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Summary of the lesson of algebra in grade 7

Theme of the lesson: "MEDIAN OF THE ORDERED SERIES".

teacher of the Lake School branch of MKOU Burkovskaya secondary school Eremenko Tatyana Alekseevna
Goals:
the concept of the median as a statistical characteristic of an ordered series; to form the ability to find the median for ordered series with an even and odd number of members; to form the ability to interpret the values ​​of the median depending on the practical situation, to consolidate the concept of the arithmetic mean set of numbers. Develop independent work skills. Build an interest in mathematics.
During the classes

oral work.
Rows are given: 1) 4; one; eight; 5; one; 2) ; nine; 3; 0.5; ; 3) 6; 0.2; ; 4; 6; 7.3; 6. Find: a) the largest and smallest values ​​of each row; b) the range of each row; c) the fashion of each row.
II. Explanation of new material.
Textbook work. 1. Consider the problem from paragraph 10 of the textbook. What does ordered row mean? I emphasize that before finding the median, you must always sort the data series. 2. On the board, we get acquainted with the rules for finding the median for series with an even and odd number of members:
median

orderly

row
numbers
with

odd

number

members
called the number written in the middle, and
median

ordered row
numbers
with an even number of members
is called the arithmetic mean of two numbers written in the middle.
median

arbitrary

row
called the median 1 3 1 7 5 4

corresponding ordered series.
I note that the indicators are the arithmetic mean, mode and median for

differently

characterize

data,

received

result

observations.

III. Formation of skills and abilities.
1st group. Exercises on the application of formulas for finding the median of an ordered and unordered series. one.
№ 186.
Decision: a) Number of members of the series P= 9; median Me= 41; b) P= 7, the row is ordered, Me= 207; in) P= 6, the row is ordered, Me== 21; G) P= 8, the row is ordered, Me== 2.9. Answer: a) 41; b) 207; at 21; d) 2.9. Students comment on how the median is found. 2. Find the arithmetic mean and median of a series of numbers: a) 27, 29, 23, 31, 21, 34; in) ; 1. b) 56, 58, 64, 66, 62, 74. Decision: To find the median, it is necessary to sort each row: a) 21, 23, 27, 29, 31, 34. P = 6; X = = 27,5; Me = = 28; 20 22 2 + 2, 6 3, 2 2 + 1125 ; ; ; 3636 21 23 27 29 31 34 165 66 +++++ = 27 29 2 +

b) 56, 58, 62, 64, 66, 74. P = 6; X = 63,3; Me== 63; in) ; one. P = 5; X = : 5 = 3: 5 = 0,6; Me = . 3.
№ 188
(orally). Answer: yes; b) no; c) no; d) yes. 4. Knowing that the ordered series contains t numbers, where t is an odd number, indicate the number of the term that is the median if t is equal to: a) 5; b) 17; c) 47; d) 201. Answer: a) 3; b) 9; c) 24; d) 101. 2nd group. Practical tasks for finding the median of the corresponding series and interpreting the result. one.
№ 189.
Decision: Number of row members P= 12. To find the median, the series must be ordered: 136, 149, 156, 158, 168, 174, 178, 179, 185, 185, 185, 194. Median of the series Me= = 176. Monthly output was more than the median for the following members of the artel: 56 58 62 64 66 74 380 66 +++++ =≈ 62 64 2 + 1125; ; ; 3636 1125 12456 18 1:5:5 6336 6 6 ++++ ⎛⎞ ++++ = = ⎜⎟ ⎝⎠ 2 3 67 174 178 22 xx + + =

