Tzav- Statistics part 2

Once again, this week we have a significant portion of the parsha dedicated to specifics of korbanot, or sacrificial offerings. Again, rather than quoting from the parsha, I've organized some of the information related to the offerings in order to analyze.

Pie Chart/Circle Graph:
Whereas the bar graphs we looked at last week compared a measured amount between different categories, a circle graph compares portion sizes of categories that together make up 100% of something. For example, out of your total budget allotment, what percentage of the budget goes to different categories (food, medical, housing costs, etc.)? Out of all after school enrollment, what percentage of students go to each of the different activities? Out of the total hours in a day, what percentage of time is spent sleeping, eating, working, etc.? The key to circle graphs is that all categories together add to 100% and create a complete circle. 

When analyzing data to convert into a circle graph, we'll need our knowledge of fractions (Parshat Vayishlach), proportions (Parshat Ki Tisa), and percentages (Parshat Vayigash) to convert the raw data into a format that will fit the circle graph.

Connection to Parsha:
Let's take a look at a sample data set from this week's parsha to walk us through the process. Let's look at what percentage of sacrifices were to be fully burned and what percentage of sacrifices were allowed to be partially eaten in some form.

We can start by making a chart to organize the information so that we see which category each sacrifice falls into.

Next, we use the chart to count up how many sacrifices are in each category out of the total number of sacrifices. According to our chart, out of the 6 total sacrifices, we have 3 sacrifices that are completely burned and 3 sacrifices that are partially burned and partially eaten.

Let's restate this as fractions- 
3/6 = burned 
3/6 = burned then eaten

If we want, we can reduce these fractions (each reduces to 1/2), but we don't have to. In this case, we will reduce them, since it will make our next calculation easier to work with. 

So, we have-
1/2 of the sacrifices are burned
1/2 of the sacrifices are burned then eaten

Now, remember that the most important part of a circle graph is that it shows a percentage out of 100%, where 100% (or all) of what you're analyzing makes up the full circle. So, if 100% of the sacrifices is all of them, we know that 1/2 of the sacrifices were burned: 100% x 1/2 = 50% and 1/2 of the sacrifices were burned then eaten: 100% x 1/2 = 50%. So now we have calculated that 50% of the sacrifices were totally burned and 50% were burned then eaten. Once we have this calculation, we can create our graph. 

While I made the graph electronically, you can also construct a circle and measure out the angle measures for each section using pencil, paper, drawing compass, and protractor. Such an activity offers a good opportunity for art/geometry integrations in math. To calculate the sections by hand, we need to first know a full circle is 360°. Since we need 1/2 of the circle for each category, we multiply 360° x 1/2 = 180°. This means that the angle measure for each section of the circle needs to be 180°. Measuring out this 180°, you'll find that you've perfectly divided the circle into two 50% sections, one for each category.

It happened that the numbers for this activity fell perfectly into two equal groups. While it may seem simplistic because of the easy numbers and category divisions, it would make a very simple way to practice going through the steps of the process and practicing drawing circles and interior angles. Once practicing with this easy example, another problem with more complex category divisions could be introduced.