Answer:
[tex]\% Error = 2.6\%[/tex]
Explanation:
Given
[tex]x: 1.54, 1.53, 1.44, 1.54, 1.56, 1.45[/tex]
Required
Determine the percentage error
First, we calculate the mean
[tex]\bar x = \frac{\sum x}{n}[/tex]
This gives:
[tex]\bar x = \frac{1.54+ 1.53+ 1.44+ 1.54+ 1.56+ 1.45}{6}[/tex]
[tex]\bar x = \frac{9.06}{6}[/tex]
[tex]\bar x = 1.51[/tex]
Next, calculate the mean absolute error (E)
[tex]|E| = \sqrt{\frac{1}{6}\sum(x - \bar x)^2}[/tex]
This gives:
[tex]|E| = \sqrt{\frac{1}{6}*[(1.54 - 1.51)^2 +(1.53- 1.51)^2 +.... +(1.45- 1.51)^2]}[/tex]
[tex]|E| = \sqrt{\frac{1}{6}*0.0132}[/tex]
[tex]|E| = \sqrt{0.0022}[/tex]
[tex]|E| = 0.04[/tex]
Next, calculate the relative error (R)
[tex]R = \frac{|E|}{\bar x}[/tex]
[tex]R = \frac{0.04}{1.51}[/tex]
[tex]R = 0.026[/tex]
Lastly, the percentage error is calculated as:
[tex]\% Error = R * 100\%[/tex]
[tex]\% Error = 0.026 * 100\%[/tex]
[tex]\% Error = 2.6\%[/tex]
