You will need

- Knowledge of math.

Instruction

1

Suppose that we are given a set of four numbers. Need to find

**average****value**of this set. To do this, first find the sum of all these numbers. Let's say the numbers 1, 3, 8, 7. Their sum is equal to S = 1 + 3 + 8 + 7 = 19. A set of numbers must consist of numbers of the same sign, otherwise the point in calculating the average value is lost.2

The average

**value**of a set of numbers equal to the sum of the numbers S, divided by the number of these numbers. That is, the**average****value**is equal to 19/4 = 4.75.3

To set the number also can be found not only

**higher**arithmetic, but also**the mean**geometric. Several geometric average of positive real numbers is called a number to replace each of these numbers so that their product has not changed. The geometric mean G is searched according to the formula: the nth root of the degree of the product of the set of numbers, where N is the number of numbers in the set. Consider the same set of numbers: 1, 3, 8, 7. Find their**average**geometric. To do this, calculate the work: 1*3*8*7 = 168. Now from among the 168 you must remove the root of the 4th degree: G = (168)^1/4 = 3.61. Thus**the average**geometric set of numbers is equal to 3.61.Note

The average value can not be greater than the largest number in the set and smaller than the small.

Useful advice

In mathematical statistics the mean value is a mathematical expectation.

# Advice 2 : How to calculate arithmetic mean

**Secondary**arithmetic, which is sometimes simply called the average, is one of the important concepts in mathematics and statistics.

**The average**arithmetic mean of any set of values is by means of two successive operations using a calculator.

You will need

- Calculator

Instruction

1

To begin, add up all the numbers from the set for which you want to find the arithmetic mean. For example, you are given a sequence of five numbers: 8, 17, 22, 14 and 29. In this case, the first step in the calculation of the arithmetic mean is finding the sum of these numbers: 8 + 17 + 22 + 14 + 29 = 90.

2

Now, when the amount is found, divide it by the number of summed numbers. In our set had 5 numbers, so we divide 90 by 5. 90 : 5 = 18. The resulting number will be the average of the original set of numbers.

Note

The arithmetic mean is intended to describe the Central tendency, however, is sometimes hindered by the influence of "large deviations". For example, the arithmetic mean of a set of numbers 2, 1, 1, 2, 1, 11 shall be three, whereas most of the elements of the series (five of six) is clearly below this value.

# Advice 3 : How to calculate the average value

Numerical characteristic of multiple functions or numbers, enclosed between the maximum and minimum values is called the average

**value**. In mathematics, under this definition it is possible to understand**the average**value of a function**average**weighted**average**chronological. In probability theory and statistics, non - parametric averages such as the mode, median and**average**value of a random variable. For each of these concepts has its own calculation algorithm.You will need

- Textbooks on higher mathematics, probability theory, statistics

Instruction

1

So, in mathematics the most common and popular calculate power average of function values according to Kolmogorov. Special cases of Kolmogorov averages are

**the average**of the arithmetic**average**squared, the**average**harmonic**average**geometric. To calculate the arithmetic mean (or simple average), add up all the numbers and divide by their number. Calculate the square root of the arithmetic mean of the squares of these numbers and you will get**the mean**squared value. The average harmonic and**the mean**of the geometric is also easy to compute by substitution of the data series in the formula2

A weighted average is calculated when we are dealing with linear combinations. Here, too, there are different algorithms. Often use

**the average**arithmetic weighted**average,**a geometric weighted**average,**a harmonic weighted. These values you can calculate using the following formulas:3

Chronological

**average**is used to calculate the average value of the absolute values changing in a certain time interval. To calculate this value, use this formula:4

In statistics, the most frequent concepts such as mode and median. They are non-parametric averages. Recall that the mode is the most frequently occurring number in the given range, and the median - a characteristic value which will divide the sample into two equal parts "upper" and "lower".

5

In probability theory

**, the average**value of a random variable is nothing but a mathematical expectation. If you have a discrete distribution, then the mathematical expectation is calculated according to the formula (1), and if continuous, but the formula (2)# Advice 4 : How to calculate arithmetic mean

**Higher**arithmetic - an important concept used in many branches of mathematics and its applications: statistics, probability theory, Economics, etc.

**Average**an arithmetic can be defined as the General notion of average.

Instruction

1

**The average**arithmetic mean of a set of numbers is defined as their sum divided by their number. The sum of all numbers of the set divided by the number of numbers in this set.The most simple case is to find the arithmetic mean of two numbers x1 and x2. Then their arithmetic mean X = (x1+x2)/2. For example, X = (6+2)/2 = 4 - the arithmetic mean of the numbers 6 and 2.

