"Frequency distribution of numerous variances"

I am working on a homework assignment from a very vague, poor teacher.

I flipped 20 coins, measured the amount of heads and so forth, and repeated this 100 times.

One of the questions involves breaking the 100 measurements of "heads" into 25 groups, where group one is the first 4 measurements, group two is the next 4, and so on. The mean and standard deviation of each group was then found.

I am now asked to "calculate the frequency distribution of the variances of the groups", which I do not understand how to do. I believe they follow a chi-squared distribution, and upon asking the professor I received an unhelpful reply.

How would I go about analyzing this? I am thoroughly lost on this question.
I already made a histogram of the experimental frequency distribution of the variances. I now need to find a calculated, theoretical frequency distribution of these variances.