Lesson summary "Chart graphs. Visual representation of the ratio of quantities (grade 7). III. Studying new material

It also turns out to be difficult for a person.

Suppose you are preparing for a school geography conference where you are tasked with painting a climate portrait of the month of May. Throughout the month, you collected information about air temperature, pressure, humidity, cloud cover, wind direction and speed. You entered the relevant information into a prepared table, and this is what you got:

Weather in May 2006

date	Temperature, ° C	Humidity, %	Pressure, mm	Wind
date	Temperature, ° C	Humidity, %	Pressure, mm	Direction	Degree	Speed, m / s
1	+ 16	25	759	S-V	130	3	It's clear
2	+ 19	30	759	S-3	320	2	It's clear
3	+20	30	759	C-B	30	2	It's clear
4	+22	26	759	WITH	350	2	20-30%
5	+21	28	760	C-B	50	1	90%
6	+22	35	759	V	90	2	70-80%
7	+ 19	52	753	C-B	30	4	60%
8	+ 12	66	750	WITH	340	3	90%
9	+ 14	58	747	C-B	40	2	Solid
10	+ 13	88	743	V	90	1	Solid
11	+ 13	71	741	V	80	1	90%
12	+ 10	81	745	S-3	310	2	Solid
13	+ 17	48	747	Calm	-	0	70-80%
14	+23	40	743	U-3	230	1	50%
15	+ 16	59	743	3	290	2	90%
16	+ 13	38	746	S-3	310	3	70-80%
17	+ 13	41	749	Calm	-	0	Solid
18	+ 15	41	750	WITH	20	2	70-80%
19	+ 17	36	745	NS	180	2	40%
20	+ 14	88	738	U-3	240	2	90%
21	+21	52	739	S-V	140	2	Solid
22	+ 15	72	740	U-3	240	5	Solid
23	+21	49	745	U-3	240	3	70-80%
24	+22	53	744	3	280	2	50%
25	+ 17	48	744	U-3	220	2	90%
26	+ 18	52	744	Calm	-	0	90%
27	+ 11	93	738	NS	160	2	90%
28	+ 13	62	741	3	270	3	90%
29	+ 16	59	735	S-V	140	1	Solid
30	+ 11	87	736	Calm	-	0	Solid
31	+ 17	51	744	S-V	130	3	Solid

Of course, you can redraw this table on a large sheet of Whatman paper and demonstrate this impressive result to classmates. But will they be able to perceive this information, process it and add up an idea of the weather in May? Most likely no.

You have collected a large amount of information, it is accurate, complete and reliable, but in a tabular form it will not be of interest to listeners, since it is not at all clear. To make the information contained in the table more visual and easily perceived (visualize information), you can use graphs and charts.

Visual representation of the processes of changing quantities

The graph depicts two coordinate axes at right angles to each other. These axes are the scales on which the representable values are plotted. One quantity is dependent on the other - independent. The independent quantity values are usually plotted on the horizontal axis (X-axis, or abscissa), and the dependent quantity, on the vertical (Y-axis, or ordinate axis). When the independent variable changes, the dependent variable changes. For example, the air temperature (dependent variable) can change over time (independent variable). Thus, the graph shows what happens to Y when X changes. In the graph, values are displayed as curves, dots, or both at the same time.

The graph allows you to track the dynamics of data changes. For example, according to the data contained in the 2nd column, you can build a graph of temperature changes during the month in question. According to the schedule, you can instantly set the warmest day of the month, the coldest day of the month, quickly calculate the number of days when the air temperature exceeded twenty degrees or was around +15 ° С. You can also indicate the periods when the air temperature was quite stable or, conversely, underwent significant fluctuations (Fig. 2.11).

A similar one is provided by the graphs of changes in air humidity and atmospheric pressure, built on the basis of the 3rd and 4th columns of the table (Fig. 2.12, 2.13).

