Question

The length of a rod as measured in an experiment was found to be 2.48m, 2.49m, 2.50m, and 2.46m. Find the average length, absolute error, and percentage error. Express the result with error limit.

Answer 1

average length= (2.48 + 2.46 + 2.49 + 2.50 + 2.48)/5 =2.482.

absolute error = 2.48 - 2.482 = |0.002|

2.46 - 2.482 = |0.022|

2.49 - 2.482 = |0.008|

2.50 - 2.482 = |0.018|

2.48 - 2.482 = |0.002|

% error = relative error*100 = mean absolute error / mean error

= [ (0.002) + (0.022) + (0.008) + (0.018) + (0.002) ] / 2.482

= (0.042) / 2.482 = 0.0169 (approx. value)

now % error = 0.0169*100 = 1.69%

Answer 2

Average length = 2.48+2.46+2.49+2.50+2.48/5=2.48m

Absolute error in different measurements:

2.48-2.48=0.00m

2.48-2.46=0.02m

2.49-2.48=0.01m

2.50-2.48=0.02m

2.48-2.48=0.00m

The absolute error=0.00+0.02+0.01+0.02+0.00/5=0.01m

Correct length=2.48+-0.01m

Percentage error=0.01/2.48*100=0.40%