Column graphs
A bar graph represents a quantitative relationship expressed by the height of the bar. For example, the dependence of the cost on the type of product, the amount of losses due to defects depending on the process, and so on. Typically, bars are shown on a graph in descending order of height from right to left. If among the factors there is a group “Other”, then the corresponding column on the graph is shown on the far right.
Pie charts
A circular graph expresses the ratio of the components of some whole parameter and the entire parameter as a whole, for example: the ratio of the amounts of revenue from sales separately by type of part and the total amount of revenue; the ratio of the types of steel plates used and the total number of plates; the ratio of the topics of work of quality circles (differing in content) and the total number of topics; the ratio of the elements that make up the cost of the product and an integer expressing the cost, and so on. The whole is taken as 100% and is expressed as a full circle. The components are expressed as sectors of a circle and are arranged in a circle in a clockwise direction, starting with the element having the largest percentage of contribution to the whole, in order of decreasing percentage of contribution. The last element is “other”. On a circular graph it is easy to see all the components and their relationships at once.
Strip charts
A strip chart is used to visually represent the ratio of the components of a certain parameter and at the same time to express changes in these components over time, for example: to graphically represent the ratio of the components of the amount of revenue from the sale of products by type of product and their changes by month (or year); to present the content of questionnaires during the annual survey and its changes from year to year; to present the causes of defects and change them by month and so on. When constructing a strip graph, the graph rectangle is divided into zones in proportion to the components or in accordance with quantitative values, and sections are marked along the length of the strip in accordance with the ratio of the components for each factor. By systematizing the strip chart so that the strips are arranged in a sequential time order, it is possible to assess the change in components over time.
Z-shaped charts
The Z-chart is used to evaluate the overall trend when recording actual data such as sales volume, production volume, and so on by month. The graph is constructed as follows: 1) the parameter values (for example, sales volume) are plotted by month (for a period of one year) from January to December and connected by straight segments - a graph formed by a broken line is obtained; 2) the cumulative amount for each month is calculated and the corresponding graph is constructed; 3) total values are calculated, changing from month to month (changing total), and a corresponding graph formed by a broken line is constructed. In this case, the changing total is taken to be the total for the year preceding the given month. The general graph, which includes three graphs constructed in this way, looks like the letter Z, which is why it got its name. The Z-graph is used, in addition to controlling sales volume or production volume, to reduce the number of defective products and the total number of defects, to reduce costs and reduce absenteeism, and so on. Based on the changing total, one can determine the trend of change over a long period. Instead of a changing total, you can plot the planned values and check the conditions for achieving these values.
Radial graphs (radiation diagrams)
Radial graph: straight lines (radii) are drawn from the center of the circle to the circle according to the number of factors. Graduation marks are applied to these radii and data values are plotted (the plotted points are connected by segments). This radiation chart is a combination of a pie and a line graph. The numerical values associated with each factor are compared with standard values achieved by other firms. It is used to analyze enterprise management, to assess quality, and so on.
Data Stratification
Stratification of data is one of the simplest statistical methods. In accordance with this method, data is stratified, that is, data is grouped depending on the conditions for its receipt and each group is processed separately.
For example, stratification can be carried out according to the following criteria:
Stratification by performers - by workers, by gender, by length of service, and so on;
Stratification by machinery and equipment - by new and old equipment, by brand of equipment, by design, and so on;
Stratification by material - by place of production, by manufacturing company, by batch, by quality of raw materials, and so on;
Layering by production method - by temperature, by technological method, by place of work.
When stratifying data, you should strive to ensure that the difference within a group is as small as possible, and the difference between groups is as large as possible.
Layering allows you to gain insight into the hidden causes of defects, and also helps to identify the cause of the defect if a difference in data is detected between the “layers”. For example, if the stratification is carried out according to the “performer” factor, then if there is a significant difference in the data, it is possible to determine the influence of one or another performer on the quality of the product; if the stratification is carried out according to the “equipment” factor - the influence of the use of different equipment.