Visual representation of the ratio of quantities

Now let's work with the "Clouds" column. According to the available data, it is very difficult to say what kind of cloud cover prevailed in May. The situation is simplified if, based on the available information, an additional table is compiled, in which the number of days with the same cloud cover is presented:

Cloudiness in May 2006

Diagrams provide a visual representation of the ratio of certain quantities. If the values to be compared add up to 100%, then pie charts are used.

The diagram (Fig. 2.14) does not indicate the number of days with a certain cloudiness, but it shows what percentage of the total number of days falls on days with a certain cloudiness.

Days with certain cloudiness correspond to their own sector of the circle. The area of this sector refers to the area of the whole circle, as the number of days with a certain cloudiness refers to the total number of days in May. Therefore, if no numerical data is given on the pie chart at all, it will still give some approximate idea of the ratio of the values under consideration, in our case - days with different cloud cover.

A large number of sectors make it difficult to perceive information on a pie chart. Therefore, a pie chart is generally not applicable for more than five to six data values. In our example, this difficulty can be overcome by reducing the number of cloud gradations: 0-30%, 40-60%, 70-80%, 90-100% (Fig. 2.15).

One glance at the diagram in Fig. 2.15 is sufficient to conclude that cloudy days prevailed in May, and there were very few clear days. We had to sacrifice accuracy to provide better visibility. Column charts (Fig. 2.16) can provide both clarity and accuracy of information in many cases.

Column charts are composed of parallel rectangles (bars) of equal width. Each bar shows one type of qualitative data (for example, one type of cloudiness) and is tied to some reference point on the horizontal axis - the category axis. In our case, the anchor points on the category axis are fixed cloud values. The height of the bars is proportional to the values of the compared values (for example, the number of days of a particular cloudiness). The corresponding values are plotted on the vertical value axis. Neither the value axis nor the bars should have breaks: the chart is used for better comparison, and the presence of breaks destroys the very purpose of presenting the results in the form of a chart.

According to the diagram in Fig. 2.16, you can not only compare the number of days with a particular cloudiness, but also indicate exactly how many days of what cloudiness were during the period under consideration.

The petal chart is special, it has its own axis for each point of the data series. The axes originate from the center of the chart.

Let's summarize:

1. With the help of graphs and diagrams (circular, bar and radial), we were able to visualize a large amount of the same type of tabular information.

2. Charts allowed us to trace the processes of changes in temperature, humidity and pressure. Charts - compare the number of days with a particular cloudiness and build a wind rose.

3. To make the information presented in one table clearer, we used three graphs and three diagrams.

4. For clarity, in some cases we had to sacrifice the accuracy of the information. Thus, the choice of this or that type of information model depends on the purpose for which we are creating this model.

Multi-row data visualization

Suppose your homeroom teacher has asked you to prepare a progress chart for a parenting meeting based on the information in the following table:

Unlike previous cases, here we are dealing with multi-row data: 1st row - estimates of Bautin Dima, 2nd row - estimates of Misha Golubev, 3rd row - estimates of Ivan Kulikov, 4th row - estimates of Radugina Alla. Here we will have to compare several values several times (at several points).

In this case, the pie chart cannot be used in principle.

You can build a bar chart by presenting data on all students at once - fig. 2.18.

In this example, the anchor points are student names. At each reference point, a group of four columns is built - according to the number of objects. Comparison here can be carried out both among rectangles belonging to the same group (we compare the performance of one student in all subjects), and between groups (we compare the performance of students with each other).

In order to visually compare the sums of several quantities at several points and at the same time show the contribution of each quantity to the total, tier charts are used.

You can understand the idea of a tiered chart by mentally transforming the bar chart. Imagine that the bars in each group are not next to each other, but one above the other. Now at each anchor point, instead of a group of columns, there will be one multi-tiered column. Its height will be determined by the sum of the heights of all components (Fig. 2.19).

Area charts, or area charts, can also be used to visualize multi-row data (Figure 2.20).

