If you talk about the definition of percentage error, it defines the difference between the actual value of an activity and a value attained through practical observation. If you know that a ball of 100 gms, when thrown from a building of ten floors, travels at a speed of \(\mathbf{80\, \mathrm{m/s}}\) this speed would be the true value. When you perform a practical, the ball travels at a speed of \(\mathbf{60\, \mathrm{m/s}}\) so this would be the observed value.
The formula for percentage error is given as
\( PE = \left( \frac{{TV - OV}}{{TV}} \right) \times 100 \)
Where the terms have the following interpretations
\( \boldsymbol{PE} \) = Percentage Error
\( \boldsymbol{TV} \) = Total Value
\( \boldsymbol{OV} \) = Observed Value
Let us go through an example to check how Percentage Error is determined.
Consider that you have to carry out an experiment by throwing a stone of weight 250 grams against the air. Apparently, you know that the speed at which the stone would travel is \(\mathbf{30\, \mathrm{m/s}}\). However, an observation has to be carried out to determine the percentage error. On throwing the stone, it is observed that the stone travels at a speed of \(\mathbf{20\, \mathrm{m/s}}\) . In accordance with this scenario, we have the following values.
To calculate percentage error, let us use the formula given below.
\( PE = \left( \frac{{TV - OV}}{{TV}} \right) \times 100 \)
Inserting the values
\( PE = \left( \frac{{30 - 20}}{{30}} \right) \times 100 \)
Percentage Error = 33.33 %
In simple terms, percentage error is also called relative error. It is the contrast between a true value and an observed value. True value is the one considered without performing any observation. On the other hand, the observed value is one that is determined after a practical observation.
If you have an assumed value that it takes 30 minutes to walk one kilometer, it is the true value. Similarly, if you walk for 1km and figure out that a time span of 25 minutes is needed, it will be the observed value. The value of relative error will be calculated by dividing the difference between true value and observed value by true value. After that, the result will be multiplied by 100.
The standard of error is determined for a complete sample instead of one individual value. The value of standard of error describes how accurately a fixed sample provides representation for a complete population.
In simple terms, margin of error is given as
\( \text{Margin of Error} = \text{Standard of Error} \times \text{Z Score} \)
Margin of error is connected to the calculation of confidence interval.
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