Numerical values of quantities in the text must be indicated with the required degree of accuracy, while in a series of quantities it is necessary to align the number of decimal places. It is unacceptable to give the following series of values: 10; 20; 16.7; 13.14. This series should look like this: 10.00; 20.00; 16.70; 13.14. The text of the work should not contain values in which the number of significant figures is more than three. 86.7897 should not be specified. For use in the text of the work, it is better to round the value to 86.8. It’s even better if the values are expressed in whole numbers. Therefore, in economic calculations, percentages expressed in whole numbers are more often used, which provide sufficient accuracy, and when describing socio-economic processes, per milles are used.
In the text of the work, numerical values of quantities with the designation of units of physical quantities and units of counting should be written in numbers, and a number without designation of physical quantities and units of counting from one to nine should be written in a word. For example: “The selection of documents is carried out five times, and the total amount for monetary documents must be at least 9 rubles.”, “The selection is carried out 15 times.” It is unacceptable to separate a unit of physical quantity from a numerical value (transfer them to different lines or pages), except for units of physical quantities placed in tables.
If the text to characterize an indicator provides a range of numerical values expressed in the same units of measurement, then the measurement units are indicated after the last numerical value of the range, for example: “the number of overpayments in the amount of 100 to 500 rubles.”
If the text of the work contains a number of numerical values expressed in the same units of measurement, then the units of measurement are indicated only after the last numerical value, for example: “200, 300, 4000 rubles.”
Conventional letters, images or signs must comply with those adopted in current legislation or state standards.
Rules for applying formulas
The text of the work usually uses mathematical formulas using the designation of parameters. Before designating the parameter, give its explanation, for example: “pair correlation coefficient r”. Formulas must have continuous numbering in Arabic numerals, which are written at the formula level on the right in parentheses. One formula is designated “(1)”. Numbering of formulas within a chapter of a thesis or coursework question is allowed. In this case, the formula number consists of the chapter or question number and the formula number, separated by a dot, for example: “(3.1)”. References in the text to serial numbers of formulas are given in parentheses, for example, “...in formula (1).”
Explanations of the symbols included in the formula should be given directly below the formula. The values of each character are given on a new line in the order in which they are given in the formula. The first line of the transcript should begin with the word “where” without a colon after it, for example:
where r is the pair correlation coefficient;
X Y- the average value of the product of the factor and the indicator;
* - average value of the indicator;
U - average factor value;
<т, - среднеквадратическое отклонение показателя; - среднеквадратическое отклонение фактора.
It is allowed to move the formula to the next line only on the signs of the operations being performed. In this case, the used character is repeated at the beginning of the next line. When transferring a formula to the multiplication sign, use the “x” sign. The order of presentation of mathematical equations in the text of the work is the same as the formulas.
Each of us has our own unique word (usually the number of the full name), which corresponds to a certain number. And it has an impact on our lives.
It is known that all letters of the Russian alphabet occupy a strictly defined place and correspond to their serial number, that is:
A – 1, A – 1, B – 2, C – 3, D – 4, D – 5, E – 6, E – 7, F –8, G – 9, I – 10, J – 11, K – 12, L – 13, M –14, N – 15, O – 16, P – 17, R – 18, S – 19, T – 20, U – 21, F – 22, X – 23, C – 24, H – 25, W – 26, Sh – 27, b – 28, Y – 29, b – 30, E – 31, Yu – 32, Z – 33.
For example, let’s define the code for the word “language” (in this case, language is a means of communication), summing up all the serial numbers of the letters, we get the number 83.
The word “number” itself is associated with the same mathematical meaning.
Language: 33 + 9 + 29 + 12 = 83.
Number: 25 + 10 + 19 + 13 + 16 = 83.
The word “numerology” and the phrase “Count all words” also have the same code in total – 116. Num er o l ogy: 15 + 21 + 14 + 6 + 18 + 16 + 13 + 16 + 4 + 10 + 33 = 116.
Reading words: 19 + 25 + 10 + 20 + 1 + 11 + 3 + 19 + 6 + 19 + 13 + 16 + 3 + 1 =116.
If each letter of the Russian alphabet is assigned a numerical value from 1 to 9, then any phrase - be it a first name, surname or just a phrase - is decomposed into simple numbers, adding which we get a certain resulting number that determines the nature of what was said.
To characterize a person in the modern Russian alphabet, the correspondence of letters to numbers (from 1 to 9) is distributed as follows:
1 - A, I, S, B.
