Errors in measurement come from three main sources: gross errors from human mistakes, systematic errors from instrument defects or environmental factors, and random errors from unknown causes. Systematic errors include instrumental errors from worn parts or friction and environmental errors from conditions like temperature or magnetic fields. Random errors occur even when systematic errors are addressed and can only be reduced by taking more readings and using statistical analysis.

1. •Errors in
Measurement

2. Types of Error
• No measurement can be made with
perfect accuracy, but it is important to find
out what the accuracy actually is and how
different errors have entered into the
measurement.
• A study of errors is a first step in finding
ways to reduce them.

3. • Error is the difference between the
measured value and the ‘true value’ of the
thing being measured.
• Uncertainty (‫صورتحال‬ ‫یقینی‬ ‫غیر‬) is a quantification
( ‫کرنا‬ ‫تعین‬ ‫کا‬ ‫مقدار‬ ) of the doubt about the
measurement result.

4. Re-call …..

8. Few Terms Related to Errors

18. •Types of Errors

19. Types of Error….
• Errors may come from different sources and are
usually classified under three main headings:-
- Gross errors: largely human errors, among them
misreading of instruments, incorrect adjustment and
improper application of instruments, and computational
mistakes.
- Systematic errors: shortcomings of the instruments,
such as defective or worn parts, and effects of the
environment on the equipment or the user.
- Random errors: those due to causes that cannot be
directly established because of random variations in the
parameter or the system of measurement.

20. Gross Errors
• This class of errors mainly covers human mistakes
in reading or using instruments.
• One common gross error frequently committed by
beginners in measurement work involves the
improper use of an instrument.
• In general, indicating instruments change
conditions to some extent when connected into a
complete circuit, so that the measured quantity is
altered by the method employed.
• The instrument may have a "loading effect" on the
circuit being measured, altering the original
situation by the measurement process.

21. Effect of Improper Use of instruments

25. • Error caused by loading
effect can be avoided by
using high-resistance
voltmeters.

26. Systematic Errors
Systematic errors: shortcomings of the instruments,
such as defective or worn parts, and effects of the
environment on the equipment .
This type of error is usually divided into two different
categories:
(1) instrumental errors, defined as shortcomings of the
instrument;
(2) environmental errors, due to external conditions
affecting the measurement.

27. Systematic Errors . . .
A Instrumental errors are errors inherent in
measuring instruments because of their
mechanical structure. For example, in the
d’Arsonval movement friction in bearings
of various moving components may cause
incorrect readings. Irregular spring tension,
stretching of the spring, or reduction in
tension due to improper handling or overloading of the
instrument will result in errors.
Other instrumental errors are calibration errors, causing the
instrument to read high or low along its entire scale. (Failure
to set the instrument to zero before making a measurement
has a similar effect.) .

28. Systematic Errors . . .
• Instrumental errors may be avoided by
• (1) selecting a suitable instrument for
the particular measurement application;
(2) applying correction factors after
determining the amount of instrumental
error;
(3) calibrating the instrument against a
standard.

29. Systematic Errors . . .
• Environmental errors are due to conditions
external to the measuring device, including
conditions in the area surrounding the
instrument, such as the effects of
temperature, humidity, barometric
pressure, or of magnetic
or electrostatic fields.

30. Random Errors
• These errors are due to unknown causes and occur
even when all systematic errors have been
accounted for. In well-designed experiments, few
random errors usually occur, but they become
important in high-accuracy work.
• This variation cannot be corrected by any method of
calibration or other known method of control and it
cannot be explained without minute investigation.
The only way to offset these errors is by increasing
the number of readings and using statistical means
to obtain the best approximation of the true value of
the quantity under measurement.

31. •Statistical
Analysis

32. Statistical Analysis

33. Statistical Analysis

40. Standard Deviation