The area diagram resembles a slice of the earth's crust. "Mountain" corresponds to a more successful student, and "hollow" corresponds to a less successful student. This is a stacked chart. The vertical slice at the pivot points allows you to represent the contribution of each data series (in our case, the grades for each subject) to the total (the total score of a particular student). "The thickness of the layer" allows you to judge the overall performance in the subject.

Briefly about the main thing

The choice of this or that type of information model depends on the purpose for which we are creating this model.

Diagram is a graphical representation that gives a visual representation of the ratio of any quantities or several values of the same quantity, of the change in their values. Many different types of charts are used.

A graph is a line that gives a visual representation of the nature of the dependence of a quantity (for example, a path) on another (for example, time). The graph allows you to track the dynamics of data changes.

A pie chart is used to compare several quantities at one point. It is especially useful if the quantities add up to something whole.

A bar chart allows you to compare multiple quantities at multiple points.

A tiered chart allows you to visually compare the sums of multiple quantities at multiple points and still show how each quantity contributes to the total.

An area chart (area chart) allows you to simultaneously track the change in the sum of several quantities at several points and at the same time show the contribution of each quantity to the total.

With the help of graphs and charts, you can visualize large amounts of the same type of tabular information. There is often a loss of information accuracy during visualization.

Questions and tasks

1. Using the motion graphs shown in the drawing, determine the speed of movement of each object and write down the formula expressing the dependence of the distance traveled on the time of the object's movement.

What objects can have the speed you specified on the schedule?

2. The figure shows the schedule of movement of the seventh grader Misha Golubev on the way to school. Define by the schedule:

1) the time of leaving the house;
2) speed on all sections of the route;
3) duration and time of stops;
4) the time of arrival at the school.

What, in your opinion, can cause the stop and increase in the student's movement speed?

3. Using the performance change graph, find the true statements:

1) rise operability starts at 8 o'clock;
2) fatigue lasts from 12 to 14 hours;
3) performance is higher in the evening than in the morning;
4) the greatest efficiency from 10 to 12 in the morning;
5) performance drops sharply at 21 hours;
6) low efficiency at 19 o'clock;
7) the highest efficiency at 17 o'clock;
8) in the afternoon, the lowest efficiency is at 15 hours;
9) a person has two periods of highest working capacity per day: from 8 am to 1:30 pm, as well as from 4:00 pm to 8:00 pm;
10) lessons should start at 7 am;
11) it is best to do your homework from 3 pm to 5 pm.

4. The table shows the schedule of lessons for one school day for students in grade 7.

Does this timetable correspond to the state of performance of schoolchildren? How can it be improved taking into account changes in the performance of schoolchildren (graph from the previous task)? Suggest your option.

5. The result of a sudden impact on the human body of any environmental factor is called trauma. Based on a diagram representing the structure child injury, write an appropriate verbal description. Back it up with real-life examples.

6. The data of the Ministry of Health of the Russian Federation on changes over ten years (1992-2001) in the structure of morbidity in children under the age of 14 are presented in a bar chart:

What can you tell by analyzing this diagram?

It is impossible to quickly and efficiently process large volumes of the same type of information presented in text form. It is much more convenient to process such information using tables.

But the perception of cumbersome tables also turns out to be difficult for a person.

Suppose you are preparing for a school geography conference where you are tasked with painting a climate portrait of the month of June. Throughout the month, you have been collecting information about air temperature, pressure, humidity, cloud cover, wind direction and speed.

You entered the relevant information into a prepared table, and this is what you got (part of the table):

You have collected a large amount of information, it is accurate, complete and reliable, but in a tabular form it will not be of interest to listeners, since it is not at all clear.

Visual representation of the processes of changing quantities

The graph depicts two coordinate axes at right angles to each other. These axes are the scales on which the representable values are plotted.

Pay attention!

