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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
numbers...

- 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
http://mathforum.org/dr.math/
```
Associated Topics:
High School Statistics

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