If, after stratifying the data, it is impossible to clearly determine the decisive factor in solving the problem, then it is necessary to conduct a more in-depth analysis of the data.
In practice, stratification is used to stratify statistical data according to various characteristics and analyze the differences identified in this case in Pareto charts, Ishikawa diagrams, histograms, scatterplots, and so on.
To assess student satisfaction we will use bar, pie, line, radiation and strip graphs.
Graphs make it possible to assess the state of the process at the moment, as well as predict a more distant result based on process trends that can be detected. When a graph shows changes in data over time, the graph is also called a time series.
The following types of graphs are usually used: Broken line (line graph), Column and Pie
Line graph
Using a line graph, display the nature of changes in the amount of annual revenue from the sale of products, and also predict the trend in revenue changes in the next two years (we will first do this using the Trend function).
|
Revenue, thousand USD |
Create a new Excel workbook. We enter the title of the work, as well as the initial data, after which we build a line graph. We edit the resulting diagram using context menus.
The nature of changes in revenue, as well as the forecast, is given by a trend line, which can be constructed by opening the context menu on the broken line and selecting the command Add a trend line .
In the dialog box that opens, on the tab Type Possible types of trend line are shown. To select the line type that best fits the data, you can do the following: place trend lines of each acceptable type in order on the chart (i.e., linear, logarithmic, second-degree polynomial, power, and exponential), specifying for each line on the tab Options forecast ahead by 1 unit (year) and placement on the diagram of the approximation reliability value. Moreover, after constructing the next line, the value of the reliability of the approximation R 2 (The most reliable trend line is the one for which the value of R 2 is equal to or close to one).
The greatest reliability of the approximation is provided by a polynomial line with degree two (R 2 = 0.6738), which we choose as the trend line. To do this, we remove all trend lines from the diagram, after which we restore a polynomial line of the second degree.
Using the approximating line, we can assume that revenue will tend to increase in the coming year.
Bar graph
A bar graph represents a quantitative relationship expressed by the height of the bar. For example, the dependence of the cost on the type of product, the amount of losses due to defects depending on the process, etc. Typically, bars are shown on a graph in descending order of height from right to left. If among the factors there is a group “Other”, then the corresponding column on the graph is shown on the far right.
The figure shows the results of Table 1 above in the form of a bar graph.
Circular graph.
A circular graph expresses the ratio of the components of an entire parameter, for example, the ratio of the amounts of revenue from sales separately by type of part and the total amount of revenue; ratio of elements that make up the cost of the product, etc.
In Fig. The ratio of combine failures by components and assemblies is shown in the form of a circular graph.
|
Type of failure |
Number of failures |
|
|
Harvest part | ||
|
Hydraulic equipment | ||
|
Thresher | ||
|
Electrical equipment | ||
|
hydraulic transmission | ||
Introduction
It is often more convenient for us to perceive information with the help of cards than with a set of numbers. For this, we use diagrams and graphs. In fifth grade, we already studied one type of diagram - circles.
Pie chart
Rice. 1. Circular dia-gram of area of oke-a-new from the total area of oke-a-new
In Figure 1 we see that the Pacific Ocean is not only the largest, but also accounts for almost the exact size of the entire world oke-a-na.
Consider another example.
What are the planes closest to the Sun called the planes of the earthly group.
You write the distance from the Sun to each of them.
58 million km to Mercury
108 million km to Ve-nera
150 million km to Earth
228 million km to Mars
We can again build a circular diagram. It will show what contribution the distance for each plan has in the sum of all the distances. But the sum of all the races has no meaning for us. A full circle does not correspond to any size (see Fig. 2).
Rice. 2 Circular diagram of the distance to the Sun
Since the sum of all the quantities has no meaning for us, there is no point in constructing a circular diagram.
Column chart
But we can depict all these distances using the simplest geometric figures - rectangular -ki, or table-bi-ki. Each person will have their own table. How many times larger is the column, how many times higher is the column. The sum of the greatness of us is not in-te-re-su-et.
To make it convenient to see you from every table, on the devil-tim de-car-to-wu si-ste-mu co-or-di-nat. On the vertical axis, make a mark in milli-o-nah kilo-meters.
