Interesting mathematics. Average value

In mathematics, the arithmetic mean of numbers (or simply average) is the sum of all numbers in a given set, divided by their number. This is the most generalized and widespread notion of average value. As you have already understood, in order to find the average value, you need to sum all the data to you numbers, and divide the result by the number of terms.

What is the arithmetic mean?

Let's look at an example.

Example 1 . Given the numbers: 6, 7, 11. We need to find their average value.

Decision.

First, we find the sum of all these numbers.

6 + 7 + 11 = 24

Now divide the resulting sum by the number of terms. Since we have three terms, respectively, we will divide by three.

24: 3 = 8

Consequently, the average value of the numbers 6, 7 and 11 is 8. Why 8? Yes, because the sum of 6, 7 and 11 will be the same as three eights. This is clearly seen in the illustration.

The average value somewhat resembles the "alignment" of a number of numbers. As you can see, piles of pencils have become one level.

Let's consider one more example to consolidate the knowledge gained.

Example 2. The numbers are given: 3, 7, 5, 13, 20, 23, 39, 23, 40, 23, 14, 12, 56, 23, 29. We need to find their average arithmetic value.

Decision.

We find the sum.

3 + 7 + 5 + 13 + 20 + 23 + 39 + 23 + 40 + 23 + 14 + 12 + 56 + 23 + 29 = 330

We divide by the number of terms (in this case - 15).

330: 15 = 22

Therefore, the average value of this series is 22.

Now consider the negative numbers. Let's remember how to summarize them. For example, you have two numbers 1 and -4. Let us find their sum.

1 + (-4) = 1 - 4 = -3

Knowing this, let us consider one more example.

Example 3. Find the average value of a number of numbers: 3, -7, 5, 13, -2.

Decision.

Find the sum of numbers.

3 + (-7) + 5 + 13 + (-2) = 12

Since the summands of S, we divide the resulting sum by 5.

12: 5 = 2.4

Consequently, the arithmetic mean of the numbers 3, -7, 5, 13, -2 is 2.4.

In our time of technological progress it is much more convenient to use computer programs to find the average value. Microsoft Office Excel is one of them. Searching for an average in Excel is quick and easy. Moreover, this program is included in the package of programs from Microsoft Office. Let's consider a brief instruction how to find the average arithmetic value using this program.

In order to calculate the average value of a number of numbers, you must use the AVERAGE function. The syntax for this function is:
= Average (argument1, argument2, ... argument255)
Where argument1, argument2, ... argument255 are either numbers or references to cells (by cells are meant ranges and arrays).

In order to be more clear, we will test the received knowledge.

1. Enter the numbers 11, 12, 13, 14, 15, 16 in cells C1 to C6.
2. Select cell C7 by clicking on it. In this cell, we will display the average value.
3. Click on the "Formulas" tab.
4. Select More Functions> Statistical to open the drop-down list.
5. Select AVERAGE. After that, a dialog box should open.
6. Select and drag cells C1-C6 there to specify a range in the dialog box.
7. Confirm your actions with the "OK" button.
8. If you did everything correctly, in cell C7 you should get the answer - 13.7. When you click on cell C7, the function (= Average (C1: C6)) will be displayed in the formula bar.

It is very convenient to use this function for accounting, invoices or when you just need to find the average of a very long series of numbers. Therefore, it is often used in offices and large companies. This allows you to keep order in the records and allows you to quickly calculate something (for example, the average income for the month). Also using Excel you can find the average value of the function.