Box plot is used to to describe the data through quartiles. It is a representation of the distribution of data based on five category of the observations or numbers in a set: minimum, first quartile, second quartile or median, third quartile and maximum.
Mean is commonly used measure for the center. However, it is affected by the extreme values, in other word by outliers. For that reason, it is recommended to use median, which is the value in the center of the data.
IQR (Interquartile Range) is more handy than standard deviation because it is not affected by outliers and it shows whether the data is skewed or not.