Question

The observations of measurement of length (in $\text{m}$) of a wooden stick are $1.22,1.23,1.23,1.24,$ and $1.25$ then the mean absolute error will be

• A. $0.01\text{m}$
• B. $0.1\text{m}$
• C. $0.008\text{m}$
• D. $0.08\text{m}$

Answer 1

The correct option is A $0.01\text{m}$

Arithmetic mean,
$a_{mean}=\frac{a_1+a_2+a_3+.....+a_n}{n}$
$\Rightarrow a_{mean}=\frac{1.22+1.23+1.23+1.24+1.25}{5}$
$\Rightarrow a_{mean}=1.234\text{m}$
On rounding off to correct decimal places, we get, $a_{mean}=1.23\text{m}$
Now, absolute error,
$|\Delta a_1|=|a_1-a_{mean}|=|1.22-1.23|=0.01\text{m}$
Similarly,
$|\Delta a_2|=0.00\text{m}$
$|\Delta a_3|=0.00\text{m}$
$|\Delta a_4|=0.01\text{m}$
$|\Delta a_5|=0.02\text{m}$
So, mean absolute error,
$\Delta a_{mean}=\frac{|\Delta a_1|+|\Delta a_2|+|\Delta a_3|+.....+|\Delta a_n|}{n}$
$\Rightarrow \Delta a_{mean}=\frac{0.01+0.00+0.00+0.01+0.02}{5}$
$\Rightarrow \Delta a_{mean}=0.008\text{m}$
On rounding off to correct decimal places, we get, $\Delta a_{mean}=0.01\text{m}$