The concept of arithmetic mean means the result of a simple sequence of calculations average size for a series of numbers determined in advance. It should be noted that this value in given time widely used by specialists in a number of industries. For example, formulas are known when carrying out calculations by economists or workers in the statistical industry, where a value of this type is required. In addition, this indicator is actively used in a number of other industries that are related to the above.
One of the features of the calculations given value is the simplicity of the procedure. Carry out calculations Anyone can do it. To do this you don't need to have special education. Often there is no need to use computer technology.
To answer the question of how to find the arithmetic mean, consider a number of situations.
The simplest option for calculating this value is to calculate it for two numbers. The calculation procedure in this case is very simple:
- Initially, you need to carry out the operation of adding the selected numbers. This can often be done, as they say, manually, without using electronic equipment.
- After addition is performed and its result is obtained, division must be performed. This operation involves dividing the sum of two added numbers by two - the number of added numbers. It is this action that will allow you to obtain the required value.
Formula
Thus, the formula for calculating the required value in the case of two will look like as follows:
(A+B)/2
This formula uses the following notation:
A and B are pre-selected numbers for which you need to find a value.
Finding the value for three
Calculating this value in a situation where three numbers are selected will not differ much from the previous option:
- To do this, select the numbers needed in the calculation and add them to get total amount.
- After this amount three will be found, you need to perform the division procedure again. In this case, the resulting amount must be divided by three, which corresponds to the number of selected numbers.
Formula
Thus, the formula necessary for calculating the arithmetic three will look like this:
(A+B+C)/3
In this formula The following notation is accepted:
A, B and C are the numbers for which you will need to find the arithmetic mean.
Calculating the arithmetic mean of four
As can already be seen by analogy with the previous options, the calculation of this value for a quantity equal to four will be in the following order:
- Four numbers are selected for which the average must be calculated arithmetic value. Next, summation is performed and the final result of this procedure is found.
- Now, to get the final result, you should take the resulting sum of four and divide it by four. The received data will be the required value.
Formula
From the sequence of actions described above to find the arithmetic mean for four, you can obtain the following formula:
(A+B+C+E)/4
In this formula the variables have the following meaning:
A, B, C and E are those for which it is necessary to find the value of the arithmetic mean.
Using this formula, it will always be possible to calculate the required value for given quantity numbers.
Calculating the arithmetic mean of five
Performing this operation will require a certain algorithm of actions.
- First of all, you need to select five numbers for which the arithmetic mean will be calculated. After this selection These numbers, as in the previous options, simply need to be added and get the final amount.
- The resulting amount will need to be divided by their number by five, which will allow you to get the required value.
Formula
Thus, similarly to the previously considered options, we obtain the following formula for calculating the arithmetic mean:
(A+B+C+E+P)/5
In this formula, the variables are designated as follows:
A, B, C, E and P are numbers for which it is necessary to obtain the arithmetic mean.
Universal calculation formula
Conducting a review various options formulas to calculate the arithmetic mean, you can pay attention to the fact that they have a general pattern.
Therefore, it will be more practical to use a general formula to find the arithmetic mean. After all, there are situations when the number and magnitude of calculations can be very large. Therefore, it would be wiser to use a universal formula and not output it every time individual technology to calculate this value.
The main thing when determining the formula is principle of calculating the arithmetic mean O.
This principle, as can be seen from the examples given, looks like this:
- The number of numbers that are specified to obtain the required value is counted. This operation can be carried out either manually with a small number of numbers or using computer technology.
- The selected numbers are summed. This operation in most situations is performed using computer technology, since numbers can consist of two, three or more digits.
- The amount obtained by adding the selected numbers must be divided by their number. This value is determined at the initial stage of calculating the arithmetic mean.
Thus, general formula to calculate the arithmetic mean of a series of selected numbers will look like this:
(A+B+…+N)/N
This formula contains the following variables:
A and B are numbers that are selected in advance to calculate their arithmetic mean.
N is the number of numbers that were taken to calculate the required value.
By substituting the selected numbers into this formula each time, we can always obtain the required value of the arithmetic mean.
As you can see, finding the arithmetic mean is a simple procedure. However, you must be careful about the calculations performed and check the results obtained. This approach is explained by the fact that even in the simplest situations there is a possibility of receiving an error, which can then affect further calculations. In this regard, it is recommended to use computer technology that is capable of performing calculations of any complexity.
What is average arithmetic number? How to find the arithmetic mean? Where and what is this value used for?
To fully understand the essence of the problem, you need to study algebra for several years at school, and then at the institute. But in everyday life, in order to know how to find the arithmetic mean of numbers, it is not necessary to know everything about it thoroughly. Explaining in simple language, is the sum of the numbers divided by the number of those numbers added.
Since it is not always possible to calculate the arithmetic mean without a remainder, the value may even turn out to be fractional, even when calculating the average number of people. This is due to the fact that the arithmetic mean is an abstract concept.
This abstract value affects many areas modern life. It is used in mathematics, business, statistics, often even in sports.
For example, many are interested in all the members of a group or the average number of foods eaten per month in terms of one day. And data on how much on average was spent on any expensive event is found in all sources of funds mass media. Most often, of course, such data is used in statistics: to know exactly which phenomenon has declined and which has increased; which product is most in demand and in what period; to easily eliminate unwanted indicators.
