AP Statistics - Lesson 1.3

mean

arithmetic average, measure of center, NOT RESISTANT, easily influenced by outliers

x-bar

the mean of a set of observations/sample (add their values and divide by the number of observations), use for reasonably symmetric distributions

? (sigma)

sum, add them all up

? (mu)

population mean

resistant measure of center

not influenced by extreme observations

median (M)

midpoint of a distribution, typical value; half the observations are smaller and half are larger; in a skewed distribution, the mean is usually farther out; RESISTANT

IQR

measures the range of the middle 50% of the data; IQR=Q3-Q1; resistant

First Quartile (Q1)

one-quarter of the way up the list, 25%; resistant

Third Quartile (Q3)

third-quarters up the list, 75%; resistant

outlier

individual value that falls outside the overall pattern, value(s) that lie outside the boundaries of: 1.5 x IQR plus Q3 or 1.5 x IQR minus Q1

five-number summary

Minimum, Q1, M, Q3, Maximum

boxplot

based on 5 number summary, useful for comparing distributions, shows spread of central half of distribution

numerical summary

should report at least its center and spread, or variability

variance (S sub-x squared)

how far a set of numbers is spread out; average squared distance of the SD

standard deviation (s sub-x)

measures the average distance of the observations from their mean; measures spread about the mean, always greater or equal to 0, not resistant, use for reasonably symmetric distributions

symmetric data

use mean and SD

skewed data

use median and IQR