For example, I have a distribution with mean = 55.46; med = 54.5; mode = 45. The Shapiro-Wilk is non significant, the data are unimodal, and there is no significant skew or kurtosis.
At a glance, the mode looks different from the mean and median. Does the non significance of the Shapiro-Wilk etc. mean that they are the same? If so, why bother discussing equivalence of the mean, median and mode, since it's not telling us any new information. If not, how to you work out the cutoffs for these numbers? How close is close enough?