2 – B, J, T, Y.
3 - V, K, U, L.
4 – G, L, F, E.
5 – D, M, X, Yu.
6 – E, N, C, Y.
7 – E, O, Ch.
8 – J, P, Sh.
9 – Z, R, Shch.
Currently, there are generally accepted characteristics for numbers from 1 to 9: 1 – unity, creativity, independence;
2 – duality, appearance;
3 – power, authority, productive force;
4 – solidity, hardness, dullness;
5 – sensuality, pleasure;
6 – perfection, harmony, balance;
7 – mysticism, mediumship, magic;
8 – materialism, success, justice;
9 – spirituality, mental achievements.
People whose names correspond to the numbers 11 and 22 are believed to be very spiritually developed. These numbers cannot be reduced to one digit. For example, in the name Ivan the letters correspond to the following numbers: I=1, B=3, A=1, H=6. Sum of numbers: 1 + 3 + 1 + 6 = 11. In accordance with the rule, the number 11 does not add up, and its value determines a highly developed and spiritual personality.
Words we don't need
Let's calculate some words and phrases that we are used to using in ordinary speech, let's try to determine whether they are compatible with the number of your name and your birth. For convenience, we repeat the table with which you can perform the calculation:
1 - A, I, S, B.
2 – B, J, T, Y.
3 - V, K, U, L.
4 – G, L, F, E.
5 – D, M, X, Yu.
6 – E, N, C, Y.
7 – E, O, Ch.
8 – J, P, Sh.
9 – Z, R, Shch.
Now let’s try to find the code for the word “count”: 8 + 9 + 1 + 3 + 1 + 6 + 3 = 3 + 1 = 4. The number 4, on the one hand, is ruled by Mercury, which is responsible for sociability and communication. On the other hand, it is the number of obligations assumed. Thus, by saying “guess” to someone, we actually force the interlocutor to take part in the conversation and force him to commit to some action. That is, “pretending.” Think for yourself, how pleasant is such a responsibility for your partner?
Let’s break down the word “tin”: 8 + 6 + 1 + 2 + 3 = 2 + 0 = 2.
In numerology, the main disadvantage of two is that it expresses self-doubt and eternal hesitation. By saying the word “tin”, we thus express our feelings. But at the same time they are rather negative in nature.
Numerology is an interesting science that will open the doors to the mysterious world of the mystery of the name. We all know that a person’s name has an impact on the fate and character of its bearer. Numerology calculated by date of birth and name will be able to show its true meaning, show the hidden talents and inclinations, aspirations of a person.
Table of correspondence between name letters and numbers:
|
Number |
Letters |
For example, let’s calculate the name “Tatyana”:
As a result, we get 2+1+2+3+6+6+1= 21, we will reduce this figure to the simple number 2+1=3.
It turns out the number of the name "Tatiana" - 3.
Have you already found out your name number? Let's find out what this number means.
Having calculated numerology by date of birth and name, let’s summarize the results of the calculation:
1. The numerology of this person’s name is rooted in leadership. A person with such a name number is ambitious, ambitious, energetic, courageous, and confident in his abilities. Such people need to occupy leadership positions or run their own business.
2. The person is active, but he needs the help of a partner. People of number 2 are peace-loving, they are oriented towards family values, such people get along well in teams. They need to find themselves in working with people; their professions are teachers, doctors, psychologists.
3. Threes are talented, well-rounded people who love to be the center of attention. They are great optimists, often the life of the party. Their strong point is the world of art, so they will make excellent writers, singers, musicians, and speakers.
4. Stability, reliability, honesty are the main features of fours. Such people are workaholics, prone to painstaking, responsible work, they are very punctual. Fours are excellent accountants, architects, and engineers.
5. Extraordinary, independent people with their own outlook on life. Numerology says about such people that they are not afraid to plunge into the abyss of novelty; they easily abandon outdated stereotypes. Fives constantly strive for intellectual development. Such people will be comfortable working in tourism, law, and journalism.
6. Sixes have a heightened sense of justice, honesty, and responsibility. They are very demanding of themselves, for which they are respected by others. They can be entrusted with any business that requires trust and responsibility. The professions of those with names with the calculated number “1” are social workers, educators, and doctors.
7. Such a person constantly strives for knowledge, he will collect, check whether theory corresponds to practice, and at the same time loves to share knowledge with others. Since Sevens do not really like physical labor, their professions are philosophers, scientists, and inventors.
