AP STAT REVIEW: exploring data

Categorical Variable

takes on values that are category names or group labels

Quantitative variable

one that takes on numerical values for a measures or counted quantity

IQR

Q₃-Q₁

Interpet the slope of the least squares regression line

for every 1 unit increase in \[x context\], the predicted \[y context\] increases/decreases by \[slope\]

Regression outlier

a point that does not follow the general trend shown in the rest of the data and has a large residual

Describing a distribution

Shape, Center, Spread, Outliers

Shape of a distribution

Skewed? symmetric? Distinct peaks?

Outliers

potential outliers if estimating, if not, Q₁-1.5(IQR), Q₃+1.5(IQR)

Center

What is the mean? If skewed, what is the median?

Spread

Standard deviation (goes with mean), IQR (goes with median)

Interpret the coefficient of determination

The coefficient of determination gives the percent of the variation of \[y context\] that is explained by the variation in \[x context\].

Skewed left graph

mean

roughly symmetric graph

mean≈median

skewed right graph

mean>median

High Leverage Point

a point having a substantially larger or smaller x-value than the other observations have

Calc function for LSRL

\#8: LinReg(a+bx)

influential point

any point that, if removed, changes the relationship substantially (big changes to slope and/or y-intercept (outliers and high-leverage points are often influential)

calculate the percentile of a specific value

percentile = # of values less than or equal to that of interest/total # values in data set

Discrete variable

countable number of values, may be infinite or finite (countable)

Continuous variable

can take on infinitely many values, but those values can not be counted (must be measured)

Correlation (r)

gives strength and direction of the linear relationship between 2 quantitative variables, can be between -1 and 1

Interpreting standard deviation

gives the typical distance that values are away from the mean

Describing relationship between 2 quantitative variables

Direction (+ or -), Unusual values, form (linear or curved), strength (weak - strong)

Interpreting the y-intercept of the LSRL

The predicted value of \[y-context\] when \[x-context\] is 0 is \[y-intercept value\].

Marginal Distribution

the distribution of values of that variable among all individuals described by the 2 way table of counts

Conditional Distribution

describes the values on that variable among individuals who have a specific value of another variable. There is a separate conditional distribution for each value of the other variable.

Association

if knowing the value of one variable helps predict the value of the other

Z score calculation

x-mean / standard deviation

Interpreting Z score

\[ \] is \[Z SCORE\] standard deviations ABOVE/BELOW the mean of \[MEAN\]