ap stats mideterm review

Statistics

The science of collecting, analyzing, and drawing conclusions from data.

Descriptive Statistics

Methods of organizing and summarizing statistics.

Inferential Statistics

Making generalizations from a sample to the population.

Population

An entire collection of individuals or objects.

Sample

A subset of the population selected for study.

Variable

Any characteristic whose value changes.

Data

Observations on single or multi-variables.

Categorical Variable

Basic characteristics (Qualitative).

Numerical Variable

Measurements or observations of numerical data (Quantitative).

Discrete Variable

Listable sets (counts).

Continuous Variable

Any value over an interval of values (measurements).

Univariate

One variable.

Bivariate

Two variables.

Multivariate

Many variables.

Symmetrical Distribution

Data on which both sides are fairly the same shape and size.

Uniform Distribution

Every class has an equal frequency (number).

Skewed Distribution

One side (tail) is longer than the other side.

Bimodal Distribution

Data of two or more classes have large frequencies separated by another class.

Shape (S.O.C.S.)

Overall type (symmetrical, skewed right/left, uniform, or bimodal).

Outliers

Gaps, clusters, etc.

Center

Middle of the data (mean, median, and mode).

Spread

Refers to variability (range, standard deviation, and IQR).

Parameter

Value of a population (typically unknown).

Statistic

A calculated value about a population from a sample(s).

Median

The middle point of the data (50th percentile) when the data is in numerical order.

Mean

μ is for a population (parameter) and x is for a sample (statistic).

Mode

Occurs the most in the data.

Variability

Allows statisticians to distinguish between usual and unusual occurrences.

Range

A single value - (Max - Min).

IQR

Interquartile range - (Q3 - Q1).

Standard Deviation

σ for population (parameter) & s for sample (statistic) - measures the typical or average deviation of observations from the mean.

Variance

Standard deviation squared.

Z-Score

A standardized score indicating how many standard deviations from the mean an observation is.

Normal Curve

A bell-shaped and symmetrical curve.

Empirical Rule

Measures 1σ, 2σ, and 3σ on normal curves from a center of μ.

Boxplots

Used for medium or large numerical data; does not contain original observations.

Sample Space

Collection of all outcomes.

Event

Any sample of outcomes.

Complement

All outcomes not in the event.

Union

A or B, all the outcomes in both circles.

Intersection

A and B, happening in the middle of A and B.

Mutually Exclusive

A and B have no intersection; they cannot happen at the same time.

Independent Events

Knowing one event does not change the outcome of another.

Experimental Probability

Number of successes from an experiment divided by the total amount from the experiment.

Law of Large Numbers

As an experiment is repeated, the experimental probability gets closer to the true probability.

Correlation Coefficient (r)

A quantitative assessment of the strength and direction of a linear relationship.

Least Squares Regression Line (LSRL)

A line of mathematical best fit that minimizes the deviations from the line.

Residuals

Vertical difference of a point from the LSRL.

Coefficient of Determination (r²)

Gives the proportion of variation in y that is explained by the relationship of (x, y).

Slope (b)

For unit increase in x, then the y variable will increase/decrease slope amount.

Extrapolation

LRSL cannot be used to find values outside of the range of the original data.

Influential Points

Points that if removed significantly change the LSRL.

Census

A complete count of the population.

Sampling Frame

A list of everyone in the population.

Sampling Design

Refers to the method used to choose a sample.

SRS (Simple Random Sample)

One chooses so that each unit has an equal chance and every set of units has an equal chance of being selected.

Stratified Sampling

Divide the population into homogeneous groups called strata, then SRS each strata.

Systematic Sampling

Use a systematic approach (every 50th) after choosing randomly where to begin.

Cluster Sample

Based on location. Select a random location and sample ALL at that location.

Random Digit Table

Each entry is equally likely and each digit is independent of the rest.

Random Number Generator

Calculator or computer program.

Bias

Error that favors a certain outcome, has to do with center of sampling distributions.

Voluntary Response

People choose themselves to participate.

Convenience Sampling

Ask people who are easy, friendly, or comfortable asking.

Undercoverage

Some group(s) are left out of the selection process.

Non-response

Someone cannot or does not want to be contacted or participate.

Response Bias

False answers can be caused by a variety of things.

Observational Study

Observe outcomes without giving a treatment.

Experiment

Actively imposes a treatment on the subjects.

Experimental Unit

Single individual or object that receives a treatment.

Factor

The explanatory variable, what is being tested.

Control Group

A group used to compare the factor to for effectiveness.

Placebo

A treatment with no active ingredients.

Blinding

A method used so that the subjects are unaware of the treatment.

Double Blinding

Neither the subjects nor the evaluators know which treatment is being given.

Randomization

Uses chance to assign the subjects to the treatments.

Random Variable

A numerical value that depends on the outcome of an experiment.

Discrete Probability Distributions

Gives values & probabilities associated with each possible x.

Fair Game

A fair game is one in which all pay-ins equal all pay-outs.

Binomial Distributions

Two mutually exclusive outcomes, fixed number of trials (n), each trial is independent.

Geometric Distributions

Two mutually exclusive outcomes, each trial is independent, probability (p) of success is the same for all trials.

Continuous Random Variable

Numerical values that fall within a range or interval.

Normal Distributions

Symmetrical, unimodal, bell-shaped curves defined by the parameters μ & σ.

Sampling Distribution

The distribution of all possible values of all possible samples.