Mistakes (or) gross Errors Systematic (or) Cumulative Errors Accidental (or) Random Errors
2. Mistakes (or) Gauss Errors:
Depends upon the observer, a mistake cannot be corrected unless the observer get training. The mistakes are errors that arise from inattention, inexperience, carelessness and poor judgement of confusion in the mind of observer.
3. Systematic Errors:
The systematic error is an error that under the same conditions will always be of the same size and sign. It is simply due to the error in instrument. These errors may be regarded as positive or negative according with whether they make the result too small (or) too great. This effect is cumulative.
4. Accidental Errors:
The Accidental Errors are those which remain after mistakes and systematical errors have been eliminated and are caused by the combination of reasons beyond the ability of the observer to control.
5. Classification of Observer Quantity:
An observer quantity may be classified as Independent Quantity Conditioned Quantity
6. Independent Quantity:
It is the one whose value is independent of the values of other quantities. It bears no relation with any other quantity and hence change in the other quantities does not affect the value of this quantity. eg. R.L of B.M
7. Conditioned Quantity:
It is the one whose value is dependent upon the values of one (or) more quantities. Its values bear a rigid relation to some other quantities. It is also called 'dependent quantities'.
The conditioned equation is the equation expressing the relation existing b/w the several dependent quantities. eg. In a ABC A+B+C= 180 . It is a conditioned equation.
An observation is a numerical value of the measured quantity and may be either direct (or) indirect.
10. Direct Observation:
A direct observation is the one made directly on the quantity being determined. Eg: Measurement of base line.
11. Indirect Observation:
An indirect observation is one in which the observed value is deduced from the measurement of some related quantities.
Eg: Measurement of Angle by repetition method.
12. Weight of an Observation:
The weight of an observation is a number giving an indication of its precision and trust worthiness, when making a comparison between several quantities of different worth.
If a certain observation of weight 4 it means that it is 4 times as much reliable as an observation of weight 1.
When two quantities (or) observations are assumed to be equally reliable, the observed values are said to be of equal weight (or) of unit weight.
13. Weighted Observations:
Observations are weighted when different weights are assigned to them. Eg: A=30040'- wt 3
It means A is measured 3 times.
14. Observed value of a Quantity:
An observed value of a quantity is a value obtained when it is corrected for all the known errors. Observed value = Measured value ± errors (or) corrections.
15. True value of Quantity:
It is the value which is obsolute free from all the errors.
A true error is the difference b/w the true value of the quantity and its observed value. True value = True value - observed value
The most probable value of the quantity is the value which is more likely to be the true value then any other value.
17. Most probable Errors:
It is defined as the quantity which added to and subtracted from the most probable value, fixes the limit within which it is an even chance the true value of the measured quantity must lie.
18. Residual Error:
It is diff b/w the most probable value of the quantity and its observed value. Residual Errors = most probable value - observed value
19. Observation Equation:
It is the relation b/w the observed quantity and its numerical value.
20. Normal Equation:
It is the education which is formed by the multiplying each equation by the co-efficient of the unknown, whose normal equation is to be formed out by adding the equation thus formed.