How to find out the representive mark from a list?

[Guest]

My class has 30 students, their marks are shown below
100,97,96,93,88,85,84,77,76,71,
66,62,62,55,53,49,48,46,46,43,
43,43,43,43,35,33,31,31,31,13

I would like to determine the most representative mark for this class for
comparing with another class.

I think the functions - average, mode are not a very representative in this
case.
Does anyone have any suggestions on how to define the most representative
mark for this class?

Thank you in advance
Eric

 

[MartinW]

Hi Eric,

Perhaps a Stem and Leaf graph may help.
I'll try one here, don't know if the formatting
will survive the trip through cyberspace.

10| 0
9| 7 6 3
8| 8 5 4
7| 7 6 1
6| 6 2 2
5| 5 3
4| 9 8 6 6 3 3 3 3 3
3| 5 3 1 1 1
2|
1| 3

You can see at a glance that the main body of your students
are in the 30 to 40 range. For ways to automate stem and
leaf graphs do a google search there are many different
approaches.

HTH
Martin

 

[David Biddulph]

In what way do you consider that AVERAGE and MODE are "not a very
representative" in this case?

What do you want to do to make it more "representative"? If you don't want
to minimise the total difference, do you want a least squares fit, or do you
want to minimise
sigma[(x i-x rep)^n],
where you define your favourite value of n?

Another option is MEDIAN.