Time periods of oscillation of the same simple pendulum measured using four different measuring clocks were recorded as $$4.62 \text{ s}, 4.632 \text{ s}, 4.6 \text{ s}$$ and $$4.64 \text{ s}$$. The arithmetic mean of these readings in correct significant figure is :

Given readings: $$4.62$$ s, $$4.632$$ s, $$4.6$$ s, $$4.64$$ s.

Calculate arithmetic mean.

$$ \text{Mean} = \frac{4.62 + 4.632 + 4.6 + 4.64}{4} = \frac{18.492}{4} = 4.623 \text{ s} $$

Apply significant figures rule.

When adding/averaging numbers, the result should have the same number of decimal places as the measurement with the fewest decimal places.

The readings have: 2, 3, 1, and 2 decimal places respectively. The least is 1 decimal place (from 4.6 s).

So the mean should be rounded to 1 decimal place: $$4.6$$ s.

The correct answer is Option (3): 4.6 s.