# What is the errors of measurement in physics?

### 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 Am and the error in measurement be ΔA. Then the true value of the quantity can be written as
At = Am ± 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

1. Systematic errors
2. Random errors
3. Gross errors