stats unit 1

12th grade ap statistics

quantitative variable

takes numerical values for a measured or counted quality

categorical variable

takes on values that are category names or group labels

bar graphs

show frequency (how many) or relative frequency (percent)

two-way table

• marginal %: B/C

• joint %: A/C

• conditional %: A/B

misleading graphs

• vertical axis must start at 0

• beware of using images for bar graphs

segmented bar graph

stack up bars to make 100%

mosaic plot

segmented bar graph where the width of bars is proportional to the group size

association

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

quantitative data

• types: discrete, continuous

• dotplots and stemplots show every individual value

• histogram shows general shape

discrete

countable number of values

continuous

infinite values

describing distribution

• shape

• outliers

• center

• variability

• context

skewed to the left

tail on left side

skewed to the right

tail on right side

variance

(standard deviation)^²

standard deviation

“the context typically varies by SD from the mean of x̅.”

outliers

• greatly affects mean and standard deviation (nonresistant)

• median is resistant to change

symmetric distributions

use mean, SD

skewed or outliers distributions

use median, IQR

1.5 x IQR method for outliers

• low outlier < Q₁ -1.5(IQR)

• high outlier > Q₃ + 1.5(IQR)

standard deviation method for outlilers

• low outlier < mean - 2(SD)

• high outlier > mean + 2(SD)

boxplots

5 number summary- minimum, Q₁, median, Q₃, maximum

comparing distributions

• shape

• outlier (1.5IQR method)

• center (mean, median)

• variability (range, IQR, SD)

• + context and comparative language