8. Eights require attention and recognition. They are in constant pursuit of new victories and achievements. Such people are practical and seek benefits always and everywhere, while expecting recognition in their deeds. The ideal habitat for Eights is finance, commerce, administration, and construction.
9. Man-harmony. He is kind, patient and strives for peace. Such people usually defend the rights of the disadvantaged, they are for world peace. Person Nine will always come to your aid in difficult times. Professions of nines are teachers, nurses, social workers, writers.
We hope that we have lifted the veil of secrecy associated with the calculation of name numerology. Check your name and you might learn something new about yourself.
The word is not a sparrow; if it flies out, you won’t catch it. Before you send any phrase “in flight, make sure that you are not releasing negative energy into the Universe. Often even seemingly harmless words have it...
Everything we say has a certain vibration. Backed by strong emotions, words can materialize - and bring both joy and sorrow.
Calculate the energy of the words that you often use and think: is it time for you to “cleanse” your speech?
In the Russian alphabet, each letter corresponds to a specific number:
1 - A, I, S, B,
2 - B, J, T, S,
3 - V, K, U, b,
4 - G, L, F, E,
5 - D, M, X, Yu,
6 - E, N, C, I,
7 - Yo, Oh, Ch,
8 - F, P, Sh,
9 - 3, R, Shch.
Add up all the numbers in the word or expression whose energy you want to know, and reduce the sum to a simple number. For example, the word “okay” (4+1+5+6+7=23. 2+3=5) has the vibration of five.
1. The unit “shows character.” It is a symbol of leadership, ambition, risk and selfishness. Words endowed with the energy of the number 1 often carry a fairly strong negative message. For example, by saying the expression “wow,” you let the Universe know that you don’t need anything. By saying the word of refusal “dismiss”, you fill the space with negative vibrations. The word “war” and the expression “not in life” also have “single” energy.
2. The energy of two is unifying and entirely positive. She charges the words with enthusiasm, warmth and love: “I love”, “God has had mercy”, “wealth”, “welcome”. The word “great” has the same energy - it’s worth saying it more often instead of the popular “cool” (number b) and “cool” (number 5).
3. Three has very strong energy and symbolizes the fulfillment of desires. By pronouncing words with the energy of three, you literally doom them to materialization: “thank you,” “good,” “dear.” Be careful about negative phrases - “threes”, try to pronounce them as rarely as possible (for example, “never in your life”).
4. Four is a symbol of a healthy body, physical strength and beauty. Words - “fours” can affect you and your life in different ways. Everything will depend on what emotions you put into them. For example, the words “I can’t” and “don’t” represent your physical impotence, refusal of good health and good mood. The words “gloriously” and “endlessly” also have the energy of the four. When admiring the appearance of a person or object, say “wow” or “lovely” - they carry a stronger positive charge.
5. Five is associated with home, family, human development, and life planning. This is a symbol of new knowledge, travel, activity, dynamics. It is better not to use negative phrases - “fives” in this sense: “mess”, “enough”, “don’t like”, “better not.” By saying them, you will not achieve positive changes in the area of responsibility of the five.
6. Six denotes hard work on the path to prosperity. It symbolizes the process of achieving a goal at any cost without regard to one’s own health and state of mind. A clear confirmation of this is the words “nightmare” or “no way.” By assessing what is happening with their help, you send a negative impulse into your own life. If you often pronounce the word “six” “of course”, you risk not achieving your dream. Replace it with the energetically more positive “definitely.”
7. Seven carries the energy of luck, success, and happiness. By pronouncing words in which the vibration of the number 7 is concentrated, you tune the Universe to a favorable attitude towards you. These words include “good” and “excellent.” The energy of the seven is also carried by the word “money”.
8. The number eight as a symbol of infinity gives words positive energy. The word “hello” is just one of its ranks. By greeting someone this way, you wish the person endless health. Based on the sum of the letters, the word “money” also appears in the eight team. By saying it often, you program the space so that your financial source never runs out. The number eight is also a symbol of responsibility and duty. When agreeing to fulfill a request, instead of “yes” (six is negative energy), say “definitely”, and the energy of the eight will help you achieve your goal.
