Question

the different measurements of length of a rod are 4.2, 4.5, 4.4, 4.3, 4.6 (in cm). calculate a) mean value b) absolute value error mean absolute error and) fractional error e) % error ?​

Answer 1

MEAN ABSOLUTE ERROR - DEFINITION

The magnitude of the difference between the individual measurement and the true value of the quantity is called the absolute error of the measurement. The arithmetic mean of all the absolute error is taken as the mean absolute error of the value of the physical quantity.

ABSOLUTE ERROR - EXAMPLE

Definition:

The magnitude of the difference between mean value and each individual value is called absolute error.

Example:

The diameter of a wire as measured by a screw gauge was found to be 1.002 cm, 1.004 cm and 1.006 cm. The absolute error in the readings will be:

Solution:

Mean=

3

1.002+1.004+1.006

=1.004cm

Hence, absolute errors

Δa

1

=1.002−1.004 =0.002cm

Δa

3

=1.004−1.004 =0.000cm

Δa

3

=1.006−1.004 =0.002cm

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