Many modern applications of online changepoint detection require the ability\nto process high-frequency observations, sometimes with limited available\ncomputational resources. Online algorithms for detecting a change in mean often\ninvolve using a moving window, or specifying the expected size of change. Such\nchoices affect which changes the algorithms have most power to detect. We\nintroduce an algorithm, Functional Online CuSUM (FOCuS), which is equivalent to\nrunning these earlier methods simultaneously for all sizes of window, or all\npossible values for the size of change. Our theoretical results give tight\nbounds on the expected computational cost per iteration of FOCuS, with this\nbeing logarithmic in the number of observations. We show how FOCuS can be\napplied to a number of different change in mean scenarios, and demonstrate its\npractical utility through its state-of-the art performance at detecting\nanomalous behaviour in computer server data.\n