These data are the means and variance of spike counts in an analysis window beginning at motion onset of the visual stimulus, within the receptive field of MT neurons recorded in anesthetized or alert non-human primates. Dot motion was presented in a range of motion directions, with 0 degrees being the preferred direction of each cell. The tuning of the variability in the response and a model accounting for these state-dependent changes is in press at PLoS Computational Biology, along with more details on the data collection and analysis. A preprint is available at: https://arxiv.org/abs/1710.10548 These data consist of a MatLab data file with two saved data structures, ‘units’ and ‘autocorrelation’. ‘units’ is an 80-element structure, one entry for each recorded extracellular single unit (putative neuron) in the recording with the following fields: ‘state’ indicates whether the subject was anesthetized or alert during the recording ‘stimDir’ is the direction of motion, in degrees, of the moving dot stimulus ‘latency’ is the latency, in milliseconds, to the response onset ‘latAlign’ are the spike counts and variance in a 150ms window beginning at response onset ‘stimAligned’ are the spike counts and variance in a 250ms window beginning at motion onset ‘MI’ is the mutual information between motion directions between +/- 90 degrees and the cumulative spike counts at a range of time points since motion onset, given in MI_time_vec. The mutual information quantity is extrapolated to the infinite data size limit via quadratic extrapolation. 'MI_time_vec' is a vector of times (in milliseconds) since motion onset used in the information calculation ‘autocorrelation’ is a scalar structure containing the fields: 'alert' is the average autocorrelation (range +/- 1) of the spike counts (analyzed in a 2ms window and smoothed over 5 bins) in the alert units during presentation of the null (no dot motion) stimulus 'anesthetized' is the average autocorrelation (computed as for the alert units) of the anesthetized units during presentation of the null stimulus 'timePoints' are the time point shifts in milliseconds corresponding to the calculated autocorrelations in 'alert' and 'anesthetized'