Which among the following error represent the limit of precision in the determination of a value & obey the laws of chance and therefore, must be handled according to the mathematical laws of probability?

Explanation:

Cumulative Errors/ Systematic errors:

• The errors that occur same size and sign under the same conditions are said to be Cumulative errors.
• They are cumulative in nature. Examples of systematic errors are Collimation in a level, Expansion of steel tape, etc.
• They are proportional to the length of the line.

Compensating errors:

• These are those which remain after mistakes and systematic errors have been eliminated and are caused by the combination of errors beyond the ability of the observer to control.
• They are proportional to the square root of the length of the line.

Accidental errors:

• They represent the limit of precision in the determination of a value.
• They obey the law of chance and must be handled according to the mathematical law of probability.
• These errors are proportional to the square root of the length of the line (√L).

Random errors:

• These are all those discrepancies remaining after the mistakes and systematic errors are removed.
• It is mainly caused by the limitations of observers and instruments and is random in nature.