AP Statistics Cumulative AP Exam Study Guide

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statistics

science of collecting and analyzing data to draw conclusion

population

entire collection of individuals/objects

sample

portion of the population

variable

any characteristic whose value changes

data

observation on variables

categorical (qualitative) data

basic characteristics

numerical (quantitative) variable

measurements of numerical data

univariate

one variable

bivariate

two variables

multivariate

many variables

symmetrical definition

data on both sides that are fairly the same shape and size ("bell curve")

uniform definition

every class has equal frequency ("rectangle")

skewed definition

one side is longer than the other side

bimodal definition

two peaks

shape definition

symmetrical, skewed, uniform, or bimodal (overall type)

outliers definition

gaps or clusters

center

mean, median, mode (middle of data)

spread

range, SD, or IQR (variability)

parameter

value of a population

variability

allows statisticians to distinguish between usual and unusual occurrences

range

max - min

IQR

Q3 - Q 1

variance

DS^2

resistant

median or IQR

non-resistant

mean, range, variance, SD, correlation coefficient (r), LSRL, coefficient of determination (r^2)

symmetrical

mean \= median

skewed right

mean \> median

skewed left

mean < median

z-score

standardized score that tells you many SD from the mean an observation is

empirical rule

68-95-99.7

sample space

collection of all outcomes

event

sample of outcomes

complement

all outcomes not in the event

union

all outcomes in both circles, A ∪ B

intersection

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

mutually exclusive (disjoint)

A and B cannot happen at the same time

independent

one event does not change the outcome of another

experiment probability

\# success / total trials

law of large numbers

as experiment is repeated, the probability gets closer and closer to true probability

correlation coefficient (r)

the strength, direction, linear association between x and y

LSRL (least square regression line)

line of mathematical best fit

residuals (error)

vertical difference of a point from LSRL

residual plot

scatter plot of residual

coefficient of determination (r^2)

approximately [r^2%] of the variation in y can be explained by the LSRL of x and y

slope

for [unit] in x, then the [y variable] will decrease/increase [slope] amount

extrapolation

LRSL cannot find values outside the range of the original data

influential points

points that significantly change LSRL when removed

census

complete population count

sampling frame

list of everyone in a population

SRS (simple random sample)

units have an equal change of being selected

stratified

divide population in homogenous groups (strata) then SRS each strata

systematic

a systematic approach after choosing randomly where to begin (ex: every 5th person)

cluster sample

based on location and samples all at that location

random digit table

each entry is equally likely and independent of the rest

bias

favoring a certain outcome

voluntary response

people choose to participate

convienience sampling

ask people who are comfortable asking

undercoverage bias

some group(s) are left out of the selection process

non-response bias

someone does not want to participate

response bias (false answers)

providing inaccurate answers

observation study

observing outcomes without treatment

experiment

imposing a treatment on subject

experimental unit

single individual/object that receives treatment

factor

explanatory variable, what is being tested

level

specific value for the factor

response variable

what you measure

treatment

experimental condition applied to each unit

control group

the group that does not receive the experimental treatment.

placebo

treatment with no active ingredients

blinding

method used so subjects are unaware of treatment

double blinding

neither subject nor evaluators know which treatment is being given