Zacharie, I think I still need your help when it comes to math!

You do! I bet you're all mixed up in your table analysis again!

You're pretty close! This time, it's not analyzing tables that's causing me problems, but analyzing graphs. My main problem is figuring out whether both are analyzed the same way.

You're right, they're analyzed in a very similar manner, since data mapping is generally done using a table. However, data can be illustrated in an even clearer manner using a graph since the elements can be compared quickly and variations can be displayed. I've got a good trick for you. When analyzing a graph, always keep in mind the steps you follow when you make one and that will serve as a guide. If you'd like to, we can make one together. Just remember the basic principles and your analysis will surely go more smoothly!

O.K.!

First of all, if you want your graph to be as informative as possible, when choosing a figure, you should keep in mind the following three points:

	The type of variable you want to describe;
	The message you want to give (time series, trends, distribution, etc.);
	The clarity of your message: your graph must be simple and uncluttered.

O.K.! I would like to draw a graph of the total consumption of milk per inhabitant in Québec during the last decade. I have to hand in a short geography assignment on that subject. So instead of inventing a graph, I might as well make one that I'll be able to use afterwards.

Good idea, you'll save time! Do you have the data you need on hand or do you have to find them?

No problem, I took them off the Web yesterday.

I hope that your data are from an official source. Navigating on the Web always involves an element of risk.

Don't worry! I always make sure my data is from reliable organizations!

O.K.! What are you going to start with when you make your graph? Go ahead, I'll correct you as you go along.

Don't be too hard on me! The first thing I do when making a graph is to label the axes. I'm using the (vertical) y-axis to represent what is being measured and the (horizontal) x-axis to represent the variable.

What I am actually doing is trying to measure the number of litres consumed per inhabitant in Québec over a given period of time. Therefore, I am going to place the litres per inhabitant on the y-axis and the years on the x-axis, not forgetting of course to enter the number of units!

Then…

Then do I choose the type of graph?

Are you sure about that?

Not really!

I'm going to help you a bit. The next step consists in finding the right scale for each axis.

Oh yes, it's coming back to me now! I have to decide on a scale for the two axes, taking into account the minimum and maximum data values and making sure that all the values can be represented over the longest length possible using the unit chosen. Then I draw the axes and graduate them.

That's right! What have you decided on as a scale for your x-axis?

I'm going to use the years from 1991 to 2001. I have enough room for all of them.

And on the y-axis?

The extreme values range from 85.4 to 98.0.

1991	98.0
1992	95.4
1993	90.8
1994	93.8
1995	94.0
1996	92.5
1997	92.0
1998	91.9
1999	88.3
2000	88.2
2001	85.4

Therefore, we could graduate the scale from 84.0 to 98.0 litres, at intervals of 2.0 litres; that way we would have seven divisions.

O.K., that suits me!

After that, I think that I have to decide on the type of graph I want.

You're quite right! You have to determine which type of graph best illustrates what you want to represent: curve graphs, tally charts, line graphs, bar graphs, or pie charts.

I've chosen to use a curve since it does a good job of illustrating data over a period of time. If I remember correctly, a curve graph is made by plotting points in the figure and then joining them up drawing as straight a line as possible. And when all this has been done, I'll have to find a title.

Very good, Marion! I think you're starting to get the hang of it!

Ya not bad! Zacharie, but I have a small question before starting my analysis.

Yes, Marion! I'm all ears!

How do I know whether the graph is well constructed?

You just have to make sure that:

	the axes are correctly graduated and named;
	the curve takes up as much space as possible;
	the curve is correctly plotted;
	the title is well placed and is meaningful.

After checking to make sure that everything has been done properly, you won't have any qualms about putting the graph in your assignment! If you agree, now that we've reviewed the steps to follow to make a graph, we can concentrate on analyzing the graph.

I feel more up to analyzing a graph now that we've just done one! You told me a few minutes ago that there are a few differences between analyzing a graph and a table. What are they?

First of all, you have to know how to read a graph! You have to do exactly what you did with the table. That is, take a look at the title, the units of measurement, the date, the source and the author. However, instead of paying attention to the columns and rows, you must read the title of the x-axis and the y-axis.

Comparing the Analysis of a Table and a Graph

Ever since Jade's teacher played a trick on her students, I always remember to pay attention to the date and the source of a graph. What their teacher did was to give them an old graph by Astérix and Obélix, and everybody fell for it! The teacher really had a good laugh! I wouldn't want to be caught in such an embarrassing situation!

Me neither! In the future, I'm going to pay more attention. I often have graphs to analyze and have a tendency to examine them a tad too quickly! Something like that could easily happen to me! I'm going to be more careful from now on!

Are there also differences in the way of interpreting the information?

Yes, there are a few. First, you must remember that, like for tables, when analyzing a graph you are going from the general to the specific. However, when analyzing graphs, the overall trend is analyzed but not the totals. Another difference is that instead of extracting meaningful data, you must find the meaningful breaks: those that show a permanent change in the general trend. Then to clarify or illustrate the trends or simply to simplify the presentation of key facts, you will have to, like you did for tables, use mathematical tools such as calculating percentages, averages, etc. Once you have gone through all these steps, you must draw up your conclusions.

Now that you know how to analyze a graph, what do you have to say about yours?

Well, I noted several facts:

	From 1991 to 2001, in total, there was a 12.6 litre drop in consumption per inhabitant.
	The highest annual drops were from 1992 to 1993 and from 1998 to 1999. In the first case, milk consumption decreased by 4.6 litres per inhabitant, whereas, in the second case, the decrease was not quite as pronounced, that is, 3.6 litres per inhabitant.
	From 1993 to 1995, there was a sudden change in the trend which started at the beginning of the decade, since, in two years, milk consumption went up 3.2 litres.
	Henceforth, Québecers started to consume less milk and this decline became even more pronounced from 1998 to 2001.
	From 1995 to 2001, the annual milk consumption per inhabitant went from 94.0 litres to 85.4 litres per year, that is, a drop of 8.6 litres per person.

Well, I think I've managed to cover everything!

Let's just say that with all the information you've extracted, you'll be able to do a three-page analysis. Now all you have to do is put your main facts together and your conclusions will be complete!