9. Nine is the number of strength and belligerence. Words endowed with the energy of the number 9 remain in the memory of the Universe for a long time. It is difficult to come up with an expression that has a more negative charge than “only over my corpse.” The word “never” also carries extremely negative energy. Think carefully before you swear, otherwise you risk regretting what you said. It is interesting that the word “truth”, which can both heal and wound, gives a nine by the sum of its letters. If you say “truth” (three) instead, then your words will very soon come true.
§ 6. Numerical and letter expressions. Formula
Addition, subtraction, multiplication, division - arithmetic operations (or arithmetic operations). These arithmetic operations correspond to the signs of arithmetic operations:
+ (read " plus") - sign of the addition operation,
- (read " minus") is the sign of the subtraction operation,
∙ (read " multiply") is the sign of the multiplication operation,
: (read " divide") is the sign of the division operation.
A record consisting of numbers interconnected by arithmetic signs is called numerical expression. Numerical expressions may also contain parentheses. For example, entry 1290 : 2 - (3 + 20 ∙ 15) is a numeric expression.
The result of performing actions on numbers in numerical expression is called the value of a numeric expression. Performing these actions is called calculating the value of a numeric expression. Before writing the value of a numerical expression, put equal sign"=". Table 1 shows examples of numerical expressions and their meanings.
Table 1
A record consisting of numbers and small letters of the Latin alphabet interconnected by signs of arithmetic operations is called literal expression. This entry may contain parentheses. For example, record a+b - 3 ∙c is a literal expression. Instead of letters, you can substitute various numbers into a letter expression. In this case, the meaning of the letters may change, so the letters in the letter expression are also called variables.
By substituting numbers instead of letters into the literal expression and calculating the value of the resulting numerical expression, they find the meaning of a literal expression for given letter values(for given values of variables). Table 2 shows examples of letter expressions.
A literal expression may have no meaning if substituting the values of the letters results in a numeric expression whose value cannot be found for natural numbers. This numerical expression is called incorrect for natural numbers. It is also said that the meaning of such an expression is “ undefined" for natural numbers, and the expression itself "doesn't make sense". For example, the literal expression a-b does not matter when a = 10 and b = 17. Indeed, for natural numbers, the minuend cannot be less than the subtrahend. For example, if you have only 10 apples (a = 10), you cannot give away 17 of them (b = 17)! Table 2 (column 2) shows an example of a literal expression. By analogy, fill out the table completely.
table 2
For natural numbers the expression is 10 -17 incorrect (does not make sense), i.e. the difference 10 -17 cannot be expressed as a natural number. Another example: you cannot divide by zero, so for any natural number b, the quotient b: 0 undefined.
Mathematical laws, properties, some rules and relationships are often written in literal form (i.e., in the form of a literal expression). In these cases, the literal expression is called formula. For example, if the sides of a heptagon are equal a,b,c,d,e,f,g, then the formula (literal expression) to calculate its perimeter p has the form: 
p =a+b+c +d+e+f+g
With a = 1, b = 2, c = 4, d = 5, e = 5, f = 7, g = 9, the perimeter of the heptagon p = a + b + c + d + e + f + g = 1 + 2 + 4 + 5 +5 + 7 + 9 = 33.
With a = 12, b = 5, c = 20, d = 35, e = 4, f = 40, g = 18, the perimeter of the other heptagon is p = a + b + c + d + e + f + g =12 + 5 + 20 + 35 + 4 + 40 + 18= 134.
Block 6.1. Dictionary
Compile a dictionary of new terms and definitions from § 6. To do this, write words from the list of terms below in the empty cells. In the table (at the end of the block), indicate the numbers of the terms in accordance with the numbers of the frames. It is recommended to carefully review § 6 before filling in the cells of the dictionary.
4. The result of performing actions on numbers in numerical expression.
- The value of a numeric expression that is obtained by substituting variables into a literal expression.
- A numeric expression whose value cannot be found for natural numbers.
10.A numerical expression whose value for natural numbers can be found.
- An alphabet whose small letters are used to write alphabetic expressions.
List of terms and definitions
Answer table
Block6 .2. Match
Match the task in the left column with the solution in the right. Write your answer in the form: 1a, 2d, 3b...
IN option 1
IN option 2
Block 3. Facet test. Numeric and alphabetic expressions
Facet tests replace collections of problems in mathematics, but differ favorably from them in that they can be solved on a computer, the solutions can be checked, and the result of the work can be immediately found out. This test contains 70 problems. But you can solve problems by choice; for this there is an evaluation table, which indicates simple tasks and more difficult ones. Below is the test.
