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In an experiment refractive index of glass was observed to be 1.45,1.56,1.54,1.44,1.54and1.53. Calculate mean value of refractive index,mean absolute error, fractional error and percentage error.
Express the result in terms of absolute error and percentage error.

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scme1702
The mean may be calculated by summing the values of the refractive index and dividing the sum by the number of experiments. This is:
Mean = (1.45 + 1.56 + 1.54 + 1.44 + 1.54 + 1.53)/6
Mean = 1.51

The mean absolute error is the sum of the absolute values of errors divided by the number of trials:
MAE = (|1.45-1.51|+|1.56-1.51|+|1.54-1.51|+|1.44-1.51|+|1.54-1.51|+|1.53-1.51|)/6
MAE = 0.043

The fractional error is the MAE divided by the actual value:
Fractional error = 0.043 / 1.51
Fractional error = 43/1510

The percentage error is the fractional error multiplied by 100:
Percentage error = 2.85%
okpalawalter8

The mean value of refractive index,mean absolute error, fractional error and percentage error is mathematically given as

  • x= 1.51
  • MAE = 0.043
  • F.E = 0.043 / 1.51
  • P.E=2.85%

What are the mean value of refractive index, mean absolute error, fractional error, and percentage error?

Question Parameter(s):

Observed to be 1.45,1.56,1.54,1.44,1.54and1.53

Generally, the equation for the mean  is mathematically given as

x=tm/n

Therefore

x= (1.45 + 1.56 + 1.54 + 1.44 + 1.54 + 1.53)/6

x= 1.51

Where he mean absolute error is

[tex]MAE =\frac{ (|1.45-1.51|+|1.56-1.51|+|1.54-1.51|+|1.44-1.51|+|1.54-1.51|+|1.53-1.51|)}{6}[/tex]

MAE = 0.043

In conclusion, The fractional error

F.E = 0.043 / 1.51

hence, percentage error is

P.E=F.E*100

P.E=0.043 / 1.51*100

P.E=2.85%

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