Question

The concentration of Nickel in Nigerian coin was determined with visible spectrophotometer, and the following results (%) were obtained: 3.65, 4.11, 3.59, 7.51, 3.95,3.87, 4.06, 1.48, 3.60, 3.76 and 3.99. if the true concentration (%) of nickel in coin as determined by atomic absorption and inductively coupled plasma atomic emissionspectrophotometer was 3.92.Use the above data to determine:(i)         Absolute error(ii)        Percentage relative error(iii)         Average error

Answer 1

i) In order to determine the absolute error, take into account that you have a set of measurement, that is, you calculate the mean absolute error.

Use the following formula:

`\text{mae}=(\sum ^n_(i\mathop=1)\lvert x_i-x\rvert)/(n)`

where xi are the different measures and x is the expected value. In this case

x = 3.92.

Replace the given data into the previous expression and simplify:

`\begin{gathered} \text{mae}=(1)/(11)\lbrack\lvert3.65-3.92\rvert+\lvert4.11-3.92\rvert+\lvert3.59-3.92\rvert+\lvert7.51-3.92\rvert+ \\ \lvert3.95-3.92\rvert+\lvert3.87-3.92\rvert+\lvert4.06-3.92\rvert+\lvert1.48-3.92\rvert+\lvert3.60-3.92\rvert+ \\ \lvert3.76-3.92\rvert+\lvert3.99-3.92\rvert\rbrack \end{gathered}`

After simplification you obtain:

`\text{mae}=(7.59)/(11)=0.69`

Hence, the mean absolute error is 0.96