One quantity is dependent on the other - independent. The independent quantity is usually plotted on the horizontal axis (X-axis, or abscissa), and the dependent quantity, on the vertical (Y-axis, or ordinate). When the independent variable changes, the dependent variable changes.

For example, the air temperature (dependent variable) can change over time (independent variable).

Thus, the graph shows what happens to Y when X changes. In the graph, values are displayed as curves, dots, or both at the same time.

The graph allows you to track the dynamics of data changes. For example, according to the data contained in the \ (2 \) -th column, you can build a graph of temperature changes during the month under consideration.

According to the schedule, you can instantly set the warmest day of the month, the coldest day of the month, quickly calculate the number of days when the air temperature exceeded twenty degrees or was in the area \ (+ 15 ° С \).

You can also indicate periods when the air temperature was sufficiently stable or, conversely, underwent significant fluctuations.

Similar information is provided by graphs of changes in air humidity and atmospheric pressure, built on the basis of \ (3 \) - it and \ (4 \) - th column of the table.

Visual representation of the ratio of quantities

Diagrams provide a visual representation of the ratio of certain quantities. If the compared values form \ (100 \)% in the sum, then use pie charts.

The chart does not show the number of days with certain cloudiness, but it shows how many percent of the total number of days fall on days with certain cloudiness.

Days with certain cloudiness correspond to their own sector of the circle. The area of this sector refers to the area of the whole circle, as the number of days with a certain cloudiness refers to the total number of days in June. Therefore, if no numerical data is given on the pie chart at all, it will still give some approximate idea of the ratio of the values under consideration, in our case - days with different cloudiness.

One glance at the chart is enough to conclude that clear days prevailed in June, with very few cloudy days. We had to sacrifice accuracy to provide better visibility. Providing both the clarity and accuracy of information in many cases allows bar charts.

In our case, the anchor points on the category axis are fixed cloud values.

The height of the bars is proportional to the values of the compared values (for example, the number of days of a particular cloudiness).

The corresponding values are plotted on the vertical value axis.

Neither the value axis nor the bars should have breaks: the chart is used for better comparison, and the presence of breaks destroys the very purpose of presenting the results in the form of a chart.

Petal chart special, it has its own axis for each point of the data series. The axes originate from the center of the chart.

Date: 17.02.2010

Grade: 7

Theme: .

The purpose of the lesson: Learn to work with spreadsheets, build graphs and diagrams based on the data in tables, and do practical work.

Lesson Objectives:

1.Educational: the formation of information culture of students, discipline, perseverance, work culture, positive motivation of the educational process.

2.Educational: development of basic mental functions, general educational skills of algorithmic thinking. Development of skills in working with spreadsheets, application of the knowledge gained in practice.

3.Educational: Improve knowledge when working with spreadsheets, building graphs and charts for visual ideas about the ratio of quantities, application of the knowledge gained in practice.

Equipment: Textbook L. Bosova "Informatics", computer

Lesson type: combined

During the classes

I. Org moment.

Hello guys, sit down. My name is Tatyana Sergeevna, and today I will teach you a lesson. The topic of our today's lesson “ Chart graphs. Visual representation of the ratio of quantities". The purpose of our lesson is to learn how to work with spreadsheets, build graphs and diagrams according to the data in tables, and do practical work.

II Checking homework

1 . Why do we need charts?

2. Why are charts needed?

3. What allows you to track the graph?

III. Learning new material

Visual representation of the ratio of quantities

Cloudiness in May 2006

Diagrams provide a visual representation of the ratio of certain quantities. If the compared values add up to 100%, then use pie charts.

The diagram (Fig. 2.14) does not indicate the number of days with a certain cloudiness, but it shows what percentage of the total number of days falls on days with a certain cloudiness.

Cloudiness in May 2006

numerical data, it will still give some approximate idea of the ratio of the values under consideration, in our case - days with different clouds.

One glance at the diagram in Fig. 2.15 is sufficient to conclude that cloudy days prevailed in May, and there were very few clear days. We had to sacrifice accuracy to provide better visibility. Providing both the clarity and accuracy of information in many cases allows bar charts (fig. 2.16).

