Four persons measure the length of a rod as 20.00 cm, 19.75 cm, 17.01 cm and 18.25cm. The relative error in the measurement of average length of the rod is :

We need to find the relative error in the measurement of the average length of a rod measured by four persons as 20.00 cm, 19.75 cm, 17.01 cm, and 18.25 cm.

Calculate the average (mean) length:

$$\bar{x} = \frac{20.00 + 19.75 + 17.01 + 18.25}{4} = \frac{75.01}{4} = 18.7525 \, \text{cm}$$

Calculate the absolute deviations from the mean:

$$|20.00 - 18.7525| = 1.2475$$
$$|19.75 - 18.7525| = 0.9975$$
$$|17.01 - 18.7525| = 1.7425$$
$$|18.25 - 18.7525| = 0.5025$$

Calculate the mean absolute deviation (mean error):

$$\Delta\bar{x} = \frac{1.2475 + 0.9975 + 1.7425 + 0.5025}{4} = \frac{4.49}{4} = 1.1225 \, \text{cm}$$

Calculate the relative error:

$$\text{Relative error} = \frac{\Delta\bar{x}}{\bar{x}} = \frac{1.1225}{18.7525} = 0.0599 \approx 0.06$$

The correct answer is Option (4): 0.06.