Analyzing a cumulative frequency graph - IB Math Exploration

Analyzing a cumulative frequency graph - IB Math Exploration

I've been searching for a preposterously long time for an IB Math Higher
Level Exploration topic. We are to find some sort of topic and analyze in
depth, showing serious mathematical ingenuity, creativity and interest. My
class is generally having problems finding topics as well. A lot of the
things we have found would simply be rehashes of what is available on the
web.
But, I think I've found a topic. I am going to capture the cumulative
frequency graph of students entering a certain Hall in my school everyday.
Every single student in the school is supposed to enter a Hall from 5:50
AM - 6:40 AM. I wish to analyze the graph. I've thought of a few things,
but I'm not exactly sure what else I should do in my analysis. I am going
to:
-Analyze the differences between the several days recorded and determine
error bars of some sort -Create a function that matches this general
curve, so it can be differentiated and analyzed -Apply cumulative
distribution functions so one can estimate how many people will be in the
Hall at a certain time -Compare the graph to other types of cumulative
distribution functions. -Attempt to determine how the times should be
changed so that x% of people will be in the D-Hall before 6:30 AM.
Is there anything else I can do? Thank you very much, community.