1) Kvitko; 4) Bobkov; 2) Baranov; 5) Rylov; 3) Antonov; 6) Astafiev. Answer: 176. 2.
№ 192.
Decision: Let's arrange the data series: 30, 31, 32, 32, 32, 32, 32, 32, 33, 35, 35, 36, 36, 36, 38, 38, 38, 40, 40, 42; number of row members P= 20. Swipe A = x max- x min = 42 - 30 = 12. Mode Mo= 32 (this value occurs 6 times - more often than others). Median Me= = 35. In this case, the range shows the greatest spread of time for processing the part; the mode shows the most typical value of the processing time; median is the processing time that half of the turners did not exceed. Answer: 12; 32; 35.
IV. Summary of the lesson.
What is the median of a series of numbers? – Can the median of a series of numbers not coincide with any of the numbers in the series? – What number is the median of an ordered series containing 2 P numbers? 2 P– 1 numbers? How to find the median of an unordered series?
Homework:
№ 187, № 190, № 191, № 254. 10 11 35 35 22 xx + + =

Statistics is an exact science that studies the 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: the number of individual groups of the population of the country and its regions, the production and consumption of various types of products, the transportation of goods and passengers by various modes of 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 a compulsory subject, because it is associated with many sciences and industries. To increase the number of sales in the store, to improve the quality of knowledge at school, to move the country in economic growth, it is necessary to conduct statistical research and draw appropriate conclusions. And everyone should be able to do this.

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

Contents Data series Size of data series Range of data series Mode of data series Median of series Arithmetic mean Ordered data series Ordered data series Table of data distributionTable of data distribution

Definition The mode of a data series is the number of the series that occurs most often in this series. A data set may or may not have a mode. So, 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 occurs twice, and the remaining numbers - less than two times. In such cases, it was agreed to consider that the series has two modes: 47 and 52. At the institute, they passed a test in higher mathematics. There were 10 people in the group, and they received the corresponding marks: 3, 5, 5, 4, 4, 4, 3, 2, 4, 5. Determine the mode of this series. Answer: 4

Definition The median with an odd number of terms is the number written in the middle. A median with an even number of terms is the arithmetic mean of 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; one; -one; 0;2; -one. 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; one; -one; 0; 2; -one. Then the arithmetic mean will be: ((-1)+0+2+(-1)):8 =2:8=0.25

PRACTICAL WORK Task: to characterize the progress of student Ivanov in mathematics for the fourth quarter. PERFORMANCE OF WORK: 1. Collection of information: Grades from the magazine are written out: 5,4,5,3,3,5,4,4,4. 2. Processing of the obtained data: volume = 9 range = = 2 mod = 4 median = 3 arithmetic mean =() : 9 4 Performance characteristics: the student is not always ready for the lesson. Mainly studies at "4". For a quarter comes "4".

Independently: It is necessary to find the volume of the series, the range of the series, the mode, the median and the 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; thirteen; 12.5; 13. Card 4. -1; 0; 2; one; -one; 0; 2; -one. 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 An ordered data series is a series in which the data is arranged according to some kind of rule. How to order a series of numbers? (Write down the numbers so that each subsequent number is no less (no more) than the previous one); or write down some names "in alphabetical order" ...

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 the number of repetitions is recorded instead of repetitions of the same number. Conversely, if the distribution table is known, then an ordered series of data can be compiled. For example: It produces such an ordered series: -3;-3;-3;-1;-1;-1;-1;5;5;7;8;8;8;8;8 Measurement result-3578 How many times occurs in a series of data34215

Complete the task: Statistical studies were carried out in a women's shoe store 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: compose an ordered data series volume of data series range of series mode of series median of series arithmetic mean of a data series

To summarize: We got acquainted with the initial concepts of how statistical data processing occurs: 1) data is always the result of some measurement 2) for a series of some data you can find: volume, range, mode, median and arithmetic mean 3) any data series you can organize and create a table of data distribution

Definition Nominative data series is NOT NUMERICAL DATA, but for example, names; titles; nominations ... For example: a 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 The probability of a 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 at which the event in question occurs For example:

