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Find the Mode of a List

Date: 02/26/2001 at 17:50:34
From: Gon
Subject: Equation for mode

I am in desperate straits over this problem. I tried to find the 
answer myself but got lost in advanced statistics (kurtosis, 
variance, etc.). I'm not sure if there even is a solution.

The problem: Using only the following information about a list of 

 - the size of the list (number of numbers)
 - the sum of the numbers
 - the standard deviation
 - the average

...find the mode of the list.

Date: 02/27/2001 at 11:39:55
From: Doctor Twe
Subject: Re: Equation for mode (please!)

Hi - thanks for writing to Dr. Math.

Because the mode is the most frequently occurring value in a data set, 
you can't determine the mode based on other statistical measures; you 
have to look at the original data.

As a counterexample, here are two data sets with the same sum, 
standard deviation, mean (average), and number of numbers, yet they 
have different modes:

              Set 1     Set 2
              -----     -----
                1         1
                2         1
                2         2
                2         3
                3         4
                4         4
                5         4
                5         5

     Sum:      24        24
     St.Dev:  1.414    1.414
     Mean:      3         3
     Count:     8         8

     Mode:      2         4

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

- Doctor TWE, The Math Forum   
Associated Topics:
High School Statistics

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