The petal chart is special, it has its own axis for each point of the data series. The axes originate from the center of the chart.

Let's summarize:

1. With the help of graphs and diagrams (circular, bar and radial), we were able to visualize a large amount of the same type of tabular information.

2. The graphs allowed us to trace the processes of changes in temperature, humidity and pressure. Charts - compare the number of days with a particular cloudiness and build a wind rose.

3. To make the information presented in one table clearer, we used three graphs and three diagrams.

IV .Practical part.

Job 9. Create charts and graphs

Task 1. Blood groups

Plot a pie chart of the distribution of people by blood group, if people with blood group 0 (1) in the world are about 46%, with blood group A (P) about 34%, group B (W) about 17%, and people with the rarest group AB (IV) is only 3%.

1. Based on the available data, create the following table in Micro soft Excel:

2.Select the table and click the button Chart Wizard toolbars Standard.

3. In the first window of the Wizard, select the type (Circular) and the view (3D version of a pie chart). Using the button Viewing the result see how the diagram will look. Then click on the button Further.

4. The second window displays the highlighted range of cells. Click on the button Further.

5. On the tabs of the third window of the Wizard, set additional chart parameters:

Set the title Distribution of people by blood group;

T place the legend (legend) at the bottom of the diagram;

In the tab Data Signatures choose Share;

6. In the fourth window? The wizards indicate the position of the chart: the name of the new sheet or the current sheet. Specify the location of the diagram on the existing sheet and click on the button Ready.

7. Save the work result in your own folder in a file named Blood groups.

Task 2. Stocks of wood

It is known that the area of the Russian Federation covered with gum vegetation is 7187 thousand to: -m 2. The total timber stock in our forests is 74.3 billion cubic meters. The table shows data on the areas occupied by the main forest-forming species in Russia, and their timber reserves.

Based on the available data, it is necessary to present, using pie charts, the proportion of tree species by area occupied and timber stock.

1.From the available data, create the following table in Micro soft Excel:

2. Calculate the missing values using the formulas: B8 = B9-B3-B4-B5-B6-B7, C8 = C9-C3-C4-C5-C6-C7.

3. Create a pie chart "The share of tree species in the total forest area in Russia." For this:

1) select the range of cells A2: B8;

2) on a new sheet, create a pie chart with the desired additional parameters.

4. Create a pie chart "The share of tree species in the total Russian timber reserves". For this:

3) moving the wash while holding down the (Ctrl) key, select the non-adjacent ranges of cells A2: A8 and C2: C8;

4) create a pie chart with the required additional parameters.

5. Save the work result in your own folder in a file named Our forest.

Task 3. Climate

1. Based on the information in § 2.9 of your textbook, build charts in Microsoft Excel:

1) cut circular "Clouds in May 2006";

2) volumetric circular "Clouds in May 2006";

3) the usual histogram "Clouds in May 2006";

4) petal "Rose of the Winds in May 2006".

2. Save the work result in your own folder in a file named Climate.

V ... Lesson summary

1. What can we do with graphs and charts?

2. What do the charts allow you to trace?

3. What determines the choice of a particular type of information model?

VI. Homework

§ 2.9 pp. 86-89.

VII .Org Moment

This concludes our lesson, goodbye.

Visual representation of the ratio of quantities

Diagrams provide a visual representation of the ratio of certain quantities. If the values to be compared add up to 100%, then pie charts are used.

The chart below does not show the number of days with certain cloudiness, but it shows the percentage of the total number of days that fall on days with certain cloudiness.

One glance at this chart is enough to conclude that cloudy days prevailed in May, and there were very few clear days. We had to sacrifice accuracy to provide better visibility. In many cases, bar charts can provide both clarity and accuracy of information.

