## AP Statistics Study Guide Ch. 1-3

observational study

where you observe individuals and collect data without trying to influence results

experiment

deliberately doing something in order to provoke responses

What is the GSOCS anagram used for?

examining and describing a distribution

GSOCS

Gaps, Spread, Outliers, Center, Shape

Ogive graph

graph of cumulative frequency

Graphs of Categorical Variables

bar graph, pie chart

Graphs of Quantitative Variables

box plot, ogive graph, stem plot, histogram, stem/leaf plot

resistant measure

a value that is resistant to extreme values

example(s) of resistant measures

median

example(s) of nonresistant measures

mean, standard deviation, correlation

pth percentile

a value such that p percent of observations fall at or below it

5 number summary

minimum, Q1, median, Q3, maximum

formulas for determining outliers

less than Q1-1.5(IQR); more than Q3+1.5(IQR)

standard deviation

the average distance from the mean

when is the standard deviation 0?

when all observations are the same value

the size of a population doesn’t matter if …

the sample is random

What is the mean of a set of z-scores?

What is the standard deviation of a set of z-scores?

1

mode

a peak in a graph

unimodal

having one peak

formula for linear transformation

a+bx=xnew

multiplying each observation by a positive number ‘b’ multiples _ by ‘b’

mean, median, IQR, stdev

adding ‘a’ to each observation adds ‘a’ to _

mean, median

what statistics are not affected by adding ‘a’ to each observation

IQR, stdev

standardizing

converting raw scores to standard deviation units called z-scores

formula for a z-score

x-mean/stdev

Chebyshev’s Inequality

In any distribution, the percent of observations falling within ‘k’ standard deviations of the mean is at least 100(1-1/k^2)

density curve

a curve that has an area of 1 underneath it

in skewed graphs, the ____ is closest to the tail (mean, median)

mean

the median of a graph is referred to as

the equal areas point

the mean of a graph is referred to as

the tipping point

Empirical Rule

in a Normal distribution, approx. 68% of the data is within 1 stdev of the mean, approx. 95% of the data is within 2 stdev’s of the mean, approx. 99.7% of the data is within 3 stdev’s of the mean

inflection point

a point located at +/- 1 stdev on a Normal curve where a change in curvature occurs

ti-nspire: how to get a z-score from a probability

invnorm(prob,mean,stdev)

response variable

measures an outcome of a study

explanatory variable

explains or influences changes in a response variable

R (correlation coefficient)

measures the direction and strength of the linear relationship between two quantitative variables

4 rules of ‘R’

1. no distinction between explanatory/response variables

2. not affected by units of measurement

3. positive R=positive correlation; negative R=negative correlation

4. always between -1 and 1

2. not affected by units of measurement

3. positive R=positive correlation; negative R=negative correlation

4. always between -1 and 1

interpolate

making predictions based on data inside of known quantities

extrapolate

making predictions based on data outside of known quantities

Least Squares Regression Line (LSRL)

describes how a response variable ‘y’ changes as an explanatory variable ‘x’ changes – used to predict y values

formula of LSRL

predicted y = a + bx

slope of LSRL

b = r(sy/sx) that passes through the point mean(x), mean(y)

residual

observed value – expected value (y-y(hat))

residual plot

scatterplot of regression residuals against explanatory variables

R^2(coefficient of determination)

tells us how well the LSRL predicts y values of a response variable – the number is the percentage of values best explained by the LSRL – the others are explained best by “other stuff”

formula of R^2

1-SSE/SST (SSE= sum of residuals squared, SST= sum of deviations squared)

influential observation

an extreme value that, if removed, has a big effect on the equation of the LSRL

lurking variable

variables not included in the explanatory/response variables of the study and may influence the interpretation of relationships

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