More meanings of the word and translation of ORDERED SERIES from English into Russian in English-Russian dictionaries.
What is and the translation of ORDERED SERIES from Russian into English in Russian-English dictionaries.

More meanings of this word and English-Russian, Russian-English translations for ORDERED SERIES in dictionaries.

  • ORDERED - adj. ordered, simply ordered, ranked; partially ordered, partially ordered; incompletely ordered, partially ordered
    Russian-English Dictionary of the Mathematical Sciences
  • ORDERED – Trimmed
  • ORDERED – Square
    Russian-American English Dictionary
  • ROW - Row
    Russian-American English Dictionary
  • ROW - 1. row; line row after row, behind a row row - row upon row row of vehicles - line of vehicles 2. ...
    English-Russian-English dictionary of general vocabulary - Collection of the best dictionaries
  • ORDERED - cosmic, well-ordered
  • ROW - 1. row; ~ row of chairs; ~ behind ~th row upon row; 2. (line) file; 3. (seats in the theater, ...
    Russian-English dictionary of general topics
  • RANGE - 1) catena 2) range 3) row 4) sequence 5) series 6) set
    New Russian-English biological dictionary
  • ROW
    Russian-English dictionary
  • ROW - m. 1. row; line row after row, row after row - row upon row row of vehicles - line of vehicles...
    Russian-English Smirnitsky abbreviations dictionary
  • SERIES - catena, family, series, set, train, variety, row
    Russian-English Edic
  • ORDERED
  • RANGE - chain, series math., range, rank, row, string, train, variety
    Russian-English dictionary of mechanical engineering and production automation
  • ROW - husband. 1) row; line 2) military (in service) file, rank 3) (certain quantity) series units. and many more h...
    Russian-English short dictionary on general vocabulary
  • ORDERED - ranked
  • RANGE - catena, (masonry, tiled roofing) course, family, (brickwork) layer, range, rank, row, series, suite architect., train, variety
    Russian-English dictionary on construction and new construction technologies
  • ORDERED – square
  • RANGE - range, rank, round, series, set, string, variety
    Russian-English economic dictionary
  • ROW - see. It is not the ranks that are thinning, but the Jews that are thinning; see Two Jews sat down in three rows
    English-Russian-English dictionary of slang, jargon, Russian names
  • ROW - 1. row; ~ row of chairs; ~ behind ~th row upon row; 2. (line) file; 3. (seats in the theater, cinema, etc.) ...
    Russian-English Dictionary - QD
  • ORDERED - . The vectors , are ordered sets of numbers. . Crystalline ice consists of a very orderly pattern of H…
  • ROW - I see also. one of ~a; by... in each ~y; series; power ~ by; whole …
    Russian-English scientific and technical translator dictionary
  • ROW - m. bank - thermal row of the spark plug
    Russian-English automobile dictionary
  • ORDERED
  • RANGE - 1) family 2) range 3) row 4) sequence 5) series
    Russian-English explanatory dictionary terms and abbreviations for VT, Internet and programming
  • RANGE - see in a number of cases; have a number of advantages; will help solve a number of problems; a whole series; syn. large number …
    Russian-English dictionary of idioms on astronautics
  • RANGE — range, TGF ranging from 10 ng/ml to 0.1 ng/ml
    Russian-English biological dictionary
  • ORDERED - adj. cosmic, well-ordered a. orderly
  • ROW - husband. 1) row line 2) military. (in service) file, rank 3) (certain quantity) series units. and many more a number, several...
    Large Russian-English Dictionary
  • ORDERED - ordered ranked
  • RANGE - row prow;a number
    Russian-English Dictionary Socrates
  • WELLORDERED - a well-ordered well-ordered
  • WELL-ORDERED - adj. ordered ordered; well organized
    Large English-Russian Dictionary
  • TIME-ORDERED - adj. ordered by time (special) ordered by time, chronological
    Large English-Russian Dictionary
  • SERIES - noun; pl. - series 1) a) series of items. mat.; sequence series of events ≈sequence of events convergent series divergent series geometric ...
    Large English-Russian Dictionary
