# Sample size needed to create bell curve

#### Connie

Hello again,
My boss has looked at my assessment data for my class of thirty children and is querying the accuracy of my data, because my data, when she plots it on a graph, doesn't form a bell curve, unlike the data submitted by my colleagues.
I'd like to argue the point that such a distribution may not necessarily arise with such a small sample, but my colleagues seem to manage to produce the desired curve.
Any suggestions?

#### Shakarri

Thirty students isn't a particularly small sample but what might be the problem is that your boss has been reviewing data for 10 teachers for 5 years, that's 50 times she has "tested" a teacher's data. The chance that an individual teacher's data looks unlike a bell curve might be small but the chance of finding one odd set of data after looking at 50 teachers' data could be very high.

If you wanted to formally test that your students' grades don't follow a bell curve you can use this online calculator for a statistical test.

The problem with this is that your students' grades never really follow a true bell curve, a true bell curve has possible values up to infinity but your students wont get over 100%. With only 30 students I doubt that none getting grades above 100% would be a problem; what could be a bigger issue is if you have grades A,B,C,...F instead of the percentage for each student.
To avoid this issue it's a good idea to compare the result of that online calculator with results from other classes/previous years which did have an acceptable bell shaped curve.

I hope this helps