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Question: Calculate the mean \(\% \) error in five observations: \(80.0\) , \(80.5\) , \(81.0\) , \(81.5\) ,...

Calculate the mean %\% error in five observations:
80.080.0 , 80.580.5 , 81.081.0 , 81.581.5 , 8282 .
A) 0.75%0.75\%
B) 1.74%1.74\%
C) 0.38%0.38\%
D) 1.38%1.38\%

Explanation

Solution

Firstly we have to figure out all the known quantities for the given question ( In this case the all the five given values of observations ). Then we have to give the correct formula to find mean value for any given observation and use it to find the mean for the given values of numbers. Then we can use it to get the error for each value. After then we can use it to get the mean error similarly and get the percentage for it.

Complete step by step answer:
Firstly we have to sort out what we have got :
Value of the first number : 80.080.0
Value of the second number : 80.580.5
Value of the third number : 81.081.0
Value of the fourth number : 81.581.5
Value of the fifth number : 8282
Step 1: Firstly we have to define the formula for the mean of any values :
total sum of the valuesnumber of total values\dfrac{{{\text{total sum of the values}}}}{{{\text{number of total values}}}}
Step 2: Now we just have to put the values in the given formula and obtain the mean error:

=  80.0+80.5+81.0+81.5+825 =4055 =81  = \;\dfrac{{80.0 + 80.5 + 81.0 + 81.5 + 82}}{5} \\\ = \dfrac{{405}}{5} \\\ = 81 \\\

Step 3: Now we have to use this value of meam=n to find the difference from mean in each value for the given quantity :
∣80−81∣=1 ∣80.5−81∣=0.5 ∣81−81∣=0 ∣81.5−81∣=0.5 ∣82−81∣=1  |80 - 81| = 1 \\\ |80.5 - 81| = 0.5 \\\ |81 - 81| = 0 \\\ |81.5 - 81| = 0.5 \\\ |82 - 81| = 1 \\\
Step 4: Now we can have the mean error similarly the way we obtained for the given values and then find the percentage by dividing by the mean :
Mean error =1+0.5+0+0.5+15=0.6 = \dfrac{{1 + 0.5 + 0 + 0.5 + 1}}{5} = 0.6
Therefore we just have use this value to find the % error :
=0.681×100 =0.74%  = \dfrac{{0.6}}{{81}} \times 100 \\\ = 0.74\% \\\
Hence the correct option would be A, 0.75%0.75\%

Note: There is no specific sign convention for the mean method. We can get the error by just subtracting, no matter the value is greater or less, all we need is difference with the mean. The slight difference of answer obtained and value given is acceptable as it is negligible when compared.