  • ROW - I 1. noun. 1) a) row, line (a set of objects, people located one after another, in one line) in rows ≈ ...
    Large English-Russian Dictionary
  • RANKED - ordered, ranked ranked data ≈ ordered data - be ranked - ranked data - ranked formula - ranked mean ...
    Large English-Russian Dictionary
  • RANK-ORDER - ordered ordered
    Large English-Russian Dictionary
  • RANGE - 1. noun. 1) a) row, line, chain (of some homogeneous objects - houses, mountains, etc.) mountain range ≈ ridge ...
    Large English-Russian Dictionary
  • PARTIALLY ORDERED
    Large English-Russian Dictionary
  • ORDERLY - 1. noun. 1) military orderly, orderly; liaison An orderly came in haste to bring him news of the battle. ≈ …
    Large English-Russian Dictionary
  • ORDERED — ordered switch ordered ordered; - * life measured lifestyle; - * set (mathematics) ordered set ordered: ~ on foreign …
    Large English-Russian Dictionary
  • LINEARLY - linearly, linearly registered algebra of linearly bounded degree ≈ algebra of linearly bounded degree bisymmetric linearly ordered groupoid ≈ bisymmetric linearly ...
    Large English-Russian Dictionary
  • LINE - I 1. noun. 1) a) line, dash; stroke to draw a line ≈ draw a line fine, thin line ≈ thin...
    Large English-Russian Dictionary
  • GROUPOID - groupoid bisymmetric linearly ordered groupoid ≈ bisymmetric linearly ordered groupoid cancellation groupoid ≈ groupoid with the abbreviation conditionally complete groupoid ...
    Large English-Russian Dictionary
  • FILE - I 1. noun. 1) file, needle file a nail file ≈ nail file 2) grinding, filing, filing to need ...
    Large English-Russian Dictionary
  • COSMIC - adj. 1) cosmic cosmic dust ≈ cosmic dust Syn: space 2) large, grandiose; colossal; world a cosmic thinker ≈ …
    Large English-Russian Dictionary
  • TOTALLY - 1) completely 2) completely 3) completely 4) totally 5) completely. theory of totally positive functions - theory of completely positive functions totally additive function - completely additive...
  • SUBCLASS - subclass disproportionate subclass numbers - disproportionate numbers in subclasses locally subclosedclass - locally closed subclass partially ordered subclass - partially ordered subclass proportional ...
    English-Russian scientific and technical dictionary
  • SPECIES - 1) biotype 2) species 3) group 4) category 5) class 6) breed 7) variety 8) genus 9) type. almost full point species - almost complete point species denumerably infinite species ...
    English-Russian scientific and technical dictionary
  • SERIES - 1) sequence 2) row 3) serial 4) series 5) stop 6) line 7) line 8) cycle. absolutely convergence series - absolutely (conditionally) convergent series absolutely convergent series - absolutely...
    English-Russian scientific and technical dictionary
  • PARTIALLY ORDERED - 1) incompletely ordered 2) semi-ordered 3) partially ordered
    English-Russian scientific and technical dictionary
  • PARTIALLY - 1) incomplete 2) partly 3) in parts 4) partially 5) privately. extra period partially balanced changeover design - partially balanced plan with an additional period partially adjoint ...
    English-Russian scientific and technical dictionary
  • ORDERED - 1) ordered 2) ordered 3) located 4) ordered. almost ordered group - almost ordered group antilexicographically ordered ring - antilexicographically ordered ring bisymmetric linearly ordered groupoid ...
    English-Russian scientific and technical dictionary
  • LINEARLY - linearly, linearly registered algebra of linearly bounded degree - algebra of linearly bounded degree bisymmetric linearly ordered groupoid - bisymmetric linearly ordered groupoid linearly ...
    English-Russian scientific and technical dictionary
  • SERIES - Many problems in mathematics lead to formulas containing infinite sums, for example, or Such sums are called infinite series, and their terms ...
    Free online English dictionaries and word translations with transcription, electronic English-Russian vocabularies, encyclopedia, Russian-English handbooks and translation, thesaurus.

