standard deviation and mode

I have a system that monitors the performance of students. It tabulates the number of students who gained a score of 1,1.25,1.5,....5 (this is our grading system). For example:

grading system     number of students
1                  12
1.25               10
1.5                15
1.75               15
2                  20
2.25               1
2.5                5
2.75               6
3                  8
5                  0

From this example, I need my system to determine which is the mode and then print it. I 开发者_如何转开发also need to get the standard deviation.

I need this in PHP. Can anyone help me with this? Your ideas, comments, and suggestions are appreciated.

Update:

Here's what I've done so far:

Finished the standard deviation...but there are still discrepancies i can't resolve...when i calculate the standard deviation manually..the answer is different from the output of my system.. >.<

While for the mode I used an array..this is my code:

$sample = array($one[$ctr],$two[$ctr],$three[$ctr],$four[$ctr],$five[$ctr],$six[$ctr],$seven[$ctr],$eight[$ctr],$nine[$ctr],$ten[$ctr],$fda[$ctr]);

         rsort($sample);
         $holder = $sample[0];
     //$holder = $mode;

The sorting is successful and I can the highest number but I need to print the value of $holder to a table using fpdf.

Any ideas, why the value is not visible in the output?

Well, the mode is easy. Just find the grade (2) which has the highest number of students (20) and there you are.

If there's more than one, then it's multi-modal and you should probably allow for that.

For the standard deviation, the method can be found here. It's basically working out the mean of all those numbers (let's simplify this by using 1, 1, 2 and 7):

1 + 1 + 2 + 7     10
-------------  =  --  = 2.5
      4            4

then calculating the square root of the variance of all those samples from that mean:

    _____________________________________________
   / (1-2.5)^2 + (1-2.5)^2 + (2-2.5)^2 + (7-2.5)^2
  /  ---------------------------------------------
\/                         4

       __________________________
      / 2.25 + 2.25 + 0.25 + 20.25
=    /  --------------------------
   \/               4

=  2.5

If you're asking a beginner-level question like how best to do this in a specific language like PHP, you should investigate the use of arrays and loops.