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/
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