What Happens when We “Divide” Something? What is “Division”?

Example #1

On one fine day, you and your best friend decide to appease your appetite with pizza. You guys decide to equally share the payment. If the price of the pizza is $1,000, you will give $500, and your friend will give $500. You ordered a pizza that has 8 slices.

Now, the big question is how to “divide” 8 slices of a pizza “equally” between 2 individuals?

Your friend takes the responsibility, and since he does not know the math of division, he starts dividing the slices by pulling slices one by one from the pizza box. He pulls the first slice and keeps it on your plate. Then, he pulls another and places it on his plate. After doing this a couple of times, both of you end up with 4 slices each on your plates.

By this, we did an amazing thing. What we just did is we took a large group (8 slices) and divided it into small groups that have an equal number of items (4 slices each).

Hence, division is making small groups of a big group that will contain the same number of items.

What would be the one number that will be representative of the number of slices you and your friend will get? That would be 4, right?

Key Takeaways:

• We make small groups from a large group in the division.

• The small groups will have the equal or same number of items.

You may ask why we are learning division in statistics. Hold your horses for a moment. We will get there.

What is the Formula of Average or Arithmetic Mean?

Average = Sum/Number of Items

Average x Number of Items = Sum

The arithmetic mean is dividing the sum of the data points by the number of observations. But what do we do with averages, and what does it actually mean?

Example #2

Let’s say you gave 5 mock tests to prepare for your IBA DU exam. The marks you received in five of these mock tests are as follows:

You are super excited about the IBA DU exam, and you want to predict or estimate around which number you will score on the real test. That is to say, if you were to give the exam tomorrow, what marks can you expect?

Notice the word “around.” Most certainly, you won’t be able to predict the exact number in most cases. But what you can do instead is to make an estimation of the number.

Let’s say, after some magic trick (I will explain the trick later), you get the number 83. This doesn’t necessarily mean you will get exactly 83 in the real test. You can, but maybe not every time.

What this number 83 represents is something profound. This means you can perhaps get 79, 81, 82, 82, or even 87 - something around 83 - probably!

And this is what the average, or arithmetic mean, does. It gives you a sense of your overall performance and sometimes helps you to estimate or have a sound general idea about a set of data points.

Warning: Not every time! The arithmetic mean can often mislead you. We will discuss this later.

The mean somewhat sets a boundary for you that you are more likely to perform in this radar or span.

Now, the question is, what do we mean when we say average? We understood one of its key applications. But still, the formula doesn’t give us a deeper understanding of the inner mechanics of the mean.

Remember, when we were discussing division, we said when we divide something, we simply take a large group and separate it into small groups that have the equal or same number of items. Notice our formula of the arithmetic mean also deploys division.

At first, it is adding all the marks you received in the 5 mock tests.

81 + 78 + 86 + 87 + 83 = 415