AP Statistics Ch 1 - 4

Quantitative Variable

takes on numerical values for a measured or counted quantity (can calculate average)

Categorical Variable

takes on values that are category name or group labels; bar graphs (counts - how many) or relative frequencies (percents); cannot be averaged

bar graph, pie chart, segmented bar graph

displays for categorical data

dot plots, stem and leaf, histogram

displays for quantitative data

shape, outliers, center, spread

“describe the distribution”

when the shape is symmetric

When do you use the mean and standard deviation?

when the shape is not symmetric

When do you use the median and IQR?

The (variable) typically varies by (standard deviation) from the mean of (mean)

“interpret the standard deviation”

min, Q1, M, Q3, max

5 number summary

< Q1 - 1.5 (IQR)

“calculate any low outliers”

> Q3 + 1.5 (IQR)

“calculate any high outliers”

percentile

the pth is the value that has p% of the data less than or equal to it

(x value) is (z score) standard deviations (above or below) the mean

“interpret the z-score”

68

What percent of the data is within 1 standard deviation in a standard normal curve?

95

What percent of the data is within 2 standard deviations in a standard normal curve?

99.7

What percent of the data is within 3 standard deviations in a standard normal curve?

There is a (weak, moderate, strong) (positive, negative) (linear, nonlinear) relationship between (x variable) and (y variable) with (no/specific unusual features).

“describe the relationship displayed in the scatterplot”

no relationship

0 < r < .25

weak relationship

.25 < r < .50

moderate relationship

.50 < r < .75

strong relationship

.75 < r < 1

(coefficient of determination) percent of the variation in the (response variable) is explained by the (linear relationship) with the (explanatory variable)

“interpret the coefficient of determination”

There is a (weak, moderate, strong) (positive, negative) (linear, nonlinear) relationship between (x variable) and (y variable)

“interpret the correlation”

With each additional (x context) the predicted (y context) will (increase/decrease) by (slope)

“interpret the slope of the regression line”

When (x = 0 context) the predicted (y context) is (y intercept)

“interpret the y intercept”

The actual (y value) was (residual) (above/below) the predicted value for (x value)

“interpret the residual”

least square regression line

minimizes the sum of the square residuals

outliers

data points that go against the pattern

high leverage point

very large x value or very small x value

influential point

if removed, big change in slope, y intercept, r

horizontal outlier

tilt line; change slope

vertical outlier

shift line up/down, slope same, y intercept changes

linear model

graph x vs y

exponential model

graph x vs log y

power model

graph log x vs log y

simple random sample

every individual has the same chance of being chosen; every group of individuals has the same chance of being chosen

stratified random sample

splits population into groups homogeneous on a characteristic that affects the response variable; perform an SRS with each strata; reduces sampling variability

cluster sample

conducts SRS on heterogeneous groups that are diverse enough to represent the entire population

systematic sample

sampling method that chooses a random starting point, then samples at equal intervals to produce desired sample size

undercoverage bias

individuals are left out of sampling frame

nonresponse bias

individuals that have been included in the sampling frame either can’t be reached or refuse to participate

response bias

interviewer affects individual’s response

wording bias

hard to follow; leads to specific results

voluntary response bias

there is no sample conducted; it is self-selected, leading to skewed results

observational study

no treatment is imposed

experimental study

treatment is imposed on experimental units

comparison of treatments, random assignment, replication, and control

well designed experiments contain

placebo effect

when a fake treatment works

randomized block design

experimental design that separates subjects into blocks and randomly assign treatments within each block

matched pairs design

experimental design where subjects are paired and randomly assigned to treatment; each subject receives 2 treatments and order is random