- Given a triangle with sides c,d,m, expressed in cm
- Given a quadrilateral with sides b,c,d,m, expressed in m
- The speed of the car in km/h is b, travel time in hours is d
- The distance traveled by the tourist in m hours is With km
- The distance covered by the tourist, moving at speed m km/h is b km
- The sum of two numbers is greater than the second number by 15
- The difference is less than the one being reduced by 7
- A passenger liner has two decks with the same number of passenger seats. In each of the rows of the deck m seats, rows on deck on n more than seats in a row
- Petya is m years old, Masha is n years old, and Katya is k years younger than Petya and Masha together
- m = 8, n = 10, k = 5
- m = 6, n = 8, k = 15
- t = 121, x = 1458
- The meaning of this expression
- The literal expression for the perimeter is
- Perimeter expressed in centimeters
- Formula for the distance s traveled by a car
- Formula for speed v, tourist movement
- Formula for time t, tourist movement
- Distance traveled by the car in kilometers
- Tourist speed in kilometers per hour
- Tourist travel time in hours
- The first number is...
- The subtrahend is equal to...
- Expression for the largest number of passengers that a liner can carry in k flights
- The largest number of passengers that an aircraft can carry in k flights
- Letter expression for Katya's age
- Katya's age
- The coordinate of point B, if the coordinate of point C is t
- The coordinate of point D, if the coordinate of point C is t
- The coordinate of point A, if the coordinate of point C is t
- Length of segment BD on the number line
- Length of segment CA on the number line
- Length of segment DA on the number line
Answers (equal, has the form, undefined):
a)1; b)s=b∙d; at 9; d) 40; d)b+c +d+m; e) 7; g) the expression does not make sense (incorrect) for natural numbers; h) 2 ∙m (m+n) ∙k; And) (m+n) -k; j) 6; l) 15; m) 3760; m)t - 3; o) the figure cannot be a triangle; n) 22; R) t - 3 ∙ 7; c) 0; t) 32; y) 59600; t) 6019; x) 2880; v) 10378; h)1440; w) you cannot divide by zero; y) 13; s) 1800; e) 496; u) 2; i) 12; aa) 14; bb) 5; cc) 35; dd) 79200; her) 1900; LJ) 118; zz) 18; ii) 12800; kk) 98; ll) 1458; mm) v =c:m; nn) 100; oo) 19900; pp)t =b:m; pp) 2520; ss)c +d+m; tt)x; yy) 1579; ff)t+2; xx) 10206; cc) 135; hh)t + 2 ∙ 7; shsh) 7 ∙x; schshch)x - 2; ыы) 7 ∙x - 2 ∙ 7; uh)t+x ∙ 7; yuyu) 10192; yaya)t+x; aaa) 123; bbb) 1456; www) 10327.
TEST INDICATORS. Number of tasks 70, completion time 2 - 3 hours, total points: 1 ∙ 22 + 2 ∙ 24 + 3 ∙ 24 = 142. For the facet test, you can use the following rating scale.
Educational game "Dungeon Treasures"
On the playing field is an illustration for R. Kipling’s book “Mowgli”. Five of the chests have padlocks, and on their reverse sides the number of points the team gets if they manage to “open the chest” is indicated. This number is different for each of the chests: for wooden - 1 point, for tin - 2, for copper - 3, for silver - 4, for gold - 5. To open the chest, you must complete the “White Cobra task”.
The task is common to all chests
Read how the money in each chest was spent and write a letter expression for that money. Then substitute the values of the variables and calculate the amount of money that was in the chest at first. This number must be entered in the response of the computer version of the game. The answers are under lock and key!
Wooden chest. Was purchased A books for 50 rubles, b paintings at a price of 250 rubles, d chairs for 300 rubles. There are 250 rubles left in the chest. Variable values: a = 40, b = 8, d = 20.
Tin chest.
It was purchased to renovate the school d kg of paint for 120 rubles, k bags of cement at a price of 200 rubles, m lamps at a price of 280 rubles. There was still a sum of money left in the chest, just like in a wooden chest, but rounded up to the nearest thousand. Values 
variables: d= 12, k = 16, m = 25.
Copper chest. From this chest they took the amount of money in the tin chest, rounded to hundreds. If you add 5,200 rubles to it, then with this money you can buy m tables by price n rubles and 5 computers for the price R rubles Variable values: m = 10,n= 400 (rubles), p = 6000 (rubles).
