Glossary

Adjacent Values: The lower adjacent value A_-, is the smallest data value greater than or equal to Q₁ - 1.5 * IQR. The upper adjacent value, A₊, is the largest data value less than or equal to Q₃ + 1.5 * IQR.

Box and Whisker Plot: A plot based on the five number summary in which (1) a box shows the location of the "central" half of the data (i.e., the data between the first and third quartiles), with the median marked inside, (2) whiskers mark the regions between the outer quartiles and the adjacent values, and (3) any points outside the whiskers are displayed individually as possible outliers.

Five Number Summary: The five number summary of a set of data consists of the three quartiles and the two adjacent values.

Interquartile Range: The interquartile range (IQR) is the spread between the first and third quartiles.

IQR = Q₃ - Q₁

Mean: The mean is the average of the data.

Median: A median (also called the second quartile, Q₂) is a midpoint of the data: that is, a point at or below which lies at least half the data and at or above which lies at least half the data.

Outlier: An extreme data value. A box and whisker plot identifies as a possible outlier any data point located below the lower adjacent value A_-, or above the upper adjacent value A₊.

Quartiles: A second quartile Q₂ is a median. A first quartile Q₁ is a point at or below which lies at least one-quarter of the data and at or above which lies at least three-quarters of the data. A third quartile Q₃ is a point at or below which lies at least three-quarters of the data and at or above which lies at least one-quarter of the data.

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 standard deviation s is:

where n is the number of observations, y_i is the i-th observation, and

is the mean of the data.