Calc Sum of Squares


Sum of Squares is easy to calculate. Plus it’s one of the most useful measures of dispersion. Here’s a video and then another example:

 

Let me give you the formula and then talk you through the process. Here’s the formula:

Like range, variance and standard deviation, Sum of Squares (SS for short) is a measure of dispersion. The more inconsistent the scores are (less homogeneous) the larger the dispersion. The more homogenous the scores (alike), the smaller the dispersion.

Using the formula above, let’s go through it, step by step Assume this is the distribution at issue:

       X
      12
       6
       5
      4
      5
    10
      3

First, each number is squared, and put into another column:

     X       X2
     12     144
      6       36
      5       25
      4       16
      5       25
    10    100
     3         9

Second, we sum each column. The sum of the first column is 45. This is called the sum of X.

The sum of the second column is the sum of X-squared. Remember, we squred the scores and then added them up. The sum of the squared-X’s is 355.

Third, we square the sum of X (45 times itself = 2025) and divide it by N (number of scores).

Since N = 7, we divide 2025 by 7 (which equals 289.29).

Fourth, we recall the sum of the X2 and subtract 240.67 from it. So 355 minus 289.29 = 65.71. The Sum of Squares is 65.71.