, the first quartile of a set of data is a number having the
property that at least one-quarter of the observations are less than or equal
to 
and at least
three-quarters of the observations are greater than or equal to 
.
First Quartile:
Denoted , the first quartile of a set of data is a number having the
property that at least one-quarter of the observations are less than or equal
to and at least
three-quarters of the observations are greater than or equal to .
Interquartile Range: The interquartile range (IQR) is a measure of spread defined as the difference between the third and first quartiles:
Mean: The
mean is the average of the data: 
Median: The median, denoted 
, is “half-way point” of the data in the sense that the same
number of observations is greater than or equal to 
as is less than or equal to it.
Nonresistant: Summary measures that can be greatly changed by one or more outliers.
Outlier: An extremely unrepresentative data point. A
box-and-whisker plot identifies any data value less than 
-1.5*IQR or greater than
+1.5*IQR as an outlier.
Resistant: Summary measures that are not greatly changed by one or more outliers.
Standard Deviation: A numerical value given to describe the
spread of values of a data set. The
larger the standard deviation, the greater the spread. The formula for finding the standard
deviation, s, is 
.
Trimming: k-times trimming consists of removing the k largest and k smallest observations from the data set. The k-times trimmed mean is the mean of the data that remain after the k-times trimming.
Third Quartile: The third quartile, 
, is a number having the property that at least
three-quarters of the observations are less than or equal to 
and at least
one-quarter of the observations are greater than or equal to 
.