Chocolate production and consumption in Australia


What sort of patterns would you expect to see in the production of consumer goods?
chocolate blocks For example, consider chocolate production in Australia from July 1957 to August 1995.
The production for the first six months of this time period was:
Year Month Production (tonnes)
1957 July 2953
1957 August 2635
1957 September 2404
1957 October 2413
1957 November 2136
1957 December 1565

Here's a graph of the full data set:

chocolate1

There seems to be some patterns in the production of chocolate. Is this what you would expect?

When do the peaks occur? What about the downward spikes?

Why do you think this is?

We could also consider the change from month to month. Here are some graphs of the changes.

chocolate2

The graph above is a simple time series graph of the changes in chocolate production over time. The change in production from month to month is not well modelled with a single normal distribution, because the variance is increasing with time. As the production increases, it varies by more.

chocolate3

The graph above is a histogram of these changes and the graph below is a Normal QQ plot of these changes. A QQ plot is a graphical method of deciding if a sample of values—in this case the 457 changes in production—are normally distributed. It plots the ordered values against quantiles of the standard normal. A straight line indicates a fairly normal distribution, which is not observed in this case.

chocolate4

Do you think the upward trend in production indicates that Australians were consuming more chocolate in 1990 than in, say, 1980?

Here are some graphs to help think about that question:

chocolate5

chocolate6

These graphs show information about chocolate production from 1978 to 1991. The total monthly production is shown in tonnes, and the average monthly production is in grams. Production per person peaks at over 700 grams in 1989.

There is an increase in production over time; however the increase do not appear so marked when we take population size into account.