In an experiment to measure focal length of a concave mirror, the values of focal length in successive observations are $17.3 c m$ , $17.8 c m$ , $18.3 c m$ , $18.2 c m$ , $17.9 c m$ and $18.0 c m$ . Calculate mean absolute error and percentage error. Express the result in a proper way.

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Solution

Mean value of the focal lenght

$f_{m e a n} = \frac{17.3 + 17.8 + 18.3 + 18.2 + 17.9 + 18}{6}$

= 17.9

Mean absolute error is

$Δ f_{m e a n}$ = $\frac{| 17.9 - 17.3 | + | 17.9 - 17.8 | + 17.9 - 18.3 | + | 17.9 - 18.2 | + | 17.9 - 17.9 | + | 17.9 - 18 |}{6}$

= $\frac{0.6 + 0.2 + 0.4 + 0.3 + 0 + 0.1}{6}$

= 0.27

Relative error is = $\frac{Δ f_{m e a n}}{f_{m e a n}}$

= $\frac{0.27}{17.9}$

= 0.02

percentage error = Relative error $\times 1000$

= 0.02 $\times 100$

= 2

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In an experiment to measure focal length of a concave mirror, the values of focal length in successive observations are 17.3 cm, 17.8 cm, 18.3 cm, 18.2 cm, 17.9 cm and 18.0 cm. Calculate mean absolute error and percentage error. Express the result in a proper way.

In an experiment to measure focal length of a concave mirror, the values of focal length in successive observations are $17.3 c m$ , $17.8 c m$ , $18.3 c m$ , $18.2 c m$ , $17.9 c m$ and $18.0 c m$ . Calculate mean absolute error and percentage error. Express the result in a proper way.