Explanation

The average length of the rod is given by the arithmetic mean of all measurements.

$$ \text{Average length} = \frac{20.00 + 19.75 + 17.01 + 18.25}{4} $$

$$ = \frac{75.01}{4} = 18.75\ \text{cm} $$

The absolute errors for each measurement are calculated with respect to the average value.

$$ |20.00 - 18.75| = 1.25 $$

$$ |19.75 - 18.75| = 1.00 $$

$$ |17.01 - 18.75| = 1.74 $$

$$ |18.25 - 18.75| = 0.50 $$

Mean absolute error is

$$ \Delta L = \frac{1.25 + 1.00 + 1.74 + 0.50}{4} $$

$$ \Delta L = \frac{4.49}{4} \approx 1.12\ \text{cm} $$

Relative error is defined as

$$ \text{Relative error} = \frac{\Delta L}{\text{Average length}} $$

$$ = \frac{1.12}{18.75} \approx 0.06 $$

Hence, the relative error in the measurement of the average length of the rod is

$$ \boxed{0.06} $$

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