My conclusion: while averages are nice, full data spreads are even better.

In addition to your averaging, try just doing a traditional scatter plot: time of day along the x axis, result values along the y axis, and a dot on the chart for every data point.

Once you've done that, things like the average for some time period or the outlines of the daily curve tend to become visually apparent, even to someone who isn't fluent in statistics.