Tis implies that the height of penguins are normally distributed.
So, either the mean or median could be the best measure of center.
Standard deviation is one of the measure of dispersion or spread of a dataset from the average value of the dataset. The standard deviation measures the absolute variability of the distribution of values.
The higher the spread or variability in the data set, the greater is the standard deviation value and thus greater will be the magnitude of the deviance of the value from their average.