Question

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

Answer 1

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

Answer 2

"Given:

Velocities = 342, 338, 318, 322

Total number of readings = 4

Sum of all the readings = (342 + 338 + 318 + 322) = 1320

Mean of the readings $=\frac { sum }{ total\quad number\quad of\quad readings } =\frac { 1320 }{ 4 } =330$

Deviation of the first reading comparing to the mean = |342 – 330 | = 12

Deviation of the second reading comparing to the mean = |338 – 330 | = 8

Deviation of the third reading comparing to the mean = |330 – 318 | = 12

Deviation of the fourth reading comparing to the mean = |330 – 322 | = 8

Mean of the deviation $=\frac { (12+8+12+8) }{ 4 }$

Mean absolute error $=\frac { 40 }{ 4 } =10$"