MATH 314 Homework 03

Due 2025-09-19 by 11:59pm

Welford's online algorithm for computing the mean and variance/standard deviation work with just one data point at a time, as if the data were streaming in and you didn't have the memory or ability to store past data.

I prefer to write the math a bit differently than the Wikipedia page linked above, but to the same effect. Initialize . Update these variables with a new observation

1. Write a Python class called OnlineMoments, which implements the following API:

   om = OnlineMoments()
   om.update(1)
   om.update(2)
   om.update(3)
   om.mean()
   om.var()
   om.count()
   om.size()
   

   Note that the mathematics above track the biased variance, where as I'm asking for unbiased variance. The class method var() needs to make the appropriate conversion:

   The constructor should accept a size argument, which defaults to 1, that sets the number of means and variances to be tracked.

2. Test your code. Create an instance of the OnlineMoments class. Generate a numpy array of random numbers. Loop through the array one number at a time, calling the method update on each element of your array. Print the mean and variance you calculated.

3. Compare the answers to what np.mean() and np.var(..., ddof=1) produce.