Distribution range is a sequence of numbers indicating the qualitative or quantitative value of a characteristic and the frequency of its occurrence.

Types of distribution series are classified according to different principles.

According to the degree of ordering, the rows are divided into:

    disordered

    ordered

Unordered row- this is a series in which the values ​​of a characteristic are written in the order in which the options arrived during the study.

Example: When studying the height of a group of students, its values ​​were recorded in cm (175,170,168,173,179).

Ordered series- this is a series obtained from an unordered one in which the values ​​of the characteristic are rewritten in ascending or descending order. An ordered series is called ranked, and the ranking procedure

(ordering) is called sorting.

Example: (Height 168,170,173,175,179)

According to the type of characteristic, the distribution series are divided into:

    attributive

    variational.

Attributive series- this is a series compiled on the basis of a qualitative characteristic.

Variation series- this is a series compiled on the basis of a quantitative characteristic.

Variation series are divided into discrete, continuous and interval.

Variational discrete, continuous and interval series are named according to the corresponding feature that underlies the compilation of the series. For example, a series by shoe size is discrete by body weight - continuous.

Methods of presenting series in practical and scientific medicine are divided into three groups:

    Tabular presentation;

    Analytical representation (in the form of a formula);

    Graphic representation.

1. The simplest table consists of two columns or two rows, one of which contains the values ​​of the characteristic x i in an ordered form, and in the other - the relative or absolute frequency of its occurrence n i , f i .

Example: Tabular presentation of grades in a group x i and the number of students who received them n i .

x i

n i

2. Graphical representation of series is based on tabular data. Graphs are constructed in a rectangular coordinate system, where attribute values ​​are always plotted horizontally X i , and vertically the absolute or relative frequency n i .

Basic ways of presenting graphs:

    Diagram in segments.

    Histogram

    Frequency polygon.

    Variation (frequency) curve.

Bar chart is a graph representing a series in the form of vertical straight line segments, the position of which on the horizontal is determined by the value of the attribute, and the length of the segment is proportional to its absolute or relative frequency.

Example: bar chart for group performance assessments.

n i

5 4 3 2 XI

Typically, segment diagrams are constructed for discretely specified characteristics with a small number of options.

Histogram- this is a graph in the form of a stepped figure of rectangles adjacent to each other, the bases of which are intervals of feature values, and the heights of the rectangles are proportional to frequency or frequency (the number of objects falling within the interval). The areas of the rectangles correspond to the number of groups in a given interval.

Histograms are graphs of interval series. They are built primarily for large volumes of aggregates.

Example: Histogram of the normal distribution of red blood cells in human blood. Horizontal - cell diameter X i (mk), vertically - frequency n i number of cells in the interval.

n i

2 4 6 8 10 12 x i

Poligon (polygon) of frequencies- a series graph represented by a broken line of a point - the vertices of which correspond to the midpoints of the intervals, and the height of the point above the horizontal is proportional to the frequency or frequency.

Polygons are constructed for continuous and discrete variation series in cases where the average values ​​of a characteristic are identified in the intervals. Polygons are preferable to histograms for continuous distribution series

Example: a frequency polygon based on a histogram of the distribution of red blood cells in human blood.

n i

2 4 6 8 10 12 x i

Variation (frequency) curve- a graph of a series obtained under the condition that the volume of the population tends to infinity ( N→∞) , and the length of the interval itself tends to zero (Δ X→0) .

For practical statistical calculations, four groups of frequency distributions have been identified as standards:

  1. Rectangular distribution.

    Bell-shaped unimodal (single-vertex) distribution.

