Question

In an experiment measurements of velocity of a object are 342,338,318,322.The mean absolute error in the measurements is?

Answer 1

The measurements of velocity of a object are 342,338,318,322.

Mean of the measurements of velocity of a object are:

$Mean=\frac{Sum of observations}{Total number of observations}$

$\overline{x}=\frac{342+338+318+322}{4}=\frac{1320}{4}=330$

Now, $|{\Delta}x_{1}|=\overline{x}-x_{1}=|330-342|=12$

$|{\Delta}x_{2}|=\overline{x}-x_{2}=|330-338|=8$

$|{\Delta}x_{3}|=\overline{x}-x_{3}=|330-318|=12$ and

$|{\Delta}x_{4}|=\overline{x}-x_{4}=|330-322|=8$

Thus, $\overline{\Delta x}=\frac{{\Delta}x_{1}+{\Delta}x_{2}+{\Delta}x_{3}+{\Delta}x_{4}}{4}=\frac{12+8+12+8}{4}=10$.

therefore, The mean absolute error in the measurements is 10.

Answer 2

measurements of velocity of an object are 342, 338, 318 , 322.

first of all, find mean !

mean = sum of observations/total number of observations

= (342 + 338 + 318 + 322)/4 = 330.

so, $\overline{x}=330$

so, $|\Delta{x_1}|=\overline{x}-x_1=|330-342|=12$

$|\Delta{x_2}|=\overline{x}-x_2=|330-338|=8$

$|\Delta{x_1}|=\overline{x}-x_1=|330-318|=12$

$|\Delta{x_1}|=\overline{x}-x_1=|330-322|=8$

so,$\overline{\Delta{x}}=\frac{12+8+12+8}{4}=10$