The most probable value of an observed quantity available from a given set of observations is the one for which the sum of the square of errors is a minimum. This statement is called
- APrinciple of least squareCorrect
- BLaw of errors
- CPrinciple of square errors
- DNone of the above
Solution
Concept
Principle of least squares
Formula
Σv² = minimum
Step-by-step solution
1. The most probable value of a quantity is the one for which the sum of squares of residual errors is minimum. 2. This statement is called the principle of least squares.
Explanation
The most probable value of a measured quantity derived from several observations is that value which makes the sum of the squares of the residuals a minimum. For equal-weight observations it is the arithmetic mean.
Shortcut
Least squares: Σv² minimum; with weights, Σ(w v²) minimum.
Common mistake
Choosing the law of errors.
Correct answer: A) Principle of least square