    Bimodal (two-vertex) distribution.

    Exponential distribution:

    growing,

    decreasing.

n i

x i

x i

x i

x i

Random equally probable events are subject to a rectangular distribution.

A wide class of phenomena (indicators of mental and physical development, height, weight, etc.) is subject to a bell-shaped symmetrical distribution. In practice, the most common unimodal distribution is the symmetrical one, which is why its classical form is called the normal distribution.

The bimodal distribution corresponds, for example, to the performance of students with and without a long break in their studies.

The exponentially decreasing distribution corresponds to the distribution of income in a capitalist society (the frequency decreases as income increases).


Statistics is exact science, studying methods of collecting, analyzing and processing data that describe mass actions, phenomena and processes Mathematical statistics is a branch of mathematics that studies methods for collecting, systematizing and processing the results of observations of random mass phenomena in order to identify existing patterns.


Statistics studies: numbers separate groups population of the country and its regions, production and consumption of various types of products, transportation of goods and passengers various types transport, natural resources and much more. The results of statistical studies are widely used for practical and scientific conclusions. Currently, statistics begins to be studied already in high school, in universities it is compulsory subject, because it is associated with many sciences and industries. To increase the number of sales in a store, to improve the quality of knowledge in school, to move the country towards economic growth, it is necessary to conduct statistical studies and draw appropriate conclusions. And everyone should be able to do this.


Formation of skills in primary processing of statistical data; depiction and analysis of quantitative information presented in different forms (in the form of tables, diagrams, graphs of real dependencies); developing ideas about important statistical ideas, namely: the idea of ​​estimation and the idea of ​​testing statistical hypotheses; developing the ability to compare the probabilities of random events occurring with the results of specific experiments. The main goals of studying the elements of statistics


Contents Data series Volume of data series Range of data series Mode of data series Median of series Arithmetic mean Ordered data seriesOrdered data series Data distribution table Data distribution table Let's summarize Nominative data series Frequency of result Percentage frequency Data grouping Methods of data processing Let's summarize












Definition The mode of a data series is the number in the series that appears most frequently in that series. A data series may or may not have a mode. Thus, in the data series 47, 46, 50, 52, 47, 52, 49, 45, 43, 53, each of the numbers 47 and 52 occurs twice, and the remaining numbers less than twice. In such cases, it was agreed that the series has two modes: 47 and 52.


Complete the task: So, in the data series 47, 46, 50, 52, 47, 52, 49, 45, 43, 53, each of the numbers 47 and 52 appears twice, and the remaining numbers appear less than twice. In such cases, it was agreed that the series has two modes: 47 and 52. At the institute they took a test in higher mathematics. There were 10 people in the group, and they received the corresponding ratings: 3, 5, 5, 4, 4, 4, 3, 2, 4, 5. Determine the fashion this series. Answer: 4


Definition of Median with not even number members is the number written in the middle. A median with an even number of terms is the arithmetic mean of the two numbers written in the middle. For example: determine the median of a series of numbers 1) 6; -4; 5; -2; -3; 3; 3; -2; 3. Answer: -3 2) -1; 0; 2; 1; -1; 0;2; -1. Answer: 0




Definition The arithmetic mean is the quotient of dividing the sum of the numbers in a series by their number. For example: given a series of numbers -1; 0; 2; 1; -1; 0; 2; -1. Then the arithmetic mean will be equal to: ((-1)+0+2+(-1)):8 =2:8=0.25




PRACTICAL WORK Assignment: characterize the performance of student Ivanov in mathematics for the fourth quarter. PERFORMANCE OF THE WORK: 1.Collection of information: Grades written out from the magazine: 5,4,5,3,3,5,4,4,4. 2. Processing of the received data: volume = 9 range = = 2 mode = 4 median = 3 arithmetic mean =(): 9 4 Characteristics of academic performance: the student is not always ready for the lesson. Mostly he studies with grades "4". For a quarter it comes out to “4”.


