Not sure about steam-and-leaf but a stem-and-leaf plot is used for numerical data.
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mean
No. A median makes no sense for categorical data. For example, if you have 10 red cars, 15 blue cars and 20 black cars, what is the median?
Categorical.
It means numerical data which can hold any value . For instance, human height is continuous. There is no set of allowable heights. It can be any number. In contrast, human sex (i.e male or female) is categorical data, because there are only two possible values.
Bar graph