Q:

For which data representation is the median the better measure of center

Accepted Solution

A:
we know that
The Median is the "middle" of a sorted list of numbers.
To find the Median, place the numbers in value order and find the middle

case a) the data is 
3,8,4,8,3
place the numbers in value order-----> 3,3,4,8,8

the middle is 4
so
the median is 4


case b) the data is 
2,2,3,5,5
place the numbers in value order-----> 2,2,3,5,5  

the middle is 3
so
the median is 3

case c) the data is 
6,2,6,2,6
place the numbers in value order-----> 2,2,6,6,6

the middle is 6
so
the median is 6

case d) the data is 
1,3,4,3,1
place the numbers in value order----->1,1,3,3,4

the middle is 3
so
the median is 3


we know that
The Mean is most often chosen when the data is continuous and symmetrical (normal). ------> case a) case c) and case d) If the data has outliers or is skewed, then the mean would paint a skewed view of centrality

The Median is especially useful with skewed distributions as it draws the line right in the middle of your data set------> case b)

therefore

the answer is
case b)