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 determine the average number

All the known numbers can be mentally laid out in a line, this line is called

**numerical**axis. It is located at the ascending of the mathematical values from minus infinity to plus infinity. And if you choose any two points, it is possible to determine by calculation how many will be between them, that is, to determine their**average**number.Instruction

1

First, it follows from these two numbers determine the minimum and maximum comparison. Then from the larger value to take less. Example. You need to determine

**the average**value between the numbers 14 and 76. Seventy-six more than fourteen. The difference between these numbers: 76-14=62, is sixty two.2

If is

**the average**value between numbers with different modules (positive and negative), then the difference should be found by the rule of subtracting numbers with different signs: from the larger number to take less and put the answer the sign of the larger number. Example: the difference between the numbers -3 and 6 to find how |6-3|=3 and assign the answer to a plus sign.3

Then, the obtained difference is divided by the number of integers among which the need to find

**the average**value. Defined in the above example**, the average**value is between two numbers, then finding the average value should be found to split the difference, equal to sixty-two by two. It turns out, 62/2=31. Answer:**the average**between the numbers fourteen and sixty-two is the number thirty-one. It is located on the**numeric**axis exactly between these values.# Advice 5 : 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 6 : How to calculate average value

In mathematics and statistics

**average**arithmetic mean (or**average**) of a set of numbers is the sum of all numbers in the set divided by the number of them. The arithmetic mean is the most common and the most common concept of average.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 7 : 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 8 : How to calculate average speed

Calculate your average speed is very simple. It is sufficient to divide the length traveled by the body the way in elapsed time. However, in practice, as well as at the decision of physical tasks, consider some of the nuances of the movement.

You will need

- calculator.

Instruction

1

The easiest way to calculate the average velocity of uniform motion of a body on some part of the way. Since the rate on the whole interval of motion does not change, it will be equal to the average speed. As a formula this can be written as follows:

Vav = Vрд, where Vav – average speed, and Vрд – speed of uniform movement on a certain site.

Vav = Vрд, where Vav – average speed, and Vрд – speed of uniform movement on a certain site.

2

To calculate the average speed of the uniformly accelerated (ravnokonechnogo) motion on a plot fold the final and initial speed. Then divide the result by two. The resulting quotient will be the average speed. More clearly, it looks as a formula:

Vav = (V + VN) / 2, where Vav – average velocity, V – final velocity, VN is the initial velocity.

Vav = (V + VN) / 2, where Vav – average velocity, V – final velocity, VN is the initial velocity.

3

If the final speed is unknown, but given the initial speed and acceleration, use the following version of the above formula:

Since uniformly accelerated motion V = VN + a * t where a is the acceleration, then:

Vav = (V + VN) / 2 = (VN + a * t + VN) / 2 = VN + a * t / 2

Since uniformly accelerated motion V = VN + a * t where a is the acceleration, then:

Vav = (V + VN) / 2 = (VN + a * t + VN) / 2 = VN + a * t / 2

4

If you know the final speed and acceleration, but not set the initial velocity, we convert the above formula to the following form:

Vav = (V + VN) / 2 = (V + V - a * t) / 2 = V - a * t / 2

Vav = (V + VN) / 2 = (V + V - a * t) / 2 = V - a * t / 2

5

If you know the length of the traversed body of the path and the time taken to walk this path, to calculate the average speed divide the distance traveled at the time. That is, use the formula:

Vav = S / t where S is the traversed path length.

In this case, note that the time necessary to consider fully, regardless of the object stayed in the passing phase or not.

Vav = S / t where S is the traversed path length.

In this case, note that the time necessary to consider fully, regardless of the object stayed in the passing phase or not.

6

Unless otherwise specified, then the average rate means the average ground speed. In its calculation under the means that is passed through the length of the path of movement of the body. If the body is in the process of moving back to completed items, such areas are also taken into account (added) to the total path length.

7

If you want to find the average travel speed as the parameter S take the distance which the object has moved in time t. Because the movement occurs in a certain direction, the value of S in this case a vector, i.e. in addition to absolute values, characterized by a more and direction. Accordingly, the value of the average rate of displacement is a vector quantity. Therefore, before solving the problem it is necessary to specify what speed you want to calculate: average travel speed, average travel speed, or simply the absolute value of the average rate of displacement.

