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1. units,dimensions and measurement — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics1. units,dimensions and measurement1 Mark
MCQ
Calculate the mean $\%$ error in five observation

$80.0,80.5,81.0,81.5,82$

  • ✓
    $0.74$
  • B
    $1.74$
  • C
    $0.38$
  • D
    $1.38$
✓

Answer

Correct option: A.
$0.74$
a
The mean percentage error can be calculated as,

$M P E=\frac{1}{n} \sum\left(\frac{x-\bar{x}}{x}\right) \times 100 \%$ $...(1)$

The mean value of the errors is calculated as,

Mean of the errors $=\frac{80+80.5+81+81.5+82}{5}$

$=81$

$x$ $x-\bar{x}$ $\frac{x-\bar{x}}{x}$
$80.0$ $1.0$ $0.0125$
$80.5$ $0.5$ $0.0062$
$81.0$ $0$ $0$
$81.5$ $0.5$ $0.0061$
$82.0$ $1.0$ $0.122$
    Sum$=0.037$

Substituting the values in equation $(1),$ we get

$M P E=\frac{1}{5} \times(0.037) \times 100 \%$

$=0.74 \%$

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