Errors In Measurement

In the experiment we may get some other value than that of the true value due to faulty equipment, carelessness or random causes. This will cause error in measurement.

There are 3 ways to express an error

(1) Absolute Error: It is the positive value of difference between the true value and measured value of the quantity. Since we don’t know the correct value of quantity the best possible value can be given by mean value of all the measured value.

Arithmetic mean v, Am =

∴ The absolute error in the measurement can be given as.

where A _m : Mean value of the measurements.

where A ₁ , A ₂ : Measured value of quantity.

Taking the arithmetic mean of all the absolute errors we get the mean absolute error  ΔA _m .

So the true value of A will be such that

(2) Relative Error: It is defined as the ratio of the mean absolute error to the mean value of the quantity being measured

Relative error  = ΔA _{m/A m}

(3) Percentage Error: The relative error can be expressed in percentage error as

% error = Relative error  x 100

Illustration11. In measurement of the period of oscillation of a Helical spring, the readings comes out to be 2.15 sec, 2.25 sec, 2.36 sec, 2.45 sec and 2.54 sec, calculate the absolute errors, relative error or percentage error.

Solution: The mean period of oscillation of the Helical spring is

= 2.35 sec

The absolute error in the measurements are

2.15 − 2.35 = − 0.20 sec

2.25 − 2.35 = − 0.10 sec

2.36 − 2.35 = 0.01 sec

2.45 − 2.35 = 0.10 sec

2.54 − 2.35 = 0.19 sec