Statistics - Sum of Square

# Statistics – Sum of Square

In statistical knowledge evaluation the whole sum of squares (TSS or SST) is a amount that seems as a part of an ordinary approach of presenting outcomes of such analyses. It’s outlined as being the sum, over all observations, of the squared variations of every remark from the general imply.

Complete Sum of Squares is outlined and given by the next operate:

## Formulation

SumÂ ofÂ SquaresÂ =âˆ‘(xiâˆ’xÂ¯)2SumÂ ofÂ SquaresÂ =âˆ‘(xiâˆ’xÂ¯)2

The place âˆ’

• xixiÂ = frequency.
• xÂ¯xÂ¯Â = imply.

### Instance

Downside Assertion:

Calculate the sum of sq. of 9 kids whose heights are 100,100,102,98,77,99,70,105,98 and whose means is 94.3.

Given imply = 94.3. To seek out Sum of Squares:

Calculation of Sum of Squares.
Column A
Worth or Rating
xixi
Column B
Deviation Rating
âˆ‘(xiâˆ’xÂ¯)âˆ‘(xiâˆ’xÂ¯)
Column C
(DeviationÂ Score)2(DeviationÂ Rating)2
âˆ‘(xiâˆ’xÂ¯)2âˆ‘(xiâˆ’xÂ¯)2
100 100-94.3 = 5.7 (5.7)2Â = 32.49
100 100-94.3 = 5.7 (5.7)2Â = 32.49
102 102-94.3 = 7.7 (7.7)2Â = 59.29
98 98-94.3 = 3.7 (3.7)2Â = 13.69
77 77-94.3 = -17.3 (-17.3)2Â = 299.29
99 99-94.3 = 4.7 (4.7)2Â = 22.09
70 70-94.3 = -24.3 (-24.3)2Â = 590.49
105 105-94.3 = 10.7 (10.7)2Â = 114.49
98 98-94.3 = 3.7 (3.7)2Â = 3.69
âˆ‘xi=849âˆ‘xi=849 âˆ‘(xiâˆ’xÂ¯)âˆ‘(xiâˆ’xÂ¯) âˆ‘(xiâˆ’xÂ¯)2âˆ‘(xiâˆ’xÂ¯)2
First Second Sum of Squares