Question
Prove that the sum of the squares of the deviations from arithmetic mean is the least i.e. less than of the squares of the deviations of observation taken from any value.
Solution
For proving the statement given in the question we take the following observations:
1,2,3, 4,5
|
X |
X-3 |
X-4 (x') |
X'2 |
|
|
(x) |
(x2) |
|||
|
1 2 3 4 5 |
-2 -1 0 +1 +2 |
4 1 0 1 4 |
-3 -2 -1 0 +1 |
9 4 1 0 1 |
|
Σ x = 15 |
Σ x2=10 |
Σ x2= 15 |
||
We take another value i.e. 4. We observe that the sum of squares of deviations taken from mean (3) is less than that taken from other value (4) is less.
