AP Statistics: Chapter 2: Modeling Distributions of Data

percentile

percentile

percent of values strictly less than or equal to

Cumulative relative frequency graph

displays the cumulative relative frequency of each class of a frequency distribution

z-score

(value-mean)/SD; tells number of standard deviation above or below the mean; data above the mean has a positive value while data below the mean has a negative value; distribution always has mean 0 and SD 1

Z-score interpretation

Context is |z| standard deviations above/below the mean.

add or subtract the same value a from each value

shape: same; center: +/- a; variability: same

Multiply or divide the same value b from each value

shape: same; center: x// b; variability: x// b

density curve

shows probability, has area=1, shows the overall pattern of large observations with a smooth curve, always above or on the x-axis, outliers are not described on the curve

skew left

median>mean; tail to the left

skew right

median<mean; tail to the right

normal curve

can find the percentage of values that fall on standard deviation bounds; unusual or rare is over 2 standard deviations away, notation: N(mean,SD)

distribution of standardized scores (z-scores)

N(0,1)