In this week's double parsha, we read of Moshe bringing together all of the Jewish people, leaders of all levels and laypeople alike. He then reviews with them the promises that Hashem made to Abraham, Isaac, and Jacob; he reviews how Hashem saved the Jewish people from slavery in Egypt; and he reviews that if they follow the commandments, they will be blessed, and if they don't, they will be cursed. Then, Moshe discusses that he has lived his complete life, and he will pass on leadership to Yehoshua ben Nun to bring the Jewish people into the land of Israel.
The content of this double-parsha struck me as the beginning of the conclusion of the first 5 books of the Torah. As we approach the end of the cycle, I thought it would be interesting to look at some statistics related to all the parshiot.
Statistics:
If we look back over the math concepts that have been touched on this year, we looked at statistics back in Parshat Bamidbar. There, we talked about the purpose of statistics for comparing data in order to learn patterns and trends about the situation you are looking at. We also looked at using statistics to create graphs in Parshat Vayikra and Parshat Tzav, where we used the graphs to help us look for trends and comparisons of information.
Below I've complied data related to the 5 Books of Torah and each of the individual parshiot. (Note: These statistics were compiled using a combination of information found on Wikipedia.org and torahtots.com.)
If we look at the charts, we can see that there are:
12 parshiot in Bereishit
11 parshiot in Shemot
10 parshiot in Vayikra
10 parshiot in Bamidbar
11 parshiot in Devarim
For some basic statistics, while we see that the parshiot are approximately evenly divided between the 5 books, Vayikra and Bamidbar have the least number of parshiot (10 each), and Bereishit has the greatest number (12). The number of parshiot in each of the 5 books ranges from 10-12 (so there is a range of 2--> 12 - 10 = 2). If we wanted to find out how many parshiot, on average, each book has, we would find the mean- add the 5 numbers together and divide by 5.
If we take a look into the statistics related to the number of letters in each parsha, number of words in each parsha, and number of pesukim (verses) in each parsha, we will find that:
V'Zot Habrachah has the fewest letters with 1,969 letters.
Nasso has the most letters with 8,632 letters.
Overall, the parshiot have a range of 8,632 - 1969 = 6,663
V'Zot Habrachah has the fewest words with 512 words.
Nasso has the most words with 2,264 words.
Overall, the parshiot have a range of 1,752 words.
Vayeilech (one of this week's parshiot) has the fewest verses with 30 verses.
Nasso has the most verses, with 176 verses.
Overall, the parshiot of a range of 146 verses.
In a full statistical analysis of each of these, a student would use either a line plot or stem-and-leaf plot to see the full view of how the number of letters, words, or verses fall on a number line. They would look to see if the numbers cluster in any spots (is there a pattern to be able to identify a smaller number range where most parshiot fall when looking at number of letters? number of words? number of verses?).
Students could calculate mean, median, and mode for the number of letters, words, or verses in the parshiot.
Students could graph the numbers of letters, words, or verses for on a bar graph to see how the numbers increase and decrease over the progression of the parshiot throughout the year.
Students can also look at how the other double-parshiot are paired for regular years, and how that effects changes in the numbers if we combine numbers for double-parshiot.
There are many statistical questions that a student could ask related to this data to compare the statistics of individual books and parshiot. These are just a sampling of some ideas.
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