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AP Statistics Exam

Terms in this set (127)

state, plane, do, conclude

steps to organize a stat problem

descriptive stat

summarizes data (to get an average)

influential stat

generalizes from sample (to make an assumption)

univariate (bivariate)

data that collects one (or two) variables

type of numerical data that measures time, height, number line values, etc.

type of numerical data that measures countable variables

type of relative frequency distribution chart used with categorical data

rudimentary histogram used with numerical data

bar chart, pie chart, relative porportion

types of charts used with *categorical data* and what you must discuss with them

stem and leaf plot, dot plot, histogram, distribution

types of charts used with *numerical data* and what you must discuss with them

frequency / # of observations in data

relative frequency =

marginal distribution

row total, column total, total totals in bar chart

make stem (with splits), add leaves, order leaves, add key

steps to making a stem and leaf plot

shape, spread, center, outlier

patterns to look for in a dot plot

center or typical value, spread of variability, general shape, location and # of peaks, gaps and outliers

what to look for in a histogram

right skewed has peak on left and vice versa

how skewed graphs look

median is less than the mean

mean and median on a skewed right graph

mean is less than the median

mean and median on a skewed left graph

unimodal, bimodal, multimodal

number of peaks a distribution can have

cumulative frequency / sample size

cumulative relative frequency =

arithmetic average that is sensitive to...

population and sample mean

exact middle of data

most often used point in a set of data

order from smallest to largest and chop off equal number from both sides

# deleted from side / n

trimmed percentage =

p hat = # of successes / n

sample proportion =

sample variance, squared standard deviation

average squared deviation from the mean, same thing as...

standard deviation

typical deviation from mean

δ = √[∑(x-mean)² ] / [n-1]

standard deviation =

Q1-(1.5xIQR) or Q3+(1.5xIQR)

how to find outliers in box plot

68%, 95%, 99.7%

within 1, 2, and 3 standard deviations of the mean

34%, 13.5%, 2.35%

other divisions for 68-95-99.7 Rule

(value - mean) / standard deviation

value such that *r* percent of observations in the data set fall below that value

y variable in scatter plot

response variable

x variable in scatter plot

explanatory variable

direction (- or +), form (clusters, curved, or linear), strength (tightly or loosely packed), outliers

used to interpret scatterplots

correlation (r), -1 to +1

measures direction and strength of the linear relationship between 2 quantitative variables, on a scale of.....

±1 to ±0.8, ±0.8 to ±0.5, ±0.5 to 0

strong correlation, medium correlation, weak correlation

the stronger a correlation is, the more it looks like a....

y hat = a + b x

regression line equation

*b* of regression line equation

a = y hat - b (x bar)

*a* of regression line equation

occur when the regression line does not perfectly fit the data

observed y - predicted y

1. Stat, edit, L3, 2nd, list, resid; 2. Turn off plot 1; 3. Turn on plot 2, plot (xList: L1 and yList: L3)

how to make residual plot in calculator

s = √(∑residuals²) / (n-2)

standard deviation of the residuals =

when we use x to estimate y, we will be off by an average of s

after finding *s*, you interpret it by saying...

coefficient of determination

percent of the variation in the values of *y* that is accounted for by the least squares regression line of *y* on *x*

r²% of the variation in y is accounted for in the linear model relating y to x

after finding *r²*, you interpret it by saying...

y hat = dependent variable, a = coefficient of constant, b = coefficient of other

how to interpret computer data

does not matter

in correlation, explanatory and response...

in regression, explanatory and response...

quantitative data

correlation and regression can only be used with...

large residuals, don't change correlation much

outliers in y direction

small residuals, change correlation a lot

outliers in x direction

convenience sample

choosing people for a sample because they are easiest to reach

voluntary response sample

using individuals who volunteer to participate

simple random sample

each individual has an equal chance of being selected

math, prb, 5: RandInt (min, max, #)

how to do simple random sampling in calculator

stratified random sample

divide people into separate groups according to characteristics, then select random sample from each group

divide people into random groups, then everyone in particular group is sampled

sampling error (convenience, voluntary response) , non-sampling error (nonresponse, response bias, bad question wording), under-coverage (didn't cover entire population

possible sampling errors

observational study

observes individuals and measures variables of interest without trying to influence the responses

imposes a treatment on individuals and then measures responses

lurking variable

not mentioned in study, but can affect the explanatory variable

two variables' effect on a response variable cannot be distinguished from one another

specific condition being applied to to individuals

experimental units

smallest collection of individuals getting a treatment

explanatory variables

control (no lurking variables), random assignment, replication (repeat trials to reduce variability)

three principles of experimental design

double-blind experiment

neither subjects nor researchers know which treatment is being received

group of experimental units that are known to be similar in some way and could affect the response of the treatments (cannot be controlled)

random sampling, population

used in *observational studies* and makes an inference about the...

random assignment, cause and effect

used in *experiments* and makes an inference about the...