2

The General formula for finding the arithmetic mean of the n numbers would look like this: X = (x1+x2+...+xn)/n. It can also be written as: X = (1/n)?xi, where the summation is for index i from i = 1 to i = n.For example, the arithmetic mean of three numbers X = (x1+x2+x3)/3, five numbers is (x1+x2+x3+x4+x5)/5.

3

Interest is the situation when the set of numbers represents the members of an arithmetic progression. As you know, members of the arithmetic progression is a1+(n-1)d, where d is the step of progression and n is the number of the member of progression.Let a1, a1+d, a1+2d,..., a1+(n-1)d - members of an arithmetic progression. Their arithmetic mean is equal to S = (a1+a1+d+a1+2d+...+a1+(n-1)d)/n = (na1+d+2d+...+(n-1)d)/n = a1+(d+2d+...+(n-2)d+(n-1)d)/n = a1+(d+2d+...+dn-d+dn-2d)/n = a1+(n*d*(n-1)/2)/n = a1+dn/2 = (2a1+d(n-1))/2 = (a1+an)/2. Thus the arithmetic mean of members of an arithmetic progression is equal to the arithmetic mean of its first and last members.

4

It is also true the property that each member of an arithmetic progression is equal to the average between the previous and the next member of the progression: an = (a(n-1)+a(n+1))/2 where a(n-1), an, a(n+1) successive members of the sequence.

Note

To find the arithmetic mean of several numbers is to be folded between them. Thereafter, the resulting amount will be divided by the number of terms. To make it clearer, let's look at how to find average of numbers, for example: 78, 115, 121 and 224. The arithmetic mean of several numbers found using Excel.

Useful advice

The calculated value is called arithmetic average or just average. Definition. The average of several numbers is the number equal to the ratio of the sum of these numbers to their number. Not only arithmetic mean shows where on the number line are the numbers of some set. Another indicator is the median a number that separates this set into two parts of equal size. Explain with examples how to find the median of various sets of numbers.

# Advice 5 : How to calculate arithmetic mean

**The average**value is one of the characteristics of a set of numbers. Is a number that cannot go beyond the range defined by the largest and smallest values in this set of numbers.

**The average**arithmetic value is the most commonly used kind of average.

Instruction

1

Add up all numbers and divide them by the number of terms to obtain the arithmetic mean. Depending on the specific conditions of calculations it is sometimes easier to divide each number by the number of a data set and sum the result.

2

Use, for example, included in the Windows calculator, if you calculate the average arithmetic value in mind is not possible. You can open it using run dialog programs. To do this, press the "hot keys" WIN + R or click start and select in the main menu the command "Run". Then type in the input box and press calc on the keypad Enter or click "OK". The same can be done via main menu - open it, go to "All programs" and in "Standard" and select "Calculator".

3

Enter the sequence number of the set, clicking on the keyboard after each one (except the last) the "Plus" key or by clicking the appropriate button in the calculator interface. To enter the numbers too as you can with the keyboard or clicking the appropriate button interface.

4

Press the slash (slash), or click the icon in the interface of the calculator after entering the last value sets and print the number of numbers in the sequence. Then press the equal sign and the calculator will calculate and display the arithmetic mean value.

5

It is possible for this purpose to use the table editor Microsoft Excel. In this case, run the editor and enter in the adjacent cell all values of the sequence numbers. If after entering each number, you press Enter or the down arrow key or the right, the editor will move the input focus into the next cell.

6

Select all entries and in the lower left corner of the editor window (in the status) will see the average value for the selected cells.

7

Click the following for the last entered number cell, if you do not enough only to see the arithmetical mean value. Open the drop-down list with the image of the Greek letter Sigma (Σ) in the group of commands "Edit" on the Home tab. Select the line "

**Average**" and the editor will insert the correct formula to calculate the arithmetic mean of the values in the selected cell. Press Enter and the value will be calculated.# Advice 6 : How to calculate average speed

To calculate the average

**speed**is not difficult. To do this, simply divide the length of the traversed path at a time. However, in practice and in solving problems sometimes arise further questions. For example, what is considered to be passed through? The speedometer or real displacement of the object? What is considered travel time if the object is half the time not really going anywhere? Without taking into account all these nuances it is impossible to correctly calculate the average speed.You will need

- a calculator or computer, speedometer

Instruction

1

To calculate the average speed of the uniform motion object, simply measure its speed at any point on the path. Since the speed is constant, then it will be average speed.

Even easier, this dependence looks as a formula:V CP=V, where

Vav – average speed, and

V – velocity of uniform motion.

Even easier, this dependence looks as a formula:V CP=V, where

Vav – average speed, and

V – velocity of uniform motion.

2

To calculate the average velocity of uniformly accelerated motion, find the arithmetic mean of initial and final speed. To do this, find the sum of these velocities and divide by two. The resulting number will be the average velocity of the object.

