Question

The length of a rod measured in an experiment was found to be 2.48, 2.46 ,2.50 ,2.48, 2.49 find the average length absolute error in each observations and percentage error

Answer 1

The average length absolute error in each observations - 2.482.

The percentage error - 1.69%

Explanation :

Given :

The length of a rod measured in an experiment was found to be :

• 2.48
• 2.46
• 2.50
• 2.48
• 2.49

To Find :

The average length absolute error in each observations and percentage error.

Solution :

Divide the observations by 5 to find average length,

So,

The average length :

$\implies\sf \dfrac{2.48 + 2.46 + 2.49 + 2.50 + 2.48}{5}\\ \\\\\implies \bf 2.482.$

The absolute error :

$\implies \sf 2.48 - 2.482 = |0.002|\\ \\ \\\implies \sf 2.46 - 2.482 = |0.022|\\ \\ \\\implies \sf 2.49 - 2.482 = |0.008|\\ \\ \\\implies \sf 2.50 - 2.482 = |0.018|\\ \\ \\\implies \sf 2.48 - 2.482 = |0.002|$

We know that :

$\bigstar\;\boxed{\bf Error\;\% = \dfrac{\textbf{Mean absolute error}}{\textbf{Mean error}}}}}$

So,

$\implies \sf \dfrac{\bigg[(0.002) + (0.022) + (0.008) + (0.018) + (0.002)\bigg]}{2.482}\\ \\ \\\implies \sf \dfrac{(0.042)}{2.482} = 0.0169\qquad[\bf Approximately\;Value]$

Now,

$\bf Error\;\% = 0.0169\times 100\\ \\ \\ \implies \bf 1.69%$