Independently: You need to find the volume of the series, the range of the series, mode, median and arithmetic mean: Card 1. 22.5; 23; 21.5; 22; 23. Card 2. 6; -4; 5; -2; -3; 3; 3; -2; 3. Card 3. 12.5; 12; 12; 12.5; 13; 12.5; 13. Card 4. -1; 0; 2; 1; -1; 0; 2; -1. Card; 130; 124; 131. Card; 100; 110.


Let's check Card 1. volume of series = 5 range of series = 10 mode = 23 median = 21.5 arithmetic mean = 13.3 Card 3. volume of series = 7 range of series = 1 mode = 12.5 median = 12.5 arithmetic mean = 12.5 Card 2. volume of series = 9 range of series = 10 mode = 3 median = -3 arithmetic mean = 1 Card 4. volume of series = 8 range of series = 3 mode = -1 median = 0 arithmetic mean = 0.25




Definition Ordered series of data are series in which the data is arranged according to some rule. How to order a series of numbers? (Write the numbers so that each subsequent number is no less (no more) than the previous one); or write down some names “alphabetically”...


Complete the task: Given a series of numbers: -1;-3;-3;-2;3;3;2;0;3;3;-3;-3;1;1;-3;-1 Arrange it in ascending order numbers. Solution: -3;-3;-3;-3;-3;-2;-1;-1;0;1;1;2;3;3;3;3 The result is an ordered series. The data itself has not changed, only the order in which they appear has changed.


Definition A data distribution table is a table of an ordered series in which, instead of repeating the same number, the number of repetitions is recorded. Conversely, if the distribution table is known, then an ordered series of data can be compiled. For example: From it the following ordered series is obtained: -3;-3;-3;-1;-1;-1;-1;5;5;7;8;8;8;8;8 Measurement result - 3578 How much times occurs in the data series 34215


Complete the task: In a women's shoe store, statistical research was carried out and a corresponding table was compiled for the price of shoes and the number of sales: Price (rubles): Quantity: For these indicators, you need to find statistical characteristics: create an ordered series of data volume of the data series range of the series mode of the series median of the series arithmetic mean of a data series




Let's summarize: We met basic concepts how statistical data processing occurs: 1) data is always the result of some kind of measurement 2) for a series of some data you can find: volume, range, mode, median and arithmetic mean 3) any series of data can be ordered and a data distribution table can be compiled


Definition A nominative series of data is NOT NUMERICAL DATA, but, for example, names; titles; nominations... For example: list of finalists of the World Cup since 1930: Argentina, Czechoslovakia, Hungary, Brazil, Hungary, Sweden, Czechoslovakia, Germany, Italy, Netherlands, Netherlands, Germany, Germany, Argentina, Italy, Brazil, Germany, France




Definition Probability random event is equal to a fraction, the denominator of which contains the number of all equally probable possibilities that make up a certain event, and the numerator contains the number of those possibilities in which the event in question occurs. For example:







34 Schedule:





Lyudmila Prokofievna Kalugina (or simply “Mymra”) in the wonderful film “Office Romance” taught Novoseltsev: “Statistics is a science, it does not tolerate approximation.” In order not to fall under the hot hand of the strict boss Kalugina (and at the same time easily solve tasks from the Unified State Examination and State Examination with elements of statistics), we will try to understand some concepts of statistics that can be useful not only in the thorny path of conquering the Unified State Examination exam, but also simply in everyday life. life.

So what is Statistics and why is it needed? The word “statistics” comes from the Latin word “status”, which means “state and state of affairs”. Statistics deals with the study of the quantitative side of mass social phenomena and processes in numerical form, identifying special patterns. Today statistics is used in almost all areas public life, ranging from fashion, cooking, gardening to astronomy, economics, medicine.

First of all, when getting acquainted with statistics, you need to study the basic statistical characteristics used to analyze data. Well, let's start with this!

