Section 1.4 – Range, IQR and Finding Outliers
1
Section 1.4
Range, IQR and Finding Outliers
In earlier sections we discussed measures of center (mean and median) and measures of
spread (variance and standard deviation).
In this section, we will introduce more
measures of spread (range and interquartile range) as well as other measures of location
(percentiles).
Using this information we will be able to learn more about our data and
will be able to identify outliers.
The
minimum
is the smallest data value.
The
maximum
is the largest data value.
The
range
of a set of data is:
Maximum – Minimum
(Sensitive to outliers.)
Another measure of dispersion is called the
interquartile range
, or
IQR
.
Before we can
discuss how to determine the IQR we will need to understand some more measures of
location, specifically
percentiles
.
The most common percentiles are the 25
th
percentile, the 50
th
percentile and the 75
th
percentile.
Quartile 1 (Q1)
is the 25
th
percentile of ordered data or median of lower half
of ordered data.
Quartile 2 (Q2)
, is the median or 50
th
percentile of ordered data.
Quartile 3 (Q3)
is the 75
th
percentile of ordered data or median of upper half of ordered
data.
Note that half of the data will fall between Q1 and Q3.