Types of Measurement & Reasons of Measurement Error

Types of Measurement

Direct Measurement such as measuring liquid density using the hydrometer in which we take a direct reading without calculation or using any law , Measuring volume using the graduated cylinder .

There is one measuring tool that is used , There is one measurement process , No mathematical  relation is applied and there is one measurement error .

Indirect Measurement such as Determining the liquid density via measuring mass by a balance and volume by a graduated cylinder , Then , dividing mass by volume , Measuring volume by multiplying length , width and height .

More than one measuring tool are used , More than one measurement process , There is a mathematical relation is applied to find the quantity and there is more than one measurement error ( cumulative error ) .

Types of measurement

Types of measurement

Error in Measurements

Man has been interested throughout history to improve measurement techniques and develop its instruments because of its obvious impact on the scientific and technological process , But , no measurement is accurate 100 % , There must be an error even if it is small .

Reasons of measurement error

There are several probable reasons for measurement error , from which :

Choosing improper tool : For example , using the beam balance instead of the sensitive balance in measuring the mass of a golden ring .

A defect in the measuring tool : Examples of defects may be the magnet inside is partially demagnetized because it is outdated , The pointer has a zero error when there is no electric current .

Wrong procedure due to unexperienced persons : Ignorance of using graduated devices like the multimeters , Looking at the device pointer or the scale at an oblique line instead of being perpendicular to the scale .

Environmental conditions such as : Temperature , Humidity , Air currents , Example : When using the sensitive balance , the air currents may produce an error , Because of this the sensitive balance is kept inside a glass box .

Estimating error of measurement

Estimating error in direct measurement

To find the error in direct measurement , There are two types of error which are Absolute error ( Δ X ) and Relative error ( r ) .

Absolute error ( Δ X )

It is the difference between the real ( actual ) value ( X0 ) and the measured value ( X ) .

Δ X = | X0 – X |

The sign |  | indicates that the result is always positive even if  the actual value is less than the measured value , It has a measuring unit which is the same measuring unit of the physical quantity .

Relative error ( r )

It is the ratio between the absolute error ( Δ X ) to the real value ( X0 )  .

r = Δ X / X0

The relative error is a better indication for the measurement accuracy than the absolute error , The measurement accuracy is considered higher as the relative error decreases .

It has no measuring unit because it is the ratio between two quantities having the same measuring units .

Note : Although the absolute error in measuring the classroom length is greater than that in measuring the pencil length , the relative error in measuring the classroom length is less than in measuring the pencil length .

This meant that Relative error is a better indication for measurement than the absolute error , As the relative error decreases , the measurement accuracy increases .

Estimating error in case of indirect measurement

The procedure of calculating error in case of indirect measurement depends on the mathematical operation applied :

Example : Measuring the volume of two amounts of a liquid , V = V1 + V2 , Finding the volume of a coin by subtracting the volume of water before dropping the coin into the measuring cylinder from that after dropping it , Vcoin = V2 – V1  .

The absolute error = The absolute error in first measurement + The absolute error in second measurement .

Δ X = Δ X1 + Δ X2 = | X01 – X1 | + | X02 – X2 |

The relative error ( r )

r =Δ X / X0

Example : Finding the area of a rectangle by measuring its length and its width then multiplying them , Finding the density of a liquid by measuring its mass and its volume then dividing them .

The relative error = The relative error in first measurement + The relative error in second measurement .

r = r1+ r2 = Δ X1 / X01 + Δ X2 / X02

The absolute error ( Δ X ) :

Δ X = r + X0

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