The corresponding values are plotted on the vertical value axis. Neither the value axis nor the bars should have breaks: the chart is used for better comparison, and the presence of breaks destroys the very purpose of presenting the results in the form of a chart.

Using the diagram above, you can not only compare the number of days with a particular cloudiness, but also indicate exactly how many days of what cloudiness were during the period under consideration.

The petal chart is special, it has its own axis for each point of the data series. The axes originate from the center of the chart.

Let's summarize

1. With the help of graphs and diagrams (circular, bar and radial), we were able to visualize a large amount of the same type of tabular information.

2. The graphs allowed us to trace the processes of changes in temperature, humidity and pressure. Charts - compare the number of days with a particular cloudiness and build a wind rose.

3. To make the information presented in one table clearer, we used three graphs and three diagrams.

4. For clarity, in some cases we had to sacrifice the accuracy of the information.

Thus, the choice of this or that type of information model depends on the purpose for which we are creating this model.

Questions and tasks

1. The result of a sudden impact on the human body of any environmental factor is called trauma. Based on the diagram showing the structure of childhood injuries, write an appropriate verbal description. Back it up with real-life examples.

2. The data of the Ministry of Health of the Russian Federation on changes over ten years (1992-2001) in the structure of morbidity in children under the age of 14 are presented in a bar chart:

What can you tell by analyzing this diagram?

3. In one of the television talk shows, the host showed the following diagram and said: "The diagram shows that the number of robberies in 2005 increased dramatically compared to 2004."

Do you agree with the journalist's conclusion based on this diagram?

Practical work No. 9
"Create charts and graphs" (tasks 1 - 3)

Task 1. Blood groups

Build a pie chart of the distribution of people by blood type, if people with a blood type 0 (I) in the world about 46%, with the blood of the group A (II) about 34%, groups B (III) about 17%, and people with the rarest group AB (IV) only 3%.

1. Based on the available data, create the following table in Microsoft Excel:

2. Select the table and click on the button Chart Wizard toolbars Standard.

3. In the first window The masters select type (Circular) and the view (3D version of pie chart)... Using the button Viewing the result see how the diagram will look. Then click on the button Further.

4. The second window displays the highlighted range of cells. Click on the button Further.

5. On the tabs of the third window The masters set additional chart parameters:

Set the title Distribution of people by blood type; place the legend (legend) at the bottom of the diagram; on the Data Signatures tab, select Share; click on the button Further.

6. In the fourth window The masters indicate the position of the chart: the name of the new sheet or the current sheet. Specify the location of the diagram on the existing sheet and click on the button Ready.

7. Blood_groups.

Task 2. Stocks of wood

It is known that the area of the Russian Federation covered with forest vegetation is 7187 thousand km. The total timber stock in our forests is 74.3 billion cubic meters. The table shows data on the areas occupied by the main forest-forming species in Russia, and their timber reserves.

Based on the available data, it is necessary to present, using pie charts, the proportion of tree species by area occupied and timber stock.

1. According to the available data, create in the program M icrosoft excel the following table:

2. Calculate the missing values using the formulas:
B8 = B9-VZ-B4-B5-B6-B7,
C8 = C9-CZ-C4-C5-C6-C7.

3. Create a pie chart "The share of tree species in the total forest area of Russia"... For this:

1) select a range of cells A2: B8;

2) on a new sheet, create a pie chart with the desired additional parameters.

4. Create a pie chart "The share of tree species in the all-Russian timber reserves"... For this:

3) moving the mouse while holding down a key (Ctrl), select non-contiguous ranges of cells A2: A8 and C2: C8;

4) create a pie chart with the required additional parameters.

5. Save the work result in your own folder in a file named Our_forest.

Visual representation of the ratio of quantities

Let's summarize

Questions and tasks

Practical work No. 9 "Create charts and graphs" (tasks 1 - 3)

Task 1. Blood groups

Task 2. Stocks of wood

Practical work No. 9
"Create charts and graphs" (tasks 1 - 3)