Plankton interact with the environment according to their size and three-dimensional (3D) structure. To study them outdoors, these translucent specimens are imaged in situ. Light projects through a specimen in each image. The specimen has a random scale, drawn from the population's size distribution and random unknown pose. The specimen appears only once before drifting away. We achieve 3D tomography using such a random ensemble to statistically estimate an average volumetric distribution of the plankton type and specimen size. To counter errors due to non-rigid deformations, we weight the data, drawing from advanced models developed for cryo-electron microscopy. The weights convey the confidence in the quality of each datum. This confidence relies on a statistical error model. We demonstrate the approach on live plankton using an underwater field microscope.