In sports we can come across the concept of an average when, for example, we are told middle age athletes or goals scored in football. How is the average score earned during competitions or at our beloved KVN calculated? Yes, for this you don’t need to do anything else but find the arithmetic mean of all the marks given by the judges!
By the way, often in school life some teachers resort to a similar method, giving quarterly and annual grades to their students. Also often used in higher education educational institutions, often in schools, to calculate the average score of students, to determine the effectiveness of the teacher or to distribute students according to their capabilities. There are still many areas of life in which this formula is used, but the goal is basically the same - to find out and control.
In business, the arithmetic average can be used to calculate and control income and losses, salaries and other expenses. For example, when submitting income certificates to some organizations, just the average monthly income is required. last six months. It is surprising that some employees whose duties include collecting such information, having received a certificate not with the average monthly salary, but simply about income for six months, do not know how to find the arithmetic average, that is, calculate the average monthly salary.
An arithmetic average is a characteristic (price, salary, population, etc.), the volume of which does not change during calculation. In simple words, when the average number of apples eaten by Petya and Masha is calculated, the result will be a number that will be equal to half of the total number of apples. Even if Masha ate ten, and Petya only got one, when will we share them? total quantity in half, then we get the arithmetic mean.
Today, many joke about Putin’s statement that the average salary of those living in Russia is 27 thousand rubles. The jokes of wits basically sound like this: “Or am I not a Russian? Or am I no longer living? And the whole question is that these wits also apparently don’t know how to find the arithmetic average of the salaries of Russian residents.
You just need to add up the incomes of oligarchs, business executives, businessmen on the one hand and salaries cleaners, janitors, salespeople and conductors on the other. And then divide the resulting amount by the number of people whose income included this amount. So we get an amazing figure, which is expressed in 27,000 rubles.
What is the arithmetic mean
The arithmetic mean of several quantities is the ratio of the sum of these quantities to their number.
The arithmetic mean of a certain series of numbers is the sum of all these numbers divided by the number of terms. Thus, the arithmetic mean is the average value of a number series.
What is the arithmetic mean of several numbers? And they are equal to the sum of these numbers, which is divided by the number of terms in this sum.
How to find the arithmetic mean
There is nothing complicated in calculating or finding the arithmetic mean of several numbers; it is enough to add all the numbers presented and divide the resulting sum by the number of terms. The result obtained will be the arithmetic mean of these numbers.
Let's look at this process in more detail. What do we need to do to calculate the arithmetic mean and obtain the final result of this number.
First, to calculate it, you need to determine a set of numbers or their number. This set can include large and small numbers, and their number can be anything.
Secondly, all these numbers need to be added and their sum is obtained. Naturally, if the numbers are simple and there are a small number of them, then the calculations can be made by writing them by hand. But if the set of numbers is impressive, then it is better to use a calculator or spreadsheet.
And fourthly, the amount obtained from addition must be divided by the number of numbers. As a result, we will get a result, which will be the arithmetic mean of this series.
Why do you need the arithmetic mean?
The arithmetic mean can be useful not only for solving examples and problems in mathematics lessons, but for other purposes necessary in everyday life person. Such goals can be calculating the arithmetic average to calculate the average financial expense per month, or to calculate the time you spend on the road, also in order to find out attendance, productivity, speed of movement, yield and much more.
So, for example, let's try to calculate how much time you spend traveling to school. Every time you go to school or return home, you spend on travel different times, because when you are in a hurry, you walk faster, and therefore the journey takes less time. But when returning home, you can walk slowly, communicating with classmates, admiring nature, and therefore the journey will take more time.
Therefore, you will not be able to accurately determine the time spent on the road, but thanks to the arithmetic average, you can approximately find out the time you spend on the road.
Let's assume that on the first day after the weekend, you spent fifteen minutes on the way from home to school, on the second day your journey took twenty minutes, on Wednesday you covered the distance in twenty-five minutes, and your journey took the same amount of time on Thursday, and on Friday you were in no hurry and returned for a whole half an hour.
Let's find the arithmetic mean, adding time, for all five days. So,
15 + 20 + 25 + 25 + 30 = 115
Now divide this amount by the number of days
Thanks to this method, you learned that the journey from home to school takes approximately twenty-three minutes of your time.
Homework
1. Using simple calculations, find the arithmetic average of the attendance of students in your class for the week.
2. Find the arithmetic mean:
3. Solve the problem:
Example 2. To courses English language on Monday 15 people came, on Tuesday - 10, on Wednesday - 12, on Thursday - 11, on Friday - 7, on Saturday - 14, on Sunday - 8. Find the average attendance of the courses for the week.
Solution: Let's find the arithmetic mean:
| 15 + 10 + 12 + 11 + 7 + 14 + 8 | = | 77 | = 11 |
| 7 | 7 |
Example 3. A racer rode for two hours at 120 km/h and an hour at 90 km/h. Find the average speed of the car during the race.
Solution: Let's find the arithmetic average of the car speeds for each hour of travel:
| 120 + 120 + 90 | = | 330 | = 110 |
| 3 | 3 |
Example 4. The arithmetic mean of 3 numbers is 6, and the arithmetic mean of 7 other numbers is 3. What is the arithmetic mean of these ten numbers?
Solution: Since the arithmetic mean of 3 numbers is 6, their sum is 6 3 = 18, similarly, the sum of the remaining 7 numbers is 7 3 = 21.
This means the sum of all 10 numbers will be 18 + 21 = 39, and the arithmetic mean is equal to
| 39 | = 3.9 |
| 10 |
