Question

The diameter of a wire as measured by a screw gauge was found to be 1.328, 1.330, 1.325, 1.326, 1.334 and 1.336 cm. Calculate
(i) Mean value of diameter
(ii) Absolute error in each measurement,
(iii) Mean absolute error,
(iv) Fractional error and
(v) Percentage error

Answer 1

Answer:

The mean diameter of the given measurements is 1.329, the mean absolute error is 0.0035, the Fractional error is 7/2658 and the percentage error is 0.26336%.

Explanation:

1) Mean = Sum of all entries / Total entries

Sum of the entries = 1.328 + 1.330 + 1.325 + 1.326 + 1.334 + 1.336 = 7.979

The total entries = 6

Mean = 7.979/6 = 1.329

2) Absolute error = measured value - mean value.

(1.328 - 1.329) = 0.001, (1.330 - 1.329) = 0.001

(1.325 - 1.329) = 0.004, (1.326 - 1.329) = 0.003

(1.334 - 1.329) = 0.005, (1.336 - 1.329) = 0.007

3) Average absolute error = total absolute error / total entries

= (0.001 + 0.001 + 0.004 + 0.003 + 0.005 + 0.007) / 6 = 0.0035

4) Fractional error = Average absolute error/ Average length

= 0.0035/1.329

35/13290 = 7/2658

5) Percentage error is given as :

7/2658 × 100% = 0.26336 %.

Answer 2

Answer:

Explanation:

1) 1.328+1.330+1.325+1.326+1.334+1.336/6

= 1.329

2)  Absolute error in each case = 1.329-1.328 = 0.001

1.330-1.329=0.001

1.329-1.325=0.004

1.329-1.326=0.003

1.334-1.329=0.005

1.336-1.329=0.007

3)Meanabsoluteerror=0.001+0.001+0.004+0.003+0.005+0.007/6 =0.0035

4) Fractional error= 0.0035/1.329= 0.0026

5) Percentage error = 0.0026*100%= 0.26336%