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Local Modes and Bimodal Distributions


Date: 10/22/2000 at 19:56:22
From: Laura
Subject: Statistics (standard normal curve)

What does it mean if a frequency distribution shows two peaks?

I know that if a distribution is sharp and peaked, then the standard 
deviation is small. So does that mean that the values tend to increase 
then decrease and increase again? Would this be the answer?


Date: 10/23/2000 at 14:18:48
From: Doctor TWE
Subject: Re: Statistics (standard normal curve)

Hi Laura - thanks for writing.

In general, yes, it would indicate that the values tend to increase 
then decrease and increase again. We call the smaller of the peaks a 
"local mode." If the two peaks are the same height we say that the 
distribution is "bimodal" or "multimodal." But you have to be 
careful that you're not over-scrutinizing the data. A small increase 
in a generally decreasing pattern may just be a glitch, an 
aberration of how the data were sampled, and may not be significant. 
Here are some examples:

      Single Modal Distribution

     |            *
     |           * *
     |          *   *
     |          *   *
     |          *   *
     |         *     *
     |        *       *
     |       *         *
     |    ***           ***
     |****                 ****
     +-------------------------


      Single Modal Distribution with Local Mode


     |            *
     |           * *
     |          *   *
     |          *   *     *
     |          *   *    * *
     |         *     *  *   *
     |        *       **    *
     |       *               *
     |    ***                 **
     |****                      ****
     +------------------------------



      Bimodal Distribution


     |            *        *
     |           * *      * *
     |          *   *    *   *
     |          *   *    *   *
     |          *   *    *   *
     |         *     *  *     *
     |        *       **       *
     |       *                  *
     |    ***                    ***
     |****                          ****
     +----------------------------------

      Single Modal Distribution with a "glitch"
      (probably just a glitch)

     |            *
     |           * *
     |          *   *
     |          *   *
     |          *   *
     |         *     *
     |        *       *
     |       *         *   *
     |    ***           *** *
     |****                   ****
     +---------------------------

I hope this helps. If you have any more questions, write back.

- Doctor TWE, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Statistics

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