LAST EDITED ON Feb-21-02 AT 10:21 PM (EST)
>There can be more than one mode or no mode. Right. But read you next statement:
>If a set of
>data contains for example, 4,4,4,5,5,5, then there is no
>mode because there is no one term that appears more than the
>others.
This can't be the reason that that sample has no mode, because, as you correctly stated, there may be more than one mode.
Here's a quote from P. Tannenbaum & R. Arnold's Excursions in Modern Mathematics, Prentice Hall, 4th edition, 2001, p 505-506:
The mode of a data set is the data that occurs with the highest frequency. ... When there are several data points (or categories) tied for the most frequent, each of them is a mode, but if all data points have the same frequency, rather than say that every data point is a mode, it is customary to say that there is no mode.
REA's Problem Solvers: Statistics, REA 1994, p 13 is more lenient:
Problem 1-20:
Find the mode of the sample 14, 16, 21, 19, 18, 24 and 17.
Solution: In this sample all the numbers occur with the same frequency. There is no single number which is observed more frequently than any other. Thus there is no mode or all observations are modes. The mode is not a useful concept here.
Math On Call, Great Source Education Group, Inc., 1998, p 276:
CASE 1: Sometimes there is one value that occurs more often than any other.
CASE 2: Sometimes there is more than one value that occurs most often. In this case, all these highest values are modes for the set of data.
CASE 3: Sometimes there is no value that occurs more often than the others. In this case, there is no mode.
>Yet one of our textbooks gives that example and
>lists both 4 and 5 as the modes. One of our colleagues who
>teaches from this particular book agrees that 4 and 5 both
>in the above example are modes. Who is correct? Please
>cite any references you may have.
The choice appears to be between not using and using the concept of the mode when it is not useful.