Bar Graphs

The bar graph represents the 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 marriage, depending on the process, and so on. Typically, the bars are shown on the 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 pie chart 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 proceeds from the sale separately by type of part and the total amount of proceeds; the ratio of the types of steel plates used and the total number of plates; the ratio of the topics of the work of quality circles (which differ 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 expressed as a full circle. The components are expressed as sectors of a circle and arranged in a circle in the clockwise direction, starting with the element with the largest percentage of contribution, into the whole, in order of decreasing percentage of contribution. The last element is "other". On a pie chart, it is easy to see all the components and their ratio at once.

Strip charts

A ribbon chart is used to visualize the ratio of the components of a certain parameter and at the same time to express the change in these components over time, for example: for a graphical representation of the ratio of the components of the amount of revenue from the sale of products by type of product and their changes by months (or years); to present the content of the questionnaires during the annual survey and its change from year to year; to present the causes of defects and change them by month, and so on. When constructing a strip chart, the rectangle of the graph is divided into zones in proportion to the components or in accordance with quantitative values, and sections are marked along the length of the tape in accordance with the ratio of the components for each factor. By arranging a strip chart so that the strips are arranged in sequential time order, it is possible to evaluate the change in the components over time.

Z-plots

The Z-plot is used to evaluate the overall trend when recording actual data by month, such as sales volume, production volume, and so on. The graph is constructed as follows: 1) the values ​​​​of the parameter (for example, sales volume) are plotted by months (for a period of one year) from January to December and connected by straight line segments - a graph formed by a broken line is obtained; 2) the cumulative amount for each month is calculated and the corresponding schedule is built; 3) the total values ​​are calculated, changing from month to month (changing total), and the corresponding graph is built, formed by a broken line. For the changing total, in this case, the total for the year preceding the given month is taken. 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-shaped chart 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. By changing the total, you can determine the trend of change over a long period. Instead of a changing total, you can plot the planned values ​​on the graph and check the conditions for achieving these values.

Radial Plots (Radiation Plots)

Radial graph: from the center of the circle to the circle, straight lines (radii) are drawn according to the number of factors. Graduation divisions are applied to these radii and the data values ​​are plotted (the delayed points are connected by segments). This radiation chart is a combination of a pie chart and a line chart. The numerical values ​​associated with each of the factors 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 (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 their receipt and each group is processed separately.

For example, stratification can be carried out according to the following criteria:

Stratification by performers - by employees, by gender, by work experience, and so on;

Stratification by machines and equipment - by new and old equipment, by brand of equipment, by design, and so on;

Stratification by material - by place of production, by manufacturer, by batch, by quality of raw materials, and so on;

Stratification according to the method of production - according to temperature, according to the technological method, according to the place of work.

When stratifying data, one 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 get an idea of ​​the hidden causes of defects, and also helps to identify the cause of a defect if a difference in data between “layers” is found. For example, if the stratification is carried out according to the “performer” factor, then with 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 was carried out according to the “equipment” factor - the impact of using different equipment.

If after data stratification it is impossible to determine visually the decisive factor in solving the problem, then a deeper analysis of the data is necessary.

In practice, stratification is used to stratify statistical data according to various characteristics and analyze the difference revealed in this case in Pareto charts, Ishikawa charts, histograms, scatterplots, and so on.

To assess student satisfaction, we will use columnar, circular, linear, radiation and strip graphs.

Such a graph represents, for example, the change over time in the technical readiness factor of the fleet, the number of cars under repair, etc. The value of the corresponding value is plotted along the ordinate axis on such a graph, and time is plotted along the abscissa axis. The points plotted on the graph are connected by straight lines.

An example of such a graph, used to express a change in an indicator, for example, car downtime due to technical malfunctions, is shown in Fig. 1.1.

The effectiveness of the information obtained will increase if, during the analysis, the data is stratified by factors such as car models, types of malfunctions, etc.

Rice. 1.1. Graph expressed by a broken line: 1 - real section of the graph; 2 - segment reflecting the trend

From the figure, one can understand the nature of the change in the number of idle cars. If we analyze the data using the least squares method, then using the segment reflecting the trend in the indicator, we can predict its value for the upcoming period of vehicle operation.

bar graph

A bar graph represents a quantitative relationship expressed by the height of the bar of factors such as the number of idle cars for various reasons for failure, the number of idle cars by model, etc.

Varieties of a bar chart can be a Pareto chart and a histogram.

Rice. 1.2. bar graph

When constructing a bar graph, the value of the indicator is plotted along the ordinate axis, and factors are plotted along the abscissa axis. Each factor corresponds to a column.

The graph shows the significance of each factor.

A more visual representation of the data is when the columns expressing the number are arranged on the graph in ascending or decreasing order of their frequency. If at the same time we construct a cumulative sum, we get a Pareto chart.

Pie chart

A pie chart expresses the ratio of the components of some whole parameter and the entire parameter as a whole. Such parameters can be the ratio of the costs of maintaining vehicles in a healthy state - fuel costs, depreciation, tire costs, maintenance, repairs, overheads, etc.

On the pie chart, you can see all the components and their ratio at once. An example of a pie chart is shown in fig. 1.3, which shows the ratio of the components of the cost of production.

Rