Units and Measurements — Physics STD 11 Science — Question
Maharashtra BoardEnglish MediumSTD 11 SciencePhysicsUnits and Measurements4 Marks
Question
Define absolute error, mean absolute error, relative error and percentage error.
✓
Answer
Absolute error:
a. For a given set of measurements of a quantity, the magnitude of the difference between mean value (Most probable value) and each individual value is called absolute error (∆a) in the measurement of that quantity.
b. absolute error = |mean value – measured value|
$\triangle a_1 = |a_{mean} – a_1|$
Similarly, $\triangle a_2 = |a_{mean} – a_2|$
. . . ..
. . . .
. . . .
$\triangle a_n = |a_{mean} – a_n|$Mean absolute error:
For a given set of measurements of a same quantity the arithmetic mean of all the absolute errors is called mean absolute error in the measurement of that physical quantity.
$\Delta a _{\text {mean }}=\frac{\Delta a _1+\Delta a _2+\ldots \ldots+\Delta a _n}{ n }=\frac{1}{ n } \sum_{ i =1}^n \Delta a _{ i }$
Relative error:
The ratio of the mean absolute error in the measurement of a physical quantity to its arithmetic mean value is called relative error.
Relative error $=\frac{\Delta_{a_{\text {mean }}}}{ a _{\text {mean }}}$
Percentage error:
The relative error represented by percentage (i.e., multiplied by 100) is called the percentage error.
Percentage error $=\frac{\Delta a _{\text {mean }}}{ a _{\text {mean }}} \times 100 \%$
[Note: Considering conceptual conventions question is modified to define percentage error and not mean percentage error.]
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