34 Schedule:

Anxiety is a child of evolution

Anxiety is a feeling familiar to absolutely everyone. Anxiety is based on the instinct of self-preservation, which we inherited from distant ancestors and which manifests itself in the form of a defensive reaction “Flight or fight”. In other words, anxiety does not arise from scratch, but has evolutionary grounds. If at a time when a person was constantly in danger in the form of an attack by a saber-toothed tiger or an invasion of a hostile tribe, anxiety really helped to survive, then today we live in the safest time in the history of mankind. But our instincts continue to operate at a prehistoric level, creating many problems. Therefore, it is important to understand that anxiety is not your personal flaw, but an evolutionary mechanism that is no longer relevant in modern conditions. Anxious impulses, once necessary for survival, have now lost their purpose, turning into neurotic manifestations that significantly limit the life of anxious people.

More word meanings and translation ORDERED SERIES from English into Russian in English-Russian dictionaries.
What is 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; partially ordered
  Russian-English Dictionary of the Mathematical Sciences
• ORDERED - Trimmed
  
• ORDERED - Square
  Russian-American English Dictionary
• ROW
  Russian-American English Dictionary
• ROW - 1. row; line row after row, row after row - row upon row a 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; ~ after ~ row upon row; 2. (line) file; 3. (seats in the theater, ...
  Russian-English Dictionary of General Subjects
• ROW - 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 a row of cars - line of vehicles ...
  Russian-English Smirnitsky abbreviations dictionary
• ROW - catena, family, series, set, train, variety, row
  Russian-English Edic
• ORDERED - ordered
  
• SERIES — chain, series math., range, rank, row, string, train, variety
  Russian-English Dictionary of Mechanical Engineering and Automation of Production
• ROW - husband. 1) row; line 2) military (in service) file, rank 3) (some number) series units. and many others. h...
  Russian-English Concise Dictionary of General Vocabulary
• ORDERED
  
• ROW - catena, (masonry, tiled roof) course, family, (brickwork) layer, range, rank, row, series, suite archit., train, variety
  Russian-English Dictionary of Construction and New Construction Technologies
• ORDERED - square
  
• ROW - range, rank, round, series, set, string, variety
  Russian-English Economic Dictionary
• ROW - see. Not the ranks of the Jews, but the Jews are thinning; see Two Jews sat in three rows
  English-Russian-English dictionary of slang, jargon, Russian names
• ROW - 1. row; ~ row of chairs; ~ after ~ 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 …
  
• SERIES - I see also. one of ~a; by... in each ~y; series; power ~ by; whole …
  Russian-English Scientific and Technical Translator's Dictionary
• SERIES - m. bank - thermal spark plug series
  Russian-English automobile dictionary
• ORDERED - ordered
  
• ROW - 1) family 2) range 3) row 4) sequence 5) series
  Russian-English explanatory dictionary of terms and abbreviations on BT, Internet and programming
• ROW - see in some cases; have a number of advantages; help solve a number of problems; whole line; syn. big number …
  Russian-English Dictionary of Space Idioms
• ROW — 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) (some number) series units. and many others. a number, several ...
  Big Russian-English Dictionary
• ORDERED - ordered ranked
  
• ROW - row prow; a number
  Russian-English Dictionary Socrates
• WELLORDERED — a well-ordered well-ordered
  
