Question

Q.5 The measured values of diameter of a metallic wire by a Screw gauge in succ-ession comes out to be :
2.04 mm , 2.06 mm , 2.08 mm
2.07 mm and 2.05 mm respectively .
Find :
1) average diameter of wire.
2) absolute error
3) mean absolute error
4) relative error , and
5) percentage relative error.

Answer 1

Answer:

Mean value of the diameter, a

m

=

4

2.620+2.625+2.628+2.626

=2.625

Thus, Δa

1

=a

m

−a

1

=2.625−2.620=0.005

Δa

2

=a

m

−a

2

=2.625−2.625=0.000

Δa

3

=a

m

−a

3

=2.625−2.628=−0.003

Δa

4

=a

m

−a

4

=2.625−2.626=−0.001

Mean absolute error , Δa

mean

=

4

∣Δa

1

∣+∣Δa

2

∣+∣Δa

3

∣+∣Δa

4

∣

=

4

0.005+0.000+0.003+0.001

=0.002

Fractional error =±

a

m

Δa

mean

=±

2.625

0.002

=±0.0008

Percentage error = fractional error ×100=±0.0008×100=0.08%