of the observations.

What does the median divide?

The ordered data into two halves.

What does a large IQR indicate?

Greater spread among the middle 50% of observations.

What does a small IQR indicate?

Less spread among the middle 50% of observations.

What does a large standard deviation indicate?

Observations tend to be farther from the mean.

What does a small standard deviation indicate?

Observations tend to be closer to the mean.

What should an FRQ graph description include?

Shape, unusual features, center, spread, and context when appropriate.

What should you compare between two distributions?

Shape, center, spread, and outliers.

What is the main purpose of an experimental control group?

Provide a baseline for comparing the treatment's effects.

Why is random assignment important?

It reduces systematic differences between treatment groups.

Why is replication important?

It reduces the influence of random variation and strengthens evidence.

Why might researchers use blocking?

To account for a variable that could affect the response.

What is a lurking/confounding variable?

A variable that mixes with the treatment or explanatory variable's effect.

Which graph is best for showing individual quantitative values?

A dotplot or stemplot, especially for smaller datasets.

Which graph is useful for large quantitative datasets?

A histogram.

Which graph is best for comparing medians and IQRs?

Side-by-side boxplots.

What is a mode?

The most frequently occurring value or category.

What does center mean when describing a distribution?

A typical or central value, often the mean or median.

What does spread mean when describing a distribution?

How much the observations vary; examples include IQR, range, and SD.

What is the safest FRQ comparison wording?

State which distribution has higher/lower center or greater/less spread in context.

What should you avoid saying about a sample's results?

Avoid claiming causation when the study only shows association.

What is the key difference between population and sample?

Population is the whole group; sample is the subset actually studied.

What is the key difference between parameter and statistic?

Parameter describes a population; statistic describes a sample.