Graphically it appears in the form of the following formula:Vav = (Vкон + Vнач) / 2, where

Vav – average speed,

Vкон – end speed,

Vнач is the initial velocity.

Graphically it appears in the form of the following formula:Vav = (Vкон + Vнач) / 2, where

Vav – average speed,

Vкон – end speed,

Vнач is the initial velocity.

3

If you set the acceleration and initial speed and final speed are unknown, then convert the formula above as follows:

Since uniformly accelerated motion Vкон = Vнач + a*t where a is the acceleration of the object, and t is the time, we have:Vav = (Vкон + Vнач) / 2 = (Vнач + a*t + Vнач) / 2 = Vнач + a*t / 2

Since uniformly accelerated motion Vкон = Vнач + a*t where a is the acceleration of the object, and t is the time, we have:Vav = (Vкон + Vнач) / 2 = (Vнач + a*t + Vнач) / 2 = Vнач + a*t / 2

4

If, on the contrary, aware of the final velocity and acceleration of the body, but the initial speed is not set, convert the formula to the following form:Vav = (Vкон + Vнач) / 2 = (Vкон + Vкон - a*t) / 2 = Vкон - a*t / 2

5

If you set the length of the traversed body of the path and the time it took to walk this distance, you simply divide this way on elapsed time. That is, use the General formula:Vav = S / t where S is the total length of the traversed path.Time spent on the passage the path is, regardless, moving the object continuously or stop.

6

If the conditions of the problem are not specifically indicated what kind of average speed you need to calculate the implied average ground speed.

To calculate the average ground speed, takes the total length of the traversed path, i.e. its trajectory. If during the movement the object was returned to the passed waypoint (this distance is also taken into account. So, for example, for cars the length of the path required to calculate the average ground speed will correspond to the speedometer display (differences display).

To calculate the average ground speed, takes the total length of the traversed path, i.e. its trajectory. If during the movement the object was returned to the passed waypoint (this distance is also taken into account. So, for example, for cars the length of the path required to calculate the average ground speed will correspond to the speedometer display (differences display).

7

If you want to calculate the average speed (displacement), then the realized path implies that the distance at which the body really moved.

Because the movement always occurs in a certain direction, the offset (S) the magnitude of the vector, i.e. is characterized by direction and absolute value. Consequently, the value of the average drift velocity is the magnitude of the vector. In this regard, the solution of such problems make sure you ask: what kind of speed you want to calculate. The average ground speed, the numerical value of the average velocity or displacement vector average velocity displacement.

In particular, if the body is in motion returns to the starting point, it is considered that the average rate of displacement is equal to zero.

Because the movement always occurs in a certain direction, the offset (S) the magnitude of the vector, i.e. is characterized by direction and absolute value. Consequently, the value of the average drift velocity is the magnitude of the vector. In this regard, the solution of such problems make sure you ask: what kind of speed you want to calculate. The average ground speed, the numerical value of the average velocity or displacement vector average velocity displacement.

In particular, if the body is in motion returns to the starting point, it is considered that the average rate of displacement is equal to zero.

# Advice 7 : How to calculate the average number

From the point of view of mathematics the average

**number**may be**higher**exponential, quadratic, harmonic, weighted, logarithmic, etc. However, in practice, the average person often have to calculate simple arithmetic average value of some set of values. In General, this**average**number can be defined as a number between the largest and smallest numbers of the given sequence.Instruction

1

Put all the numbers of the original sequence, and then divide them by the total number of numbers to get

**the average**arithmetic value. If the task has an applied character, the result may need rounding to get the answer in the form of "half digger".2

If such a computation is ad-hoc, and the numbers in the source sequence is not much, for the practical calculation of the values you can use the calculator built into Google search or Nigma. Specify and enter the required mathematical operation in the search query box of the system. For example, if you need to find

**the average**number of goals conceded by CSKA in their last five games, enter the query: "(0+1+2+1+1)/5". The search result will show without you click send request.3

If the sequence numbers are not so small, it is better to use the tabular editor such as Microsoft Office Excel. Editor, you will be given a table to fill in values for the original sequence of numbers. This can be done entering the numbers manually, but if it is possible to copy and paste the numeric sequence in the text format, it will be much easier. In this case, preferably by using any text editor before copying replace all delimiters between values of a sequence to characters of a string - then after pasting into Excel, the values will line up in the column. If instead of end-of-string use the tab character, they will line up in a row.

4

Select the column (or row) that contains the entered values by clicking on its header. The arithmetic mean can be seen in the table below in the status bar.

5

If you only know this value is not enough, then use the formula to calculate the average. To do this, click the cell where you want to see the result, open the drop-down list on the button with the pictogramme the Greek letter Sigma Σ in the section "Edit". Select the list item 'Average', and then select the filled range of table cells and press Enter. Excel will calculate and display

**the average**value.