Question

Repeated observations in an experiment gave the values `1.29 , 1.33 , 1.34 , 1.35 , 1.32 , 1.36, 1.30, and 1.33`. Calculate the mean value, absolute eror , relative error, and percentage error.

Answer 1

Here, mean value of quantity measured ,
` v = ( 1.29 + 1.33 + 1.34 + 1.35 + 1.32 + 1.36 +1.30 +1.33)/( 8)`
`x = 1.3275 = 1.33` ( rounded off to two places of decimal).
Absolute errors in measurement are :
`Delta x_(1) = 1.33 - 1.29 = 0.04`, ` Delta x_(2) = 1.33 - 1.33 = 0.00`
`Delta x_(3) = 1.33 - 1.34 = -0.01`, `Delta x_(4) = 1.33 - 1.35 = -0.02`
`Delta x_(5) = 1.33 - 1.32 = + 0.01`, `Delta x_(6) = 1.33 - 1.36 = -0.03`
`Delta x_(7) = 1.33 - 1.30 = + 0.03 ` , `Delta x_(8) = 1.33 - 1.33 = 0.00`
Mean absolute error , ` bar (Delta x) = (sum _(i = 1)^( i = n)|( Delta x)_(i)|)/( n)`
`= ( 0.04 + 0.00 + 0.01 + 0.02 +0.01+ 0.03 + 0.03 + 0.00)/(8)`
`= (0.14)/(8) = 0.0175 = 0.02`
Relative error ` = +- (bar Delta x)/( x) = +-(0.02)/(1.33) = +- 0.015 = +- 0.02`
Percentage error `= +- 0.015 xx 100 = 1.5%`