AP Statistics Cumulative AP Exam Study Guide

AP Statistics Exam Flashcards

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. “Bell Curve”

Uniform Distribution

Every class has an equal frequency (number) “a rectangle”

Skewed Distribution

One side (tail) is longer than the other side. The skewness is in the direction that the tail points (left or right)

Bimodal Distribution

Data of two or more classes have large frequencies separated by another class between them. “double hump camel”

Shape (S.O.C.S.)

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

Outliers (S.O.C.S.)

Gaps, clusters, etc.

Center (S.O.C.S.)

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

Spread (S.O.C.S.)

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. There can be more then one mode, or no mode at all if all data points occur once.

Variability

Allows statisticians to distinguish between usual and unusual occurrences.

Range

A single value – (Max – Min)

IQR

Interquartile range – (Q3 – Q1)

Standard Deviation

Measures the typical or average deviation of observations from the mean – sample standard deviation is divided by df = n-1

Variance

Standard deviation squared

Resistant

Not affected by outliers.

Trimmed Mean

Use a % to take observations away from the top and bottom of the ordered data. This possibly eliminates outliers.

Z-Score

Is a standardized score. This tells you how many standard deviations from the mean an observation is. It creates a standard normal curve consisting of z-scores with a μ = 0 & σ = 1.

Normal Curve

Is a bell-shaped and symmetrical curve.

Empirical Rule (68-95-99.7)

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

Boxplots

Are for medium or large numerical data. It does not contain original observations. Always use modified boxplots where the fences are 1.5 IQRs from the ends of the box (Q1 & Q3). Points outside the fence are considered outliers. Whiskers extend to the smallest & largest observations within the fences.

5-Number Summary

Minimum, Q1 (1st Quartile – 25th Percentile), Median, Q3 (3rd Quartile – 75th Percentile), Maximum

Sample Space

Is 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 (Disjoint)

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

Independent

If knowing one event does not change the outcome of another.

Experimental Probability

Is the number of success 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 and closer to the true (theoretical) probability. The difference between the two probabilities will approach “0”.

Conditional Probability

Takes into account a certain condition.

Correlation Coefficient (r)

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

Least Squares Regression Line (LSRL)

Is a line of mathematical best fit. Minimizes the deviations (residuals) from the line. Used with bivariate data.

Residuals (error)

Is vertical difference of a point from the LSRL. All residuals sum up to “0”.

Residual Plot

A scatterplot of (x (or ŷ) , residual). No pattern indicates a linear relationship.

Coefficient of Determination (r^2)

Gives the proportion of variation in y (response) that is explained by the relationship of (x, y). Never use the adjusted r^2.

Extrapolation

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

Influential Points

Are points that if removed significantly change the LSRL.

Outliers

are points with large residuals.

Census

A complete count of the population.

Sampling Frame

Is 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 # Generator

Calculator or computer program

Bias

Error – favors a certain outcome, has to do with center of sampling distributions – if centered over true parameter then considered unbiased

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

Wording of the Questions

Leading questions.

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

Is the explanatory variable, what is being tested

Level

A specific value for the factor.

Response Variable

What you are measuring with the experiment.

Treatment

Experimental condition applied to each unit.

Control Group

A group used to compare the factor to for effectiveness – does NOT have to be placebo

Placebo

A treatment with no active ingredients (provides control).

Blinding

A method used so that the subjects are unaware of the treatment (who gets a placebo or the real treatment).

Double Blinding

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

Control (Principles of Experimental Design)

Keep all extraneous variables (not being tested) constant

Replication (Principles of Experimental Design)

Uses many subjects to quantify the natural variation in the response.

Randomization (Principles of Experimental Design)

Uses chance to assign the subjects to the treatments.

Completely Randomized Design

All units are allocated to all of the treatments randomly

Randomized Block Design

Units are blocked and then randomly assigned in each block –reduces variation

Matched Pairs Design

Are matched up units by characteristics and then randomly assigned. Once a pair receives a certain treatment, then the other pair automatically receives the second treatment. OR individuals do both treatments in random order (before/after or pretest/post-test). Assignment is dependent

Confounding Variables

Are where the effect of the variable on the response cannot be separated from the effects of the factor being tested – happens in observational studies – when you use random assignment to treatments you do NOT have confounding variables!

Random Variable

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

Discrete Random Variable

A count of a random variable

Continuous Random Variable

A measure of a random variable

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, the probability (p) of success is the same for all trials,

Random variable (Binomial)

Is the number of successes out of a fixed # of trials. Starts at X = 0 and is finite.

Geometric Distributions

Two mutually exclusive outcomes, each trial is independent, probability (p) of success is the same for all trials. (NOT a fixed number of trials)

Random Variable (Geometric)

When the FIRST success occurs. Starts at 1 and is ∞.