Layer (L)2 is a major output of primary sensory cortex that exhibits very sparse spiking, but the structure of sensory representation in L2 is not well understood. We combined two-photon calcium imaging with deflection of many whiskers to map whisker receptive fields, characterize sparse coding, and quantitatively define the point representation in L2 of mouse somatosensory cortex. Neurons within a column-sized imaging field showed surprisingly heterogeneous, salt-and-pepper tuning to many different whiskers. Single whisker deflection elicited low-probability spikes in highly distributed, shifting neural ensembles spanning multiple cortical columns. Whisker-evoked response probability correlated strongly with spontaneous firing rate, but weakly with tuning properties, indicating a spectrum of inherent responsiveness across pyramidal cells. L2 neurons projecting to motor and secondary somatosensory cortex differed in whisker tuning and responsiveness, and carried different amounts of information about columnar whisker deflection. From these data, we derive a quantitative, fine-scale picture of the distributed point representation in L2.