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 concept of medium size. As you already understood, to find the average value, you need to sum all the numbers given to you, and divide the result by the number of terms.
What is arithmetic mean?
Let's look at an example.
Example 1 The numbers are given: 6, 7, 11. It is necessary to find their average value.
Decision.
First, find the sum of all these numbers.
6 + 7 + 11 = 24
Now we divide the resulting amount by the number of terms. Since we have three terms, respectively, we will divide by three.
24: 3 = 8
Therefore, the average of 6, 7, and 11 is 8. Why exactly 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 is somewhat reminiscent of the "alignment" of a series of numbers. As you can see, piles of pencils have become the same level.
Consider another 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. It is necessary to find their arithmetic average value.
Decision.
Find the amount.
3 + 7 + 5 + 13 + 20 + 23 + 39 + 23 + 40 + 23 + 14 + 12 + 56 + 23 + 29 = 330
Divide by the number of terms (in this case - 15).
330: 15 = 22
Therefore, the average value of this series of numbers is 22.
Now consider the negative numbers. Recall how to summarize them. For example, you have two numbers 1 and -4. Find their amount.
1 + (-4) = 1 - 4 = -3
Knowing this, consider another example.
Example 3. Find the average value of a series of numbers: 3, -7, 5, 13, -2.
Decision.
Find the sum of numbers.
3 + (-7) + 5 + 13 + (-2) = 12
Since there are 5 terms, we divide the resulting amount by 5.
12: 5 = 2.4
Therefore, the arithmetic mean of the numbers 3, -7, 5, 13, -2 is 2.4.
Nowadays, technological progress is much more convenient to use computer programs to find the average value. Microsoft Office Excel is one of them. Finding the average in Excel is quick and easy. Moreover, this program is included in the software package from Microsoft Office. Consider a brief instruction on
how to find the arithmetic mean value using this program.
In order to calculate the average value of a series 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 cell references (cells are ranges and arrays).
To make it more clear, we will test the knowledge gained.
- Enter the numbers 11, 12, 13, 14, 15, 16 into cells C1 - C6.
- Select cell C7 by clicking on it. In this cell, we will display the average value.
- Click on the Formulas tab.
- Select More Functions> Statistical to open the drop-down list.
- Select AVERAGE. After that a dialog box should open.
- Select and drag cells C1 – C6 to define a range in the dialog box.
- Confirm your actions with the OK button.
- If you did everything correctly, in cell C7 you should see 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 value from a very long series of numbers. Therefore, it is often used in offices and large companies. This allows you to maintain order in the records and makes it possible to quickly calculate something (for example, average monthly income). You can also use Excel to find the average value of a function.