Quoted annually, divided by the period count. That is the convention paired with an arithmetic mean.
Hypothetical illustration, computed only from the series entered. Ex-post: it measures a past record and projects nothing.
The standard deviation uses the n minus 1 sample denominator. Annualizing by the square root of the period count assumes the period returns are independent and identically distributed; serial correlation, a short sample, or fat tails break that assumption in either direction. The ratio treats upside and downside swings alike.
The Sharpe ratio divides the return a portfolio earned above the risk-free rate by how much that return bounced around. Two portfolios can finish the year in the same place; the one that got there with smaller swings has the higher ratio. It measures a record that already happened.
Twelve monthly returns averaging 0.75% a month, against a 4.5% annual risk-free rate, leave about 0.375% a month in excess return. If those returns have a standard deviation of 2.4%, the monthly ratio is about 0.16, and multiplying by the square root of 12 annualizes it to about 0.54.
Annualizing with the wrong periodicity. The factor is the square root of the number of periods in a year, so labelling a monthly series as daily multiplies the answer by roughly 4.6.