Comparing different sized samples, statistics help needed.

earl_grey

It has been a long time since I've done any statistics, so apologies in advance if I'm asking elementary questions.

I wanted to do some nice statistics for a charity event that was held. The data I have is:

Group A, 20 volunteers (total people in group 100 people.)
Group B, 15 volunteers (total size of group 50 people.)
Group C, 10 volunteers (total size of group 30 people.)
Group D, 5 volunteers (total size of group 20 people.)

I have shown a breakdown of how many people volunteered per group.
e.g. # of volunteers / total # of volunteers,
Group A: 20/50 = 40% of volunteers were from Group A
Group B: 15/50 = 30% of volunteers were from Group B
Group C: 10/50 = 20% of volunteers were from Group C
Group D: 5/50 = 10% of volunteers were from Group D

This shows that Group A has contributed the most amount of volunteers. However, this doesn't take into account the size of the groups. So, I calculated the number of volunteers relative to size of the group.

Volunteers (relative to size of the group)
Group A, 20/100 = 0.2 (20% of people in this group volunteered)
Group B, 15/50 = 0.3 (30% of people in this group volunteered)
Group C, 10/30 = 0.33 (33% of people in this group volunteered)
Group D, 5/20 = 0.25 (25% of people in this group volunteered)

From this view, Group C has contributed the most amount of volunteers (per # of people.)

How can I represent this data?
There has been a total of (20+15+10+5) 50 volunteers, from 200 people (group A+B+C+D). So only 25% of people volunteered for the event.

I want to show statistics around this 25% of people, relative to the amount of people per groups.

Can you recommend other analysis that I should perform?

Any help (or reference to the types of topics that I should study) would be appreciated.

Thank you

Stephen Tashi

The field of mathematical statistics can't tell you what you are trying to accomplish. Until you state some objectives, it isn't clear what kind of statistics should be used.

Perhaps you only want to "explore" or "get a feel" for the data. Then you should look into descriptive statistics.

Perhaps you want evidence for some theory. ( -for example, something about one group being more likely to volunteer than another.) This is the field of "hypothesis testing".

Perhaps you want to estimate a quantitative effect. For example, if the groups were determined by the size of their monetary donations or by their age, you might want a formula that predicts the probability of volunteering vs that quantity. This is the field of estimation, or statistical prediction.