And now, they’ve built 4 tables, depending on the distance from the Sun to the planet ( see Fig. 3).
58 million km to Mercury
108 million km to Ve-nera
150 million km to Earth
228 million km to Mars
Rice. 3. Column-cha-taya dia-gram-ma distance to the Sun
Let's compare two diagrams (see Fig. 4).
The column-cha-taya dia-gram is more useful here.
1. It immediately shows the smallest and largest distance.
2. We see that each next distance increases by approximately the same amount well - 50 million km.
Rice. 4. Comparison of types of diagrams
Thus, if you are wondering which diagram is better for you to build - a circular one or a columnar one, then you need to answer :
Do you need the sum of all quantities? Does it make sense? Do you want to see the contribution of each person to the total, to the sum?
If yes, then you need a round one, if not, then a pillar.
The sum of the area of the ocean makes sense - this is the area of the World Ocean. And we built a cool diagram.
The sum of the distances from the Sun to different planets did not make sense to us. And for us it turned out to be a pillar.
Problem 1
Build a diagram from the average temperature for each month of the year.
Temp-pe-ra-tu-ra at-ve-de-na in table 1.
If we add up all the temperatures, then the resulting number will not have much meaning for us. (It will make sense if we divide it by 12 - we get the average temperature, but this is not the topic of our lesson. )
So, we will build a columnar diagram.
Our minimum value is -18, maximum value is 21.
This means that on the vertical axis there will be up to a hundred precise values, from -20 to +25 for example.
Now we depict 12 tables for each month.
The table-bi-ki, corresponding to the ri-tsa-tel-noy temperature, ri-su-em down (see Fig. 5).
Rice. 5. Column dia-gram from the average temperature for each month in the same year
What does this diagram mean?
It is easy to see the coldest month and the warmest one. You can see a specific temperature value for each month. It can be seen that the warmest summer months are less distant from each other than autumn or spring.
So, to build a columnar diagram, you need:
1) Draw the axes of the co-or-di-nat.
2) Look at the minimum and maximum values and mark the vertical axis.
3) Draw a bi-table for each item.
Let's see what unexpected things may arise during construction.
Example 1
Build a column diagram of distance from the Sun to the nearest 4 planets and the nearest star.
We already know about the plane, and the nearest star is Prok-si-ma Tsen-tav-ra (see Table 2).
All distances are again indicated in milli-o-ki-lo-metres.
We build a columnar diagram (see Fig. 6).
Rice. 6. Column dia-gram of distance from the sun to the planet earth and the nearest star
But the distance to the star is so huge that against its background the distance to four planets becomes indistinguishable. We.
The diagram still makes all the sense.
The conclusion is this: you can’t build a diagram based on data that is a thousand or more times apart from each other.
So what to do?
It is necessary to divide the data into groups. For planets, build one diagram, as we did, for stars, another one.
Example 2
Build a column diagram for the melting temperature of metals (see Table 3).
Table 3. Temperature of melting metals
If we build a diagram, we see almost no difference between copper and gold (see Fig. 7).
Rice. 7. Column-cha-taya dia-gram-ma temp-pe-ra-tour of melting of metal-loving (grad-di-rov-ka from 0 grad-du-sov)
All three metals have a temperature up to one hundred and high. The area of the dia-gram is below 900 degrees for us. But then it’s better not to depict this area.
Let's start with 880 degrees (see Fig. 8).
Rice. 8. Column-cha-taya dia-gram-ma temp-pe-ra-tour of melting of metal-loving (grad-du-i-rov-ka with 880 grad-du-sov)
This allowed us to more accurately depict the table.
Now we can clearly see these temperatures, as well as which ones are higher and by how much. That is, we simply removed the lower parts of the tables and depicted only the tops, but closer.
That is, if everyone knows a lot about it, then the city can begin with this knowledge -che-nii, and not from scratch. Then the diagram will turn out to be more visual and useful.
