I am trying to better understand what it means to be a "sufficient statistic".
"In statistics, a statistic is sufficient with respect to a statistical model and its associated unknown parameter if "no other statistic that can be calculated from the same sample provides any additional information as to the value of the parameter" . "
Based on this definition, here is how I conceptualize it:
In a unimodal distribution, the "mean" provides more information about the unimodal distribution - relative to the amount of information provided by the "mean" in a biomodal distribution. Thus in this case, the "mean" is more of a sufficient statistic in a unimodal distribution compared to a biomodal distribution.
For example, in a distribution of basketball player heights that is unimodal - the "mean" would well describe the average height of a basketball player. But if you were to have a distribution of heights corresponding to penguins, ostriches and giraffes - and this distribution was not unimodal, it is more likely that the "mean" would not sufficiently characterize the height of the average measurement in this sample.
Is this interpretation correct?