• WELL-ORDERED - adj. ordered ordered; well organized
  Big English-Russian Dictionary
• TIME-ORDERED - adj. ordered by time (special) ordered by time, chronological
  Big English-Russian Dictionary
• SERIES - noun; pl. - series 1) a) a series of tzh. mat.; series of events sequence convergent series divergent series geometric …
  Big English-Russian Dictionary
• ROW - I 1. n. 1) a) row, line (a set of objects, people located one after another, in one line) in rows ≈ ...
  Big English-Russian Dictionary
• RANKED - ordered, ranked ranked data ≈ ordered data - be ranked - ranked data - ranked formula - ranked mean ...
  Big English-Russian Dictionary
• RANK-ORDER - sorted ordered
  Big English-Russian Dictionary
• RANGE - 1. noun 1) a) row, line, chain (of some kind of homogeneous objects - houses, mountains, etc.) mountain range ≈ ridge ...
  Big English-Russian Dictionary
• PARTIALLY ORDERED
  Big English-Russian Dictionary
• ORDERLY - 1. noun 1) military orderly, orderly; contact An orderly came in haste to bring him news of the battle. ≈ …
  Big English-Russian Dictionary
• ORDERED - ordered switch ordered ordered; - * life measured way of life; - * set (mathematics) ordered set ordered: ~ on foreign ...
  Big English-Russian Dictionary
• LINEARLY - linearly, linearly registered algebra of linearly bounded degree ≈ algebra of linearly bounded degree bisymmetric linearly ordered groupoid ≈ bisymmetric linearly ...
  Big English-Russian Dictionary
• LINE - I 1. n. 1) a) line, line; stroke to draw a line - draw a line fine, thin line - thin ...
  Big English-Russian Dictionary
• GROUPOID — groupoid bisymmetric linearly ordered groupoid ≈ bisymmetric linearly ordered groupoid cancellation groupoid ≈ groupoid with reduction conditionally complete groupoid …
  Big English-Russian Dictionary
• FILE - I 1. n. 1) file, needle file a nail file ≈ nail file 2) grinding, filing, filing to need ...
  Big English-Russian Dictionary
• COSMIC - adj. 1) space cosmic dust ≈ space dust Syn: space 2) big, grandiose; colossal; world a cosmic thinker ≈ …
  Big English-Russian Dictionary
• TOTALLY - 1) completely 2) completely 3) completely 4) totally 5) entirely. theory of totally positive functions - theory of totally positive functions totally additive function - completely additive ...
  
• SUBCLASS - subclass disproportionate subclass numbers - disproportionate numbers in subclasses locally closed subclass - 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 full point view 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 convergent 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) incompletely 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 - an almost ordered group antilexicographically ordered ring - an 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 words translations with transcription, electronic English-Russian vocabularies, encyclopedia, Russian-English handbooks and translation, thesaurus.

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 the State Academic Examination with elements of statistics), we will try to understand some of the concepts of statistics that can be useful not only in the thorny path of conquering the exam in the Unified State Examination, but also just in everyday life. life.

So what is statistics and why is it needed? The word "statistics" comes from the Latin word "status" (status), which means "the state and state of affairs / things." Statistics deals with the study of the quantitative side of mass social phenomena and processes in numerical form, revealing special patterns. Today, statistics is used in almost all spheres of public life, ranging from fashion, cooking, gardening and ending with astronomy, economics, and medicine.

First of all, when getting acquainted with statistics, it is necessary to study the main statistical characteristics used for data analysis. Well, let's start with this!

Statistical characteristics

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

1. sample size,
2. sample size,
3. average,
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 Span

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

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

The range of the presented sample is cm.

Average

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

Determine the average height of the players.

Well, let's get started? We have already figured out that; .

We can immediately boldly substitute everything into our formula:

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

Well, 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 in a week are given below:

Find the average number of solved problems.

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

Now we can safely proceed to the calculation of the arithmetic mean of the solved problems, knowing that, a:

Thus, on average, 9th grade students solved the tasks.

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?

Decision.

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

Well, did you understand? Then count yourself average in the following samples:

Answers: .

Mode and median

Let's go back to our soccer team example:

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 other players is not repeated. Everything should be clear and understandable here, and the word is familiar, right?

Let's move on to the median, you should know it from the geometry course. But it is not difficult for me to recall that in geometry median(translated from Latin - “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, back to our sample of football players?