Silver chest.
From the silver chest they took an amount of money equal to the amount of money in the copper chest rounded to the nearest thousand. Then they reported 12,000 rubles and bought x microscopes by price y rubles and r
chemical kits by price z rubles .
Variable values: x = 15, y = 8600 (rub), r = 16, z = 1500 (rub).
Golden chest. With the money from this chest, the mathematics classroom was repaired, which took an amount of money equal to the money in the silver chest. With the remaining money it was planned to buy for the gym: mats at a price r ( rubles) , the balls are not p( rubles), sports uniforms at a price z(rubles). Each of the items k things . However, the price of the ball and uniform increased by m rubles Therefore, I had to take out 5,200 rubles on credit. Variable values: k = 20, r = 3200, m = 200, p = 400, z = 1200.
iʞwɐε ɐн imıqw doɔdʎʞ ǝɯɓǝʚɐн wɐҺɐɓɐε ʞ ıqɯǝʚɯо qɯɐнεʎ ıqƍоɯҺ
Educational game "Leopold the cat's lessons"
Fatty and Genius set up ambushes in various places on the playing field; they are numbered on the field. There are five ambushes in total. Hover your cursor over the ambush number and receive tasks. Enter your answers into the windows on the screen. If the answers are correct, then the ambush has been found, and the mice ask Leopold for forgiveness. In case of an error, the game must be repeated.
Trap No. 1
Identify each of the unshaded shares and enter the answer. Use slashes to write fractions. For example: 1/2, 1/3, 1/4, etc.
Trap No. 2
Convert to Arabic numerals and solve: 
- IX+III = ?
- VI - IV = ?
- II + X1 = ?
- X - V = ?
|
Trap No. 3 Solve the chain
Substitute the values of the variables in your answer. At what value of the variable a is the literal expression 4 ? |
Trap No. 4 Solve the chain
4 becomes incorrect if all variables are natural numbers ? |
Trap No. 5 Solve the chain
Substitute the values of the variables in your answer. At what value of the variable with literal expression 4 becomes incorrect if all variables are natural numbers ? |
Answers to the game "Leopold's Lessons"
Trap 1: 1/2, 1/3, 2/3, 7/8.
Trap 2. 12, 2, 13 5.
Trap 3. 6
Trap 4. 15.
In medicine and healthcare, signs expressed by numbers are often used, which can take on different numerical values in different units of the population, often repeated in several units. In each given population and in these specific conditions, this feature is characterized by a certain value (level), which differs from the value of this feature in another population, in the presence of other conditions. Pulse, blood pressure, body temperature, duration of temporary disability, length of hospital stay differ (vary) in patients even with the same diagnosis.
The value of the studied characteristic can take either discrete (discontinuous) or continuous numerical values. Examples of discrete quantities in which the values are expressed as integers: the number of children in the family, the number of patients in the ward, the number of bed days, the number of any medical devices in the institution, pulse. Examples of continuously changing quantities, when the values are expressed in fractional quantities, can gradually transform into one another: height, body weight, temperature, blood pressure.
The values obtained during the study are first recorded chaotically, that is, in the order in which the researcher receives them. A series in which the ordering and the corresponding frequencies are compared (by degree of increasing or decreasing) is called variational. Individual quantitative expressions of a characteristic are called options(V), and the numbers showing how often these options are repeated are frequencies(R).
For a generalized numerical characteristic of the characteristic being studied in a population of subjects, average values are calculated, the advantage of which is that one value characterizes a large set of homogeneous phenomena.
There are several types of averages: arithmetic average, geometric average, harmonic average, progressive average, chronological average. In addition to the indicated averages, sometimes special averages of a relative nature - mode and median - are used as generalizing values of a variation series.
Fashion (Mo) is the most frequently repeated option. Median (Me) - the value of the variant dividing the variation series in half; on either side of it there is an equal number of options.
The most commonly used is the arithmetic average. The arithmetic mean, which is calculated in a variation series, where each option occurs only once (or all options occur with the same frequency) is called simple arithmetic mean. It is determined by the formula:
M - arithmetic mean;
V- the value of the variational characteristic;
n is the total number of observations.
If one or more options are repeated in the series under study, then the weighted arithmetic mean is calculated. In this case, the weight of each option is taken into account and the greater the frequency of a given option, the greater its influence on the arithmetic average. This average is calculated using the formula.