Statistical characteristics

The main statistical characteristics of a data sample (what kind of “sample” is this!? Don’t be alarmed, everything is under control, this incomprehensible word is just for intimidation, in fact, the word “sample” simply means the data that you are going to study) include:

  1. sample size,
  2. sample range,
  3. arithmetic mean,
  4. fashion,
  5. median,
  6. frequency,
  7. relative frequency.

Stop, stop, stop! How many new words! Let's talk about everything in order.

Volume and Scope

For example, the table below shows the height of the players of the national football team:

This selection is represented by elements. Thus, the sample size is equal.

The range of the presented sample is cm.

Arithmetic mean

Not very clear? Let's look at our example.

Determine the average height of the players.

Well, shall we get started? We have already figured out that; .

We can immediately safely substitute everything into our formula:

Thus, the average height of a national team player is cm.

Or like this example:

For a week, 9th grade students were asked to solve as many examples from the problem book as possible. The number of examples solved by students per week is given below:

Find the average number of problems solved.

So, in the table we are presented with data on students. Thus, . Well, let’s first find the sum (total number) of all problems solved by twenty students:

Now we can safely begin to calculate the arithmetic mean of the solved problems, knowing that:

Thus, on average, 9th grade students solved each problem.

Here's another example to reinforce.

Example.

On the market, tomatoes are sold by sellers, and prices per kg are distributed as follows (in rubles): . What is the average price of a kilogram of tomatoes on the market?

Solution.

So, what's in in this example equals? That's right: seven sellers offer seven prices, which means ! . Well, we’ve sorted out all the components, now we can start calculating the average price:

Well, did you figure it out? Then do the math yourself arithmetic mean in the following samples:

Answers: .

Mode and median

Let's look again at our example with the national football team:

What is the mode in this example? What is the most common number in this sample? That's right, this is a number, since two players are cm tall; the growth of the remaining players is not repeated. Everything here should be clear and understandable, and the word should be familiar, right?

Let's move on to the median, you should know it from your geometry course. But it’s not difficult for me to remind you that in geometry median(translated from Latin as “middle”) - a segment inside a triangle connecting the vertex of the triangle with the middle of the opposite side. Keyword MIDDLE. If you knew this definition, then it will be easy for you to remember what a median is in statistics.

Well, let's get back to our sample of football players?

Did you notice an important point in the definition of median that we haven’t seen here yet? Of course, “if this series is put in order”! Shall we put things in order? In order for there to be order in the series of numbers, you can arrange the height values ​​of football players in both descending and ascending order. It is more convenient for me to arrange this series in ascending order (from smallest to largest). Here's what I got:

So, the series has been sorted, what other important point is there in determining the median? That's right, an even and an odd number of members in the sample. Have you noticed that even the definitions are different for even and odd quantities? Yes, you're right, it's hard not to notice. And if so, then we need to decide whether we have an even number of players in our sample or an odd one? That's right - there are an odd number of players! Now we can apply to our sample a less tricky definition of the median for an odd number of members in the sample. We are looking for the number that is in the middle in our ordered series:

Well, we have numbers, which means there are five numbers left at the edges, and height cm will be the median in our sample. Not so difficult, right?

Now let’s look at an example with our desperate children from grade 9, who solved examples during the week:

Are you ready to look for mode and median in this series?

To begin with, let's order this series of numbers (arrange from the smallest number to the largest). The result is a series like this:

Now we can safely determine the fashion in this sample. Which number occurs more often than others? That's right! Thus, fashion in this sample is equal.

We have found the mode, now we can start finding the median. But first, answer me: what is the sample size in question? Did you count? That's right, the sample size is equal. A is an even number. Thus, we apply the definition of median for a series of numbers with an even number of elements. That is, we need to find in our ordered series arithmetic mean two numbers written in the middle. What two numbers are in the middle? That's right, and!

Thus, the median of this series will be arithmetic mean numbers and:

- median the sample under consideration.

