1) when to use the median to describe the measure of center of a data set, 2) what measures of spread can we find when using box-plots, 3) what measure of spread is most appropriate to describe symmetrical data sets, 4) how does an outlier affect the mean of data set and give an example,

1.  You should use the median to describe the measure of center of a data set when an outlier is present in a data set.  Having an outlier will skew the mean of the data.  This means it will adjust the average to be smaller or greater than what the actual numbers are showing.  The median should be used as the measure of center in these circumstances.

2) Using a box plot, you can find the range and interquartile range.  The range is the distance from the smallest number to the largest.  The interquartile range is the distance from the first quartile to the third quartile.  All these values are found on a box plot.

 3)The best measure of spread to describe symmetrical data sets is the mean absolute deviation. This tells us how far on average the numbers are spread out from the mean.
 
4) See the answer given in #1 for the explanation.  An example would be a student who scores 8, 9, 10, 9, 10, 2 on 6 quizzes.  The mean would be an average of 8, which is not a good number to represent the score this student normally gets.  The median of 9 is a better number to show how this student normally performs.