Interquartile Range and Standard Deviation

Date: 11/24/97 at 05:32:15
From: Anonymous
Subject: Interquartile range

I am working on a statistics presentation to a year 12 group.

I am okay with calculating the various measures of average (mean, mode 
and median) and with calculating the interquartile range and the 
standard deviation. However, I am not too sure that I am clear on the 
particular uses of each type of measurement, espercially interquartile 
range and standard deviation.

Any help would be gratefully received.

Dave C 
Duchess's County High School, Alnwick.

Date: 11/24/97 at 09:37:24
From: Doctor Statman
Subject: Re: Interquartile range

Dear Dave,

Three important characteristics of distributions of data are the 
shape, the center, and the spread. Shapes can be symmetric or skewed, 
with gaps, outliers, or other interesting features.

It sounds as if you are ready to explain centers, like means and 
medians.

The third characteristic, spread, is a little more slippery. I suggest 
an example such as the one found at:

  http://renoir.vill.edu/~short/handouts/normal_temperatures.html   

In this example the normal monthly temperatures for two cities in the 
U.S., St. Louis and San Francisco, are presented. The centers for 
these two distributions are very similar, but the spreads are quite 
different. The example illustrates the importance of considering 
spread (variability) in the description of a distribution.

The interquartile range and the standard deviation both measure
spread, but the IQR is more resistant to outliers. The standard
deviation is sensitive to outliers or extreme observations. Their
relation is much like that between the mean and the median - the mean 
is sensitive and the median is resistant.

Good luck!  Say "hello" to the year 12 students for Doctor Math!

-Doctor Statman,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   
    

For more on the meanings of "quartile" and mathematicians' 
disagreements about them, see

  Defining Quartiles
  http://mathforum.org/library/drmath/view/60969.html

- Doctor Melissa, The Math Forum
  http://mathforum.org/dr.math/