By the way, if an object in motion will return to the starting point, his average speed will be equal to zero.

By the way, if an object in motion will return to the starting point, his average speed will be equal to zero.

# Advice 9 : How to calculate average value

To calculate the average

**value**when there are multiple different values may be necessary in work, studies or everyday life. Average values are often used to generate statistics so you can learn, for example, the average income per capita or the average cost of vegetables in Russia.You will need

- a sheet of paper
- handle

Instruction

1

Average in mathematics called "arithmetic mean". In order to calculate the arithmetic mean, for a start write down all your numbers on a sheet of paper.

2

This method is often used in educational institutions for the issuance of quarter grades. For example, the success of the student Vasi Pugovkin in mathematics was extremely doubtful until the teacher was called into school by his parents. Dad did the Bob suggestion, and by the end of the quarter Bob Pugovkin corrected. Look at Wasini assessment: 2 3 3 2 4 4 5 4. That will put teacher Bob for a quarter?

3

The average arithmetic mean calculated by the formula: the sum of all numbers divided by the number of numbers. Add up all the numbers between them. 2+3+3+2+4+4+5+4 = 27.

4

Divide the resulting number by the number of Wusinich assessments. 27 divided by 8 equals 3.375. That number is closer to three than to four. Then, the teacher will have to put the Bob the three, despite his recent successes. However, if Bob Pugovkin will get another five, the score will be controversial, as 32:9 is approximately equal to 3.5.

Note

It is important to remember that if the numbers to multiply, not add, you need to use the geometric, not the arithmetic mean. The most common confusion arises when calculating the return on investment in Finance.

Caution should be when calculating data such as phases or angles. For example, a naive computation of the arithmetic mean of 1° and 359° yields a result of 180°, which is incorrect.

Caution should be when calculating data such as phases or angles. For example, a naive computation of the arithmetic mean of 1° and 359° yields a result of 180°, which is incorrect.

Useful advice

When rounding numbers, remember that the number is rounded depending on the digits after the decimal point. If the digit after the decimal point more than five, the number is rounded in favor of the more; if less, in favor of a smaller. In addition, all digits after the decimal point more than five "I" unit of the previous figure. Due to this, the number of 3.57, for example, is approximately equal to 3,6 and 3,6 can be rounded up to four.

# Advice 10 : 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 11 : 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.# Advice 12 : How to find average time

While the regulation of working time is a quantity surveyor needs to know how many minutes or seconds it takes to execute the same operation. While productivity may be different even among people with the same qualifications. For calculations is taken to be the average time required to perform this operation.

You will need

- - stopwatch;
- calculator;
- - a computer with Microsoft Excel.

Instruction

1

Several times note the time, which are one and the same process. For example, how many all unit employees perform the same operation. Record the results.

2

For convenience, put the result in seconds. Don't forget that the time is not calculated in decimal, but in shestidesyatye system.

3

Divide the result by the number of employees performing this operation. This will be average time. For the determination of rules usually are using this method. It is possible to calculate the average time required for this assignment the specific qualifications.

4

In school textbooks in mathematics often found the task a bit of a different kind, but also on the calculation of the average time. For example, when an employee performs during the day several different operations, you need to calculate how much average time it spends on each. Surgery can be of different complexity. Note the time that the employee spends on all operations. Divide the result by the number of jobs.

5

To calculate the average time it allows the program Microsoft Excel. This can be done in two ways. For example, to convert all values to seconds, to fold and divide the sum by the number of measurements, i.e. to perform an action in the same way as in the previous method.

6

When using the software does not necessarily convert the time into smaller units. The program allows you to operate the formula CC.MM.SS. Transmit the data to the table, in the cells in one column or in one row. Select the cell under the numbers if they are written in a column, or right.

7

Look in the top menu of the home tab, and "Edit". In the option "Amount", select "Average".

8

It may be so that the total amount of time intervals will be longer than 24 hours. In this case you need to change the format of the resulting cells. This is done through the top menu. Find the tab "Format" and "Cells". Find consistently the option of "Number" and "Time" and set 37:30:55.