"Their counted ones, for the tribe of Shimon: fifty-nine thousand, three hundred." ~Bamidbar 1;23
"Their counted ones, for the tribe of Gad: forty-five thousands, six hundred and fifty." ~Bamidbar 1;25
"Their counted ones, for the tribe of Judah: seventy-four thousand, six hundred." ~Bamidbar 1;27
"Their counted ones, for the tribe of Issachar: fifty-four thousand, four hundred." ~Bamidbar 1;29
"Their counted ones, for the tribe of Zevulun: fifty-seven thousand, four hundred." ~Bamidbar 1;31
"Their counted ones, for the tribe of Ephraim: forty thousand, five hundred." ~Bamidbar 1;33
"Their counted ones, for the tribe of Menasheh: thirty-two thousand, two hundred." ~Bamidbar 1;35
"Their counted ones, for the tribe of Binyamin: thirty-five thousand, four hundred." ~Bamidbar 1;37
"Their counted ones, for the tribe of Dan: sixty-two thousand, seven hundred." ~Bamidbar 1;39
"Their counted ones, for the tribe of Asher: forty-one thousand, five hundred." ~Bamidbar 1;41
"Their counted ones, for the tribe of Naftali: fifty-three thousand, four hundred." ~Bamidbar 1;43
"...these were all the counted ones of the Children of Israel, according to their fathers' house, from twenty years of age and up, everyone who goes out to the army in Israel; All their counted ones were six hundred and three thousand, five hundred and fifty." ~Bamidbar 1;45-46
This week's parsha begins with Hashem telling Moshe to take a census of all the men in Israel from the age of 20 and older. Hashem appoints one person from each tribe as a prince to help Moshe take the census.
What is Statistics?
In simple terms, statistics is the mathematical study of data (numbers in a certain situation) in order to provide information about the situation. For example, if I have test scores from a class of students, I could use statistics to find out information about how the whole class performed on the test. Or, if I want to know information about the general height of students in the class, I can use statistics to analyze the heights of the students in the class. The data for these examples would be the list of all the test scores, or the list of each students' height.
What could we do with these sets of data? There are 3 different calculations that are known as the statistical averages:
1) mean
2) median
3) mode
Each of these averages can be more or less meaningful in given situations.
*Mean is calculated by adding all of the numbers in your data set together and dividing by the number of numbers that were added together. So, if I have 5 numbers in my data set, I would add them together and divide that sum by 5. That quotient would be the mean of my data set. (This is the classic "average", or arithmetic average, that we learn about in Elementary school)
*Median is identified by finding the exact middle number of the data set. The first step is to put all the numbers in numerical order. Next, identify the middle number- for younger children, it's easier to methodically cross off numbers alternating between the top number that's left and the bottom number that's left until they're just left with the middle number (or two numbers). If there is an odd amount in the data set, then the middle number is the median; if there is an even amount, then the number that is exactly halfway between the two middle data points is the median.
*Mode is identified by finding the number that appears the most times in the data set. If every number appears evenly in the data set, then there is no mode. There can also be more than one mode in a data set.
One other important term that is usually introduced with these 3 averages is range. Range is the distance spanned by the numbers in a data set. Range is calculated by taking the highest number in the set minus the smallest number in the set. The resulting difference is the range.
Parsha Connection:
We can take the census numbers from the 12 tribes and calculate the range and averages of the number of men aged 20 and older. Let's start by rewriting our data.
Reuven- 46,500
Shimon- 59,300
Gad- 45,650
Judah- 74,600
Issachar- 54,400
Zevulun- 57,400
Ephraim- 40,500
Menasheh- 32,200
Binyamin- 35,400
Dan- 62,700
Asher- 41,500
Naftali- 53,400
Now, let's put those numbers in numerical order:
Menasheh- 32,200
Binyamin- 35,400
Ephraim- 40,500
Asher- 41,500
Gad- 45,650
Reuven- 46,500
Naftali- 53,400
Issachar- 54,400
Zevulun- 57,400
Shimon- 59,300
Dan- 62,700
Judah- 74,600
Before doing any calculations, we can look at the newly organized data and see that Menasheh had the smallest number of 20+ men, and Judah had the most. Now let's do those statistical calculations.
Range:
Most of the census numbers range between 32,000-60,000, while Judah had much more. The actual range of census numbers is
74,600 - 32,200 = 42,400
Mode:
We see that each tribe had a unique number of men, so there is no mode to this data.
Median:
Since there are 12 tribes here, the median will be exactly between the 6th and 7th tribes; between Reuven & Naftali. So how do we find the midpoint between 46,500 and 53,400? We can add them together and divide by 2.
46,500 + 53,400 = 99,900
99,900 ÷ 2 = 49,950
So, the median number of men in each tribe was 49,950.
Mean:
We start by adding all 12 numbers together. When added together, the sum is 603,550 (notice that this is the exact number that the parsha gives us for the total census for the 12 tribes together). Next we divide 603,550 ÷ 12 = 50,295.8
So, the mean number of men in each tribe was 50,295.8 (or approximately 50,296 men)
Everyday Connection:
What are some hot topics in your house that you can use for data collection? How much time do your children spend, on average, working on homework each night? Are they getting enough sleep; what's the average number of hours of sleep that they get each night?
You have a very good way of explaining things! (p.s. "mean, median and mode" were always some of my favorite things to teach in homeschooling. This Parsha Math brings back nice memories)
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