INTERQUARTILE RANGE

INTERQUARTILE RANGE (LET)

Let Subcommand

Compute the interquartile range for a variable.

The interquartile range is:
IQ = UPPER QUARTILE - LOWER QUARTILE

That is, it is the difference betweeen the 75th and 25th percentiles of a variable.

The interquartile range is used as a robust measure of scale. That is, it is an alternative to the standard deviation. The interquartile range is less effected by extremes than the standard deviation. It is the measure of scale used by the box plot.

The normalized interquartile range is

NIQ = 0.7413*IQ

This normalization is based on the fact that for a normal distribution, the interquartile range is approximately 1.349 times the standard deviation. The NORMALIZED INTERQUARTILE RANGE command returns the normalized interquartile range.

LET <par> = INTERQUARTILE RANGE <y>
                        <SUBSET/EXCEPT/FOR qualification>
where <y> is the response variable;
            <par> is a parameter where the computed interquartile range is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET <par> = NORMALIZED INTERQUARTILE RANGE <y>
                        <SUBSET/EXCEPT/FOR qualification>
where <y> is the response variable;
            <par> is a parameter where the computed normalized interquartile range is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET A = INTERQUARTILE RANGE Y1
LET A = INTERQUARTILE RANGE Y1 SUBSET TAG > 2
LET A = NORMALIZED INTERQUARTILE RANGE Y1

Dataplot statistics can be used in a number of commands. For details, enter
HELP STATISTICS

None

IQ RANGE is a synonym for INTERQUARTILE RANGE.
IQR is a synonym for INTERQUARTILE RANGE.
NORMALIZED IQ RANGE is a synonym for NORMALIZED INTERQUARTILE RANGE.
NORMALIZED IQR is a synonym for NORMALZIED INTERQUARTILE RANGE.
SCALED INTERQUARTILE RANGE is a synonym for NORMALIZED INTERQUARTILE RANGE.
SCALED INTER QUARTILE RANGE is a synonym for NORMALIZED INTERQUARTILE RANGE.
SCALED IQ RANGE is a synonym for NORMALIZED INTERQUARTILE RANGE.
SCALED IQR is a synonym for NORMALZIED INTERQUARTILE RANGE.

AVERAGE ABSOLUTE DEVIATION	= Compute the average absolute deviation of a variable.
MEDIAN ABSOLUTE DEVIATION	= Compute the median absolute deviation of a variable.
STANDARD DEVIATION	= Compute the standard deviation of a variable.
VARIANCE	= Compute the variance of a variable.
RANGE	= Compute the range of a variable.

Robust Data Analysis

2001/10

LET Y1 = LOGISTIC RANDOM NUMBERS FOR I = 1 1 100
LET A1 = INTERQUARTILE RANGE Y1

SKIP 25
READ GEAR.DAT DIAMETER BATCH
TITLE AUTOMATIC
XLIMITS 1 10
MAJOR XTIC MARK NUMBER 10
MINOR XTIC MARK NUMBER 0
XTIC OFFSET 1 1
X1LABEL BATCH
Y1LABEL INTERQUARTILE RANGE OF DIAMETER
IQ RANGE PLOT DIAMETER BATCH