Frequency and relative frequency

That is frequency determines how often a particular value is repeated in a sample.

Let's look at our example with football players. We have before us this ordered series:

Frequency is the number of repetitions of any parameter value. In our case, it can be considered like this. How many players are tall? That's right, one player. Thus, the frequency of meeting a player with height in our sample is equal. How many players are tall? Yes, again one player. The frequency of meeting a player with height in our sample is equal. By asking these questions and answering them, you can create a table like this:

Well, everything is quite simple. Remember that the sum of the frequencies must equal the number of elements in the sample (sample size). That is, in our example:

Let's move on to the next characteristic - relative frequency.

Let us turn again to our example with football players. We have calculated the frequencies for each value; we also know the total amount of data in the series. We calculate the relative frequency for each growth value and get this table:

Now create tables of frequencies and relative frequencies yourself for an example with 9th graders solving problems.

Graphical representation of data

Very often, for clarity, data is presented in the form of charts/graphs. Let's look at the main ones:

  1. bar chart,
  2. pie chart,
  3. histogram,
  4. polygon

Column chart

Column charts are used when they want to show the dynamics of changes in data over time or the distribution of data obtained as a result of a statistical study.

For example, we have the following data on evaluations of written test work in one class:

The number of people who received such an assessment is what we have frequency. Knowing this, we can make a table like this:

Now we can build visual bar graphs based on such an indicator as frequency(the horizontal axis shows the grades; the vertical axis shows the number of students who received the corresponding grades):

Or we can construct a corresponding bar graph based on the relative frequency:

Let's consider an example of the type of task B3 from the Unified State Examination.

Example.

The diagram shows the distribution of oil production in countries around the world (in tons) for 2011. Among countries, the first place in oil production was occupied by Saudi Arabia, seventh place - United United Arab Emirates. Where did the USA rank?

Answer: third.

Pie chart

To visually depict the relationship between parts of the sample under study, it is convenient to use pie charts.

Based on our table with the relative frequencies of the distribution of grades in the class, we can construct pie chart, dividing the circle into sectors proportional to the relative frequencies.

A pie chart retains its clarity and expressiveness only with a small number of parts of the population. In our case, there are four such parts (in accordance with possible estimates), so the use of this type of diagram is quite effective.

Let's look at an example of the type of task 18 from the State Academic Inspectorate.

Example.

The diagram shows the distribution of family expenses during a seaside holiday. Determine what the family spent the most on?

Answer: accommodation.

Polygon

The dynamics of changes in statistical data over time are often depicted using a polygon. To construct a polygon, mark in coordinate plane points, the abscissas of which are moments in time, and the ordinates are the corresponding statistical data. By connecting these points successively with segments, a broken line is obtained, which is called a polygon.

Here, for example, we are given the average monthly air temperatures in Moscow.

Let's make the given data more visual - we'll build a polygon.

The horizontal axis shows the months, and the vertical axis shows the temperature. We build the corresponding points and connect them. Here's what happened:

Agree, it immediately became clearer!

A polygon is also used to visually depict the distribution of data obtained as a result of a statistical study.

Here is the constructed polygon based on our example with the distribution of scores:

Let's consider typical task B3 from the Unified State Exam.

Example.

In the figure, bold dots show the price of aluminum at the close of exchange trading on all working days from August to August of the year. The dates of the month are indicated horizontally, and the price of a ton of aluminum in US dollars is indicated vertically. For clarity, the bold points in the figure are connected by a line. Determine from the figure what date the aluminum price at the close of trading was the lowest for the given period.

Answer: .

Histogram

Interval data series are depicted using a histogram. A histogram is a stepped figure made up of closed rectangles. The base of each rectangle is equal to the length of the interval, and the height is equal to the frequency or relative frequency. Thus, in a histogram, unlike a regular bar chart, the bases of the rectangle are not chosen arbitrarily, but are strictly determined by the length of the interval.

