Why does MODE function return erroneous results in my script in MATLAB 8.0 (R2012b)?

Consider the following:

pts = [-0.6 -6;-0.2 0;0 3;-0.8 -9;-2 1;-0.4 -3];   

m=(pts(2:end,2)-ones(length(pts(:,1))-1,1)*pts(1,2)) ./ (pts(2:end,1)-ones(length(pts(:,1))-1,1)*pts(1,1))

The output is:

 m =

    15.0000

    15.0000

    15.0000

    -5.0000

    15.0000

However, when I type 'mode(m)' I get a clearly incorrect answer:

mode(m)

 ans =

     -5

And, when I do the following, I get the correct answer:

zz=str2num(num2str(m));

mode(zz)

 ans =

     15

Can you explain what is going on here?

Answer 1

[MathWorks Support Team]

The observed behavior is expected as the numbers '15' in the array 'm' are not all equal. This can be verified by changing the display format to 'long':

>> format long

>> m

 m =

   15.000000000000002

   15.000000000000000

   14.999999999999995

   -5.000000000000000

   15.000000000000004

When all the elements are different, MODE just returns the smallest, which in this case is '-5'.

The MODE function is most useful with discrete or coarsely rounded data. Hence, 'rounding' the data or reducing the precision will be useful here. There are many ways to reduce the precision:

>> mnew = double(single(m));

>> mode(mnew)

 ans =

     15

>> mnew = str2num(num2str(m)); % NUM2STR by default uses a precision of 16 digits

>> mode(mnew)

 ans =

     15

By the way, If we use a ’32-digit’ precision with NUM2STR, we get:

>> mnew2 = str2num(num2str(m,32))

>> mode(mnew2)

 mnew2 =

   15.000000000000002

   15.000000000000000

   14.999999999999995

   -5.000000000000000

   15.000000000000004

 ans =

     -5

In conclusion, it is recommended to use coarsely rounded inputs along with MODE function to avoid precision issues such as the above.