Vayikra- Statistics part 1

About the Parsha:
In Parshat Vayikra we have 5 chapters that just list different types of sacrificial offerings that can be brought. Rather than quoting sections of the parsha, I've reduced the information into the summary below:

olah-offering-- male cattle
olah-offering--male sheep or goat
olah-offering--turtledoves or young doves
meal-offering--fine flour, oil, frankincense

meal-offering--first fruits

peace-offering--male or female cattle

peace-offering-- male or female from flock (sheep or goat)

Kohen's sin-offering-- young male cattle

Community sin-offering-- young bull (male cattle)

Ruler sin-offering-- male goat

individual sin-offering-- female goat or sheep

guilt-offering--female sheep or goat

guilt-offering-- two turtledoves or two young doves (if can't afford sheep/goat)

guilt-offering-- flour (if can't afford doves)

guilt-offering-- ram

What is a graph?
A graph is a visual representation of information in order to easily compare information in a given situation. There are many types of graphs- line graphs, bar graphs, pie charts, histograms, venn diagrams- each type of graph is suited to a certain type of information and a certain format. A pie chart, for example, gives information about the division of categories within a total group, or sectional percentages out of 100%.

For the next few weeks, I'd like to look at different types of graphs and statistical analysis of information that's given in the parshiot.

For this week, we'll look at bar graphs. Bar graphs are graphs that are used to compare categories. A vertical bar graph has the names of the categories on the bottom of the graph, and the left side of the graph has the number scale to show how much is measured in each category. A horizontal bar graph can display the same exact information, but the graph is turned sideways- the names of categories are on the left of the graph, and the number scale is along the bottom of the graph.

It's interesting to look at different ways that the same information can be graphed- each graph bringing out different aspects of the information.

Let's first make a graph showing how many options there are for each type of offering. First we'll organize our data:

*olah-offering: (3 options)
--cattle
--sheep/goat
--doves
*meal-offering: (2 options)
--fine flour mixture
--first fruits mixture
*peace-offering: (2 options)
--cattle
--sheep/goat
*sin-offering: (4 options)
--Kohen (cattle)
--community (cattle)
--ruler (goat/sheep)
--individual (goat/sheep)
*guilt-offering: (4 options)
--sheep/goat
--doves
--flour
--ram

Now that we have our data organized the way we want it, we can graph it (chart on top, graph underneath):

Number of Options for Sacrifice Types:

Now, what if we make a graph of how many must be male animals, must be female animals, could be either male or female, or are grain/fruit?

Again, let's first organize our data:

*male animals: (8 options)

--olah-offering (x3)
--sin-offerings (x3)
--guilt-offering (x2)
*female animals: (2 options)
--sin-offering (x1)
--guilt-offering (x1)
*male or female: (2 options)
--peace-offering (x2)
*grain/fruit: (3 options)
--meal-offering (x2)
--guilt-offering (x1)

Now that we have our data organized the way we want it, we can graph it (chart on top, graph underneath):

Number of Sacrifices by Animal Type:

So, here we have two very different graphs, both based on the same exact data set, but focusing on different aspects of the information; one looks at which sacrifices have the most options for what can be offered for that type of sacrifice, and the other looks at how many sacrifice types each animal can be used for. 

Some good questions for testing for understanding of graphs might be: Which category has the most options? Which category has the least? Are there any that have the same amount? How much difference is there between two given categories? These questions can be tailored for each specific graph that you're reading.