Question

11. The five observations of length of a rod are 3.54 m, 3.49 m, 3.52 m, 3.51 m, and 3.50 m respectively.
Find the mean absolute error and relative percentage error in the measurement.
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Answer 1

Answer: Mean absoulte error = 0.0144m

              relative percentage error = 0.41 %

Explanation:

Average length= 3.54m+3.49m+3.52m+3.51m+3.50m         17.56m

                            -----------------------------------------------------  = ------------ =   3.512m

                                                         5                                        5

                 Absolute errors in different measurements are ,  

Δl1= 3.512-3.54= -0.028

Δl2= 3.512-3.49=0.022

Δl3=3.512-3.52=-0.008

Δl4=3.512-3.51=0.002

Δl5= 3.512-3.50= 0.012            

Mean absoulte error = -0.028+0.022-0.008+0.002+0.012            

                                        ------------------------------------------------- =  0.0144m

                                                                  5

correct length = (3.512  + or - 0.0144 ) m

percentage error = 0.0144                                  

                                -------------x 100 = 0.41 %

                                   3.512