IDENTIFY the CIRCUMSTANCES in which the median ratherthan the mean is the preferred measure of central tendency.

define median and mean, so we know why one is better than the other for some uses.

mean is the average amount, you total all the values, and divide by the number of values.
median is the value that is middle value, of an odd number of total values, or
median is the mean or average of the two middle values of an even number of values.

so if you have a data set of values that are not uniform, they one over the other would be more useful.

example
if you have a data set of 1,1,1,1.
then the mean and median are the same. And so not advantage is for one over the other.
if you data set is 1,1,1. similarly no advantage because same result.

but if your data set is 10,80,90.
you mean is (10+80+90)/3)= 180/3 =60.
while your median is 80.
so which do you think is more useful for that data set?

I prefer bigger exaggerations though :)

Say you have a large population, and every body gets around $ 250 every month, with the population size being 1000. Then, you have the King, getting $ 1,000,000 a month.

Now, say you want to go live in that country. But first, you want to estimate your monthly revenue. Would you take the mean or the median?

Median = $ 250
Mean = [(250*1000) + 1000000]/(1000+1) = $ 1248

As you can see, if you take the mean, you get an exaggeration and you'll be deceived when you get there. The median here, is therefore a better estimate.



So, can you see/guess why the median is better here and not the mean?