For example, we have the following data on the growth of players called up to the national team:

So we are given frequency(number of players with corresponding height). We can complete the table by calculating the relative frequency:

Well, now we can build histograms. First, let's build based on frequency. Here's what happened:

And now, based on the relative frequency data:

Example.

To the exhibition innovative technologies Representatives of the companies arrived. The chart shows the distribution of these companies by number of employees. The horizontal line represents the number of employees in the company, the vertical line shows the number of companies with given number employees.

What percentage are companies with a total number of employees of more than one person?

Answer: .

Brief summary

    Sample size- the number of elements in the sample.

    Sample range- the difference between the maximum and minimum values ​​of the sample elements.

    Arithmetic mean of a series of numbers is the quotient of dividing the sum of these numbers by their number (sample size).

    Mode of number series- the number most often found in a given series.

    Medianordered series of numbers with an odd number of terms- the number that will be in the middle.

    Median of an ordered series of numbers with an even number of terms- the arithmetic mean of two numbers written in the middle.

    Frequency- the number of repetitions of a certain parameter value in the sample.

    Relative frequency

    For clarity, it is convenient to present data in the form of appropriate charts/graphs

  • ELEMENTS OF STATISTICS. BRIEFLY ABOUT THE MAIN THINGS.

    • Statistical sampling- a specific number of objects selected from the total number of objects for research.

    Sample size is the number of elements included in the sample.

    Sample range is the difference between the maximum and minimum values ​​of sample elements.

    Or, sample range

    Arithmetic mean of a series of numbers is the quotient of dividing the sum of these numbers by their number

    The mode of a series of numbers is the number that appears most frequently in a given series.

    The median of a series of numbers with an even number of terms is the arithmetic mean of the two numbers written in the middle, if this series is ordered.

    Frequency represents the number of repetitions, how many times over a certain period a certain event occurred, a certain property of an object manifested itself, or an observed parameter reached a given value.

    Relative frequency is the ratio of frequency to the total number of data in the series.

Well, the topic is over. If you are reading these lines, it means you are very cool.

Because only 5% of people are able to master something on their own. And if you read to the end, then you are in this 5%!

Now the most important thing.

You have understood the theory on this topic. And, I repeat, this... this is just super! You are already better than the vast majority of your peers.

The problem is that this may not be enough...

For what?

For successful passing the Unified State Exam, for admission to college on a budget and, MOST IMPORTANTLY, for life.

I won’t convince you of anything, I’ll just say one thing...

People who received good education, earn much more than those who did not receive it. This is statistics.

But this is not the main thing.

The main thing is that they are MORE HAPPY (there are such studies). Perhaps because many more opportunities open up before them and life becomes brighter? Don't know...

But think for yourself...

What does it take to be sure to be better than others on the Unified State Exam and ultimately be... happier?

GAIN YOUR HAND BY SOLVING PROBLEMS ON THIS TOPIC.

You won't be asked for theory during the exam.

You will need solve problems against time.

And, if you haven’t solved them (A LOT!), you’ll definitely make a stupid mistake somewhere or simply won’t have time.

It's like in sports - you need to repeat it many times to win for sure.

Find the collection wherever you want, necessarily with solutions, detailed analysis and decide, decide, decide!

You can use our tasks (optional) and we, of course, recommend them.

In order to get better at using our tasks, you need to help extend the life of the YouClever textbook you are currently reading.

How? There are two options:

  1. Unlock all hidden tasks in this article -
  2. Unlock access to all hidden tasks in all 99 articles of the textbook - Buy a textbook - 899 RUR

Yes, we have 99 such articles in our textbook and access to all tasks and all hidden texts in them can be opened immediately.

Access to all hidden tasks is provided for the ENTIRE life of the site.

And in conclusion...

If you don't like our tasks, find others. Just don't stop at theory.

“Understood” and “I can solve” are completely different skills. You need both.

Find problems and solve them!