A traversable measuring device (15) for determining a cross direction profile of a property of a moving lignocellulose-containing fiber web (2). The measuring device has a property measuring sensor (23) for determining a measurement result representing the property of the web at multiple cross directional measurement positions (P1, P2, P3, P4), a position measuring sensor (24) for determining the cross directional measurement position of the property measuring sensor associating to the respective measurement result, and an analysis device (25) for receiving the measurement results and the respective cross directional measurement positions (P1, P2, P3, P4) and for allocating the measurement results with the respective cross directional measurement positions for forming the cross direction profile of the web property (2). The measuring device has a mounting bracket (16) that is detachably fixable with quick clamping for fastening the measuring device at a measurement site in a fiber web machine (1).