Did you notice an important point in the definition of the median that we have not yet met here? Of course, "if this row is ordered"! Shall we put things in order? In order to have order in the series of numbers, it is possible to arrange the height values ​​of the players both in descending order and in ascending order. It is more convenient for me to build this series in ascending order (from smallest to largest). Here's what I got:

So, the series has been ordered, what else is there an important point in determining the median? Correct, even and odd number of members in the sample. Noticed that even the definitions are different for even and odd numbers? Yes, you're right, it's hard not to notice. And if so, then we need to decide whether the number of players in our sample is even or odd? That's right - players, so the number is odd! 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 a number that turned out to be in the middle in our ordered series:

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

And now let's look at an example with our desperate guys from grade 9, who solved examples during the week:

Ready to look for mode and median in this series?

First, let's arrange this series of numbers (arrange from the smallest number to the largest). The result is this row:

Now we can safely determine the fashion in this sample. Which number is the most common? That's right! Thus, fashion in this sample is equal.

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

So the median of this series will be average numbers and:

- median considered sample.

Frequency and relative frequency

I.e frequency determines how often one or another value is repeated in the sample.

Let's look at our example with football players. Before us is such an ordered row:

Frequency is the number of repetitions of some 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 make 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 - the relative frequency.

Let's go back to our soccer player example. We 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 the following table:

And now make tables of frequencies and relative frequencies yourself for an example with 9-graders solving problems.

Graphical display of data

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

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

bar chart

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

For example, we have the following data about the grades of a written test in one class:

The number of those 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 plot the corresponding bar graph based on the relative frequency:

Consider an example of the type of task B3 from the exam.

Example.

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

Answer: third.

Pie chart

For a visual representation of the relationship between parts of the sample under study, it is convenient to use pie charts.

From our plate with the relative frequencies of the distribution of grades in the class, we can build a pie chart by breaking the circle into sectors proportional to the relative frequencies.

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

Consider an example of the type of task 18 from the GIA.

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 is often depicted using a polygon. To construct a polygon, points are marked in the coordinate plane, the abscissas of which are points in time, and the ordinates are the corresponding statistical data. By connecting these points in series 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 - let's build a polygon.

Months are shown on the horizontal axis, temperatures are shown on the vertical axis. We build the corresponding points and connect them. Here's what happened:

Agree, it immediately became clearer!

A polygon is also used to visualize 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:

Consider a typical task B3 from the exam.

Example.

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

Answer: .

bar graph

Interval data series are depicted using a histogram. The 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.

Here, 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, we will build on the basis of the frequency. Here's what happened:

Now, based on the relative frequency data:

Example.

Representatives of companies came to the exhibition on innovative technologies. The diagram shows the distribution of these companies by the number of employees. The horizontal line shows the number of employees in the company, and the vertical line shows the number of companies with a given number of employees.

What percentage are companies with a total number of employees more people?

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).

Number series fashion- the number most often found in this series.

Medianan ordered series of numbers with an odd number of members is the number in the middle.

Median of an ordered series of numbers with an even number of members- 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.

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

The sample size is the number of items in the sample.

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

Or, sample range

Average 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 occurs most frequently in a given series.

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

The frequency is the number of repetitions, how many times during a certain period an event occurred, a certain property of an object manifested itself, or an observed parameter reached a given value.

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

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

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

Now the most important thing.

You've figured out the theory on this topic. And, I repeat, it's ... it's 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 the successful passing of the exam, for admission to the institute on the budget and, MOST IMPORTANTLY, for life.

I will not convince you of anything, I will just say one thing ...

People who have received a good education earn much more than those who have not received 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 much 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 exam and be ultimately ... happier?

FILL YOUR HAND, SOLVING PROBLEMS ON THIS TOPIC.

On the exam, you will not be asked theory.

You will need solve problems on time.

And, if you haven’t solved them (LOTS!), you will definitely make a stupid mistake somewhere or simply won’t make it in time.

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

Find a collection anywhere you want necessarily with solutions, detailed analysis and decide, decide, decide!

You can use our tasks (not necessary) and we certainly recommend them.

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In conclusion...

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

“Understood” and “I know how to solve” are completely different skills. You need both.

Find problems and solve!