Spreadsheets
Manual drawing of diagrams is up to a hundred-precisely a long and laborious task. Nowadays, in order to quickly make a beautiful diagram of any type, use Excel spreadsheets or ana. Logical programs, for example Google Docs.
You need to enter the data, and the program itself builds a diagram of any type.
By constructing a diagram, illustrating for a certain number of people which language is their native language.
Data taken from Wi-ki-pedia. We write them in an Excel table (see Table 4).
You de-lim the table with the data. Let's look at the types of pre-la-ha-e-my diagrams.
There are both round and columnar ones here. I build them both.
Circular (see Fig. 9):
Rice. 9. Circular diagram of the parts of languages
Pillar-cha-taya (see Fig. 10)
Rice. 10. Column-cha-ta-dia-gram-ma, ill-lu-stri-ru-yu-shchaya, for how many people what language is native
What kind of diagram we need will need to be decided every time. This diagram can be cut down and inserted into any document.
As you can see, creating diagrams today does not require any work.
Application of diagrams in real life
Let's see how in real life the diagram works. Here is the information on the number of lessons in the basic subjects in the sixth grade (see Table 5).
|
Academic subjects |
6th grade |
|
|
Number of lessons per week |
Number of lessons per year |
|
|
Russian language |
||
|
Literature |
||
|
English language |
||
|
Mathematics |
||
|
Story |
||
|
Social science |
||
|
Geography |
||
|
Biology |
||
|
Music |
||
Not very convenient for perception. Below is the same diagram (see Fig. 11).
Rice. 11. Number of lessons per year
And here it is, but these races are in descending order (see Fig. 12).
Rice. 12. Number of lessons per year (descending)
Now we can clearly see which lessons are the most and which are the least. We see that the number of English lessons is two times less than Russian, which is logical, because Russian is our native language and we want to speak, read, and write on it much more often.
source of abstract - http://interneturok.ru/ru/school/matematika/6-klass/koordinaty-na-ploskosti/stolbchatye-diagrammy
video source - http://www.youtube.com/watch?v=uk6mGQ0rNn8
video source - http://www.youtube.com/watch?v=WbhztkZY4Ds
video source - http://www.youtube.com/watch?v=Lzj_3oXnvHA
video source - http://www.youtube.com/watch?v=R-ohRvYhXac
presentation source - http://ppt4web.ru/geometrija/stolbchatye-diagrammy0.html
Before you draw up any chart, you need to decide what types of charts you are interested in.
Let's look at the main ones.
bar chart
The very name of this species is borrowed from the Greek language. The literal translation is to write in a column. This is a kind of columnar type that can be three-dimensional, flat, display contributions (rectangle within a rectangle), etc.
Spot diagram
Shows the mutual relationship between numerical data in a certain number of rows and represents a pair of groups of digits or numbers in the form of a single row of points in coordinates. These types of charts display clusters of data and are used for scientific purposes. When preparing to build a scatter plot, all the data you want to place on the x-axis should be placed in one row/column, and the values on the x-axis should be placed in an adjacent row/column.
Ruled diagram And schedule
A bar chart describes a certain relationship between individual data. In such a diagram, values are located along the vertical axis, while categories are located along the horizontal axis. It follows that such a chart pays more attention to comparisons of data than to changes occurring over time. This type of diagram exists with the “accumulation” parameter, which allows you to show the contribution of individual parts to the overall final result.
The graph displays the sequence of changes in numerical values over absolutely equal periods of time.
These types of diagrams are most often used for plotting.
Area Charts
The main purpose of such a chart is to highlight the amount of change in data over a period by showing the summation of the entered values. It also displays the share of individual values in the total.
Donut and pie charts
The diagrams are quite similar in purpose. Both of them display the role of each element in the total. Their only difference is that a donut chart can contain several rows of data. Each individual nested ring represents an individual series of values/data.
Bubble
One of the varieties of spot. The size of the marker depends on the value of the third variable. During preliminary preparation, you should arrange the data in the same way as when preparing to create a scatter plot.
