### What is the errors of measurement in physics?

Errors of measurement = True value of a quantity – Measured value of a quantity

Suppose, the measured value of quantity be A_{m} and the error in measurement be ΔA. Then the true value of the quantity can be written as

A_{t} = A_{m} ± ΔA

### Absolute error, Relative error and Percentage error

#### Absolute error

Suppose a physical quantity be measured n times and the measured values be \( a_1, a_2, a_3 — a_n \). The arithmetic mean of these values is given by,

$$ a_m = \frac{a_1 + a_2 + a_3 + … + a_n }{n}$$

The absolute errors in the individual measurement values are

$$ \Delta a_1 = a_m – a_1 $$

$$ \Delta a_2 = a_m – a_2 $$

$$ \Delta a_3 = a_m – a_3 $$

………….

$$ \Delta a_n = a_m – a_n $$

#### Mean absolute error

Mean absolute error \( \Delta a_m\) of a physical quantity is given by,

$$ \Delta a_m = \frac {|\Delta a_1| + |\Delta a_2| + |\Delta a_3| +…+ |\Delta a_n|}{n} $$

#### Relative error

Relative error \( R_e\) is given by,

$$ \ R_e = \frac{\Delta a_m}{a_m}$$

#### Percentage error

Percentage error \( p_e\) is given by,

$$ P_e = \frac{\Delta a_m}{a_m} \times 100 \% $$

### Types of errors

- Systematic errors
- Random errors
- Gross errors