Question: For the census of the United States or Canada, or an equivalent source, generate the value of a variable for a region containing at least 30 subareas. For example, you could look at some characteristic of the population for the counties within a state or province.

a. Calculate the mean and variance for the variable of interest across the subareas.

b. Group contiguous subareas in pairs so that there are 15 or more zones; calculate the mean and variance for the variable of interest across the newly constructed zones.

c. Group contiguous zones in part (b) to get eight or more areas; find the mean and variance of the variable of interest across these areas.

d. Continue the process of aggregating regions into larger geographical units until there are only two subregions. At each step calculate the mean and variance of the variable of interest across the areas.

e. The mean of the variable at each step should be equal. Why?

f. Construct a graph of the variance of the variable (Y-axis) versus the number of subareas (X-axis). What does it reveal?