Exchange diagram
The use of this is often an integral part of the process of selling shares or other securities. It is also possible to construct it to visually determine the change. For three and five values, this type of graph can contain a pair of axes: the first - for bars that represent the interval of certain fluctuations, the second - for changes in the price category.
These are just a few of the types of charts you might need. The types of charts in Excel are very diverse. The choice always depends on the goals. So decide what you want to get in the end, and the build wizard will help you decide!
During this lesson we will become familiar with bar charts and learn how to use them. Let's determine in which cases it is more convenient to use pie charts and in which it is more convenient to use column charts. Let's learn how to apply diagrams in real life.
Rice. 1. Pie chart of ocean areas versus total ocean area
In Figure 1 we see that the Pacific Ocean is not only the largest, but also occupies almost exactly half of the entire world's oceans.
Let's look at another example.
The four closest planets to the Sun are called terrestrial planets.
Let's write down the distance from the Sun to each of them.
Mercury is 58 million km away
Venus is 108 million km away
150 million km to Earth
228 million km to Mars
We can again create a pie chart. It will show how much the distance for each planet contributes to the sum of all distances. But the sum of all distances does not make sense to us. A full circle does not correspond to any value (see Fig. 2).
Rice. 2 Pie chart of distances to the Sun
Since the sum of all quantities does not make sense to us, there is no point in constructing a pie chart.
But we can depict all these distances using the simplest geometric shapes - rectangles or columns. Each value will have its own column. How many times greater is the value, the higher is the column. We are not interested in the sum of quantities.
To make it easier to see the height of each column, let’s draw a Cartesian coordinate system. On the vertical axis we will mark in millions of kilometers.
And now we will build 4 columns with a height corresponding to the distance from the Sun to the planet (see Fig. 3).
Mercury is 58 million km away
Venus is 108 million km away
150 million km to Earth
228 million km to Mars
Rice. 3. Bar chart of distances to the Sun
Let's compare the two diagrams (see Fig. 4).
A bar chart is more useful here.
1. It immediately shows the shortest and greatest distances.
2. We see that each subsequent distance increases by approximately the same amount - 50 million km.
Rice. 4. Comparison of chart types
Thus, if you are wondering which chart is better for you to build - a pie chart or a column chart, then you need to answer:
Do you need the sum of all quantities? Does it make sense? Do you want to see the contribution of each value to the total, to the sum?
If yes, then you need a circular one, if not, then a columnar one.
The sum of the areas of the oceans makes sense - this is the area of the World Ocean. And we built a pie chart.
The sum of the distances from the Sun to different planets did not make sense to us. And the columnar one turned out to be more useful for us.
Construct a diagram of the change in average temperature for each month throughout the year.
Temperatures are given in Table 1.
|
September |
|
Table 1
If we add up all the temperatures, the resulting number will not make much sense to us. (It makes sense if we divide it by 12 - we get the average annual temperature, but this is not the topic of our lesson.)
So, let's build a bar chart.
Our minimum value is -18, maximum - 21.
Now let's draw 12 columns for each month.
We draw the columns corresponding to negative temperatures downwards (see Fig. 5).
Rice. 5. Column chart of the change in average temperature for each month during the year
What does this diagram show?
It's easy to see the coldest month and the warmest. You can see the specific temperature value for each month. It can be seen that the warmest summer months differ less from each other than the autumn or spring months.
So, to build a bar chart, you need:
1) Draw coordinate axes.
2) Look at the minimum and maximum values and mark the vertical axis.
3) Draw bars for each value.
Let's see what surprises may arise during construction.
Construct a bar graph of the distances from the Sun to the nearest 4 planets and the nearest star.
We already know about the planets, and the nearest star is Proxima Centauri (see Table 2).
Table 2
All distances are again in millions of kilometers.
We build a bar chart (see Fig. 6).
Rice. 6. Bar chart of the distance from the sun to the terrestrial planets and the nearest star
But the distance to the star is so enormous that against its background the distances to the four planets become indistinguishable.
The diagram has lost all meaning.
The conclusion is this: you cannot build a chart based on data that differs from each other by a thousand or more times.
