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