Rev. Notes > AS > Measuring techniques Previous Topic Measuring techniques Next Topic Topics
 Measurements Errors Random error Systematic error Uncertainty Total uncertainity in addition / subtraction Total uncertainty in multiplication and division Total uncertainty in power factor Total uncertainty in the average value of many measurements Total uncertainty in the timing experiment Total uncertainty in the timing experiment Example 1 - Calculation of uncertainty Least count Spring Balance Digital Balance Protractor Micrometer Vernier calliper Digital Ammeter Cathode Ray Osciloscope

## Total uncertainty in the average value of many measurements

1. Find the average value of measured values.
2. Find deviation of each measured value from the average value.
3. The mean deviation is the uncertainty in the average value.
4. For example, the six reading of the micrometer screw gauge to measure the diameter of a wire in mm are

1.20,1.22,1.23,1.19,1.22,1.21.
Then          Average =  (1.20 + 1.22 + 1.23 + 1.19 + 1.22 + 1.21) / 6

Then         Average =  1.21 mm

The deviation of the readings , which are thedifference without regards to the sign, between each readings and average value are

0.01, 0.01, 0.02, 0.02, 0.01, 0

Mean deviations = (0.01 + 0.01 + 0.02 + 0.02 + 0.01 + 0) / 6

Mean deviation = 0.01 mm

Thus, likely uncertainty in the mean diameter 1.21 mm is 0.01 mm recorded as 1.21 ± 00.1 mm.

 Yunzila Said : but we have calculated the value with the given radius then what is the need of division by 2......??? 07/12/17 12:21 PM

 Yunzila Said : why in the ans is 0.6.......??? bcz after calculation we get 1.2.....!!! 07/12/17 12:17 PM

 unknown Said : ^to calculate the radius, diameter needs to be divided by 2. thus, 1.22/2 = 0.61 02/01/15 12:33 AM

 Bilal Said : where did 0.6 come from in result 09/09/14 02:51 PM