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What measure of central tendency is best for nonnumerical data?
The mode.
Which measure of central tendency works best when you have an outlier?
The median, as long as you don't want to do any serious statistical testing.
What is the best measure of central tendency?
There is no universal best. The mode is sometimes mentioned as a measure of central tendency but it is not really one. For example, if studying rolls of a die, the mode has nothing whatsoever to do with central tendency. However, it is the only summary measure that makes sense when the observed variable is nominal or categoric. For example, if the data are about the colours of cars, the mean or median colour makes no sense. The mean and median have advantages over the other in different circumstances. The Central Limit Theorem and Normal approximation favour the mean but the unrestricted mean is vulnerable to outliers.
Which measure of central tendency best describes this situation the number of times students wake up for school?
If you want to ask questions about "this situation", then I suggest that you make sure that there is some information about the situation in the question.
Which type of graph is best for revealing measures of spread and central tendency of a data set?
box-and-whisker plot