So what to do?
You need to split the data into groups. For planets, construct one diagram, as we did, for stars, another.
Construct a bar chart for the melting temperatures of metals (see Table 3).
Table 3. Melting temperatures of metals
If we build a diagram, we hardly see the difference between copper and gold (see Fig. 7).
Rice. 7. Column chart of melting temperatures of metals (graduation from 0 degrees)
All three metals have quite high temperatures. The area of the diagram below 900 degrees is not interesting to us. But then it is better not to depict this area.
Let's start the calibration from 880 degrees (see Fig. 8).
Rice. 8. Column chart of melting temperatures of metals (graduation from 880 degrees)
This allowed us to depict the bars more accurately.
Now we can clearly see these temperatures, as well as which one is higher and by how much. That is, we simply cut off the lower parts of the columns and depicted only the tops, but in approximation.
That is, if all values start from a sufficiently large value, then calibration can begin from this value, and not from zero. Then the diagram will be more visual and useful.
Manual drawing of diagrams is a rather long and labor-intensive task. Today, to quickly make a beautiful chart of any type, you use Excel spreadsheets or similar programs such as Google Docs.
You need to enter the data, and the program itself will build a chart of any type.
Let's build a diagram illustrating how many people speak which language as their native language.
Data taken from Wikipedia. Let's write them down in an Excel table (see Table 4).
Table 4
Let's select the table with the data. Let's look at the types of diagrams offered.
There are both circular and columnar ones. Let's build both.
Circular (see Fig. 9):
Rice. 9. Pie chart of language shares
Columnar (see Fig. 10)
Rice. 10. A bar chart illustrating how many people speak which language as their mother tongue.
What kind of diagram we need will need to be decided each time. The finished diagram can be copied and pasted into any document.
As you can see, creating diagrams today is not difficult.
Let's see how the diagram helps in real life. Here is information on the number of lessons in basic subjects in sixth grade (see Table 5).
|
Academic subjects |
Number of lessons per week |
Number of lessons per year |
|
Russian language |
||
|
Literature |
||
|
English language |
||
|
Mathematics |
||
|
Story |
||
|
Social science |
||
|
Geography |
||
|
Biology |
||
|
Music |
Table 5
Not very easy to read. Below is a diagram (see Fig. 11).
Rice. 11. Number of lessons per year
And here it is, but the data is arranged in descending order (see Fig. 12).
Rice. 12. Number of lessons per year (descending)
Now we can clearly see which lessons are the most and which are the least. We see that the number of English lessons is two times less than Russian, which is logical, because Russian is our native language and we have to speak, read, and write in it much more often.
Bibliography
- Vilenkin N.Ya., Zhokhov V.I., Chesnokov A.S., Shvartsburd S.I. Mathematics 6. - M.: Mnemosyne, 2012.
- Merzlyak A.G., Polonsky V.V., Yakir M.S. Mathematics 6th grade. - Gymnasium. 2006.
- Depman I.Ya., Vilenkin N.Ya. Behind the pages of a mathematics textbook. - M.: Education, 1989.
- Rurukin A.N., Tchaikovsky I.V. Assignments for the mathematics course for grades 5-6. - M.: ZSh MEPhI, 2011.
- Rurukin A.N., Sochilov S.V., Tchaikovsky K.G. Mathematics 5-6. A manual for 6th grade students at the MEPhI correspondence school. - M.: ZSh MEPhI, 2011.
- Shevrin L.N., Gein A.G., Koryakov I.O., Volkov M.V. Mathematics: a textbook-interlocutor for grades 5-6 of secondary school. - M.: Education, Mathematics Teacher Library, 1989.
http://ppt4web.ru/geometrija/stolbchatye-diagrammy0.html
Homework
1. Construct a bar chart of precipitation (mm) per year in Chistopol.
2. Draw a bar graph using the following data.
3. Vilenkin N.Ya., Zhokhov V.I., Chesnokov A.S., Shvartsburd S.I. Mathematics 6. - M.: Mnemosyne, 2012. No. 1437.