P(A∪B) = P(A) + P(B)

probability of A or B when mutually exclusive

P(A∪B) = P(A) + P(B) - P(A∩B)

probability of A or B when NOT mutually exclusive

should be used when dealing with two variables that are not mutually exclusive

P(A∩B) = P(A) x P(B)

probability of A and B when independent

P(A∩B) = P(A) x P(B | A)

probability of A and B when NOT independent

should be used when dealing with two variables that are not independent

probability of B given A when independent

conditional probability example

P(B|A) = [P(A∩B)] / [P(A)]

probability of B given A when NOT independent

probability of at least one, probability of none

compliment probability example

P(not) = 1 - P(does)

probability of none occurring

P(at least 1) = 1 - P(none)

probability of at least one occurring

look at # of B and A and divide by total # of A, see if it equals total # of B divided by total #

how to tell if A and B are independent using a two way table

standard normal deviations

normal distribution with a mean of 0 and standard deviation of 1

area that z-table finds

z = (X - µ) / (δ)

standard normal deviations =

histogram (bell shaped, symmetric, single peaked), 68-95-99.7 Rule, normal probability plot

how to tell if data is normal

2nd Vars, 2:normalcdf(min,max,µ, δ)

calculator to find z-score

random variable

takes numerical value that describes the outcome of a chance process

probability distribution

gives values and their respective probabilities in a chart

expected value (mean)

long run average value of the variables after many repetitions of a chance process

µx = ∑xi(pi)

expected value =

on average, the outcome of x will differ from the mean by about δx

after finding *δ*, you can interpret it by saying....

δx = √∑(xi-µi)² pi

standard deviation of random variable =

stat, edit, L1=random variable values, L2=probability values, stat, calc, 1-var stat, List 1: L1 and FreqList: L2

standard deviation of random variable on a calculator

continuous random variable

x takes on all values in an interval or numbers and have infinitely many values

when normal distribution is square

calculate height (area must equal one), multiply the amount between the two values given (lenght) by the height

how to solve a uniform normal distribution problem

state random variable (x=?), state probability (P[x≤?]), answer

when solving a random variable problem...

multiplies mean, median, quartiles, and percentiles by x; multiplies range, IQR, and sd by |x|; shifts distribution but does not change shape

multiplying or dividing a random variable by *x*...

adds x to mean, median, quartiles, and percentiles; doesn't change range, IQR, or sd; doesn't change shape

adding or subtracting *x* from a random variable...

µt = µx + µy ; δt = √(δx² + δy²)

random variables *X* + *Y* = ?

µt = µx - µy ; δt = √(δx² + δy²)

random variables *X* - *Y* = ?

gives set number of trials

binary, independent, number of set trials, success of probability is same

binomial conditions

p(x=k) = (nCk) (p) ^(k) (1 - p) ^(n-k); n=# of trials; k=# of successes; p=prob. of success

binomial (explain variables) =

µx = n x p ; δx = √(n x p [1 - p] )

mean and standard deviation of a binomial

trials until success

binary, independent, trials until success, success of probability is same

geometric conditions

p(x=k) = (1-p) ^(k-1) (p)¹; k=# of trials until success; p=prob. of success

geometric (explain variables) =

µx = 1/p ; δx = not possible

mean and standard deviation of a geometric

binompdf(n,p,k); binomcdf(n,p,k); 1 - binomcdf(n,p,k)

Binomial for P ( x = k ) , P ( x ≤ k ) , and P ( x ≥ k )

geometpdf(p,k); geometcdf(p,k); 1 - geometcdf(p,k)

Geometric for P ( x = k ) , P ( x ≤ k ) , and P ( x ≥ k )

invNorm(area to left, µ, δ)

use the calculator to find a *z* if you already have the area

matched pairs design

randomized blocked experiment in which each block consists of a matching pair of similar experimental units

take pulse sitting, take pulse standing, find difference between the two and plot points

example of a matched pair design

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