AP Statistics Study Guide Ch. 1-3 – Flashcards
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observational study
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where you observe individuals and collect data without trying to influence results
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experiment
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deliberately doing something in order to provoke responses
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What is the GSOCS anagram used for?
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examining and describing a distribution
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GSOCS
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Gaps, Spread, Outliers, Center, Shape
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Ogive graph
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graph of cumulative frequency
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Graphs of Categorical Variables
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bar graph, pie chart
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Graphs of Quantitative Variables
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box plot, ogive graph, stem plot, histogram, stem/leaf plot
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resistant measure
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a value that is resistant to extreme values
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example(s) of resistant measures
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median
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example(s) of nonresistant measures
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mean, standard deviation, correlation
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pth percentile
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a value such that p percent of observations fall at or below it
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5 number summary
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minimum, Q1, median, Q3, maximum
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formulas for determining outliers
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less than Q1-1.5(IQR); more than Q3+1.5(IQR)
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standard deviation
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the average distance from the mean
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when is the standard deviation 0?
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when all observations are the same value
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the size of a population doesn't matter if ...
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the sample is random
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What is the standard deviation of a set of z-scores?
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1
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mode
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a peak in a graph
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unimodal
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having one peak
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formula for linear transformation
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a+bx=xnew
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multiplying each observation by a positive number 'b' multiples _ by 'b'
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mean, median, IQR, stdev
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adding 'a' to each observation adds 'a' to _
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mean, median
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what statistics are not affected by adding 'a' to each observation
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IQR, stdev
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standardizing
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converting raw scores to standard deviation units called z-scores
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formula for a z-score
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x-mean/stdev
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Chebyshev's Inequality
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In any distribution, the percent of observations falling within 'k' standard deviations of the mean is at least 100(1-1/k^2)
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density curve
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a curve that has an area of 1 underneath it
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in skewed graphs, the ____ is closest to the tail (mean, median)
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mean
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the median of a graph is referred to as
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the equal areas point
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the mean of a graph is referred to as
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the tipping point
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Empirical Rule
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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
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inflection point
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a point located at +/- 1 stdev on a Normal curve where a change in curvature occurs
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ti-nspire: how to get a z-score from a probability
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invnorm(prob,mean,stdev)
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response variable
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measures an outcome of a study
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explanatory variable
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explains or influences changes in a response variable
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R (correlation coefficient)
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measures the direction and strength of the linear relationship between two quantitative variables
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4 rules of 'R'
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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
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interpolate
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making predictions based on data inside of known quantities
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extrapolate
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making predictions based on data outside of known quantities
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Least Squares Regression Line (LSRL)
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describes how a response variable 'y' changes as an explanatory variable 'x' changes - used to predict y values
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formula of LSRL
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predicted y = a + bx
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slope of LSRL
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b = r(sy/sx) that passes through the point mean(x), mean(y)
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residual
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observed value - expected value (y-y(hat))
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residual plot
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scatterplot of regression residuals against explanatory variables
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R^2(coefficient of determination)
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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"
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formula of R^2
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1-SSE/SST (SSE= sum of residuals squared, SST= sum of deviations squared)
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influential observation
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an extreme value that, if removed, has a big effect on the equation of the LSRL
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lurking variable
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variables not included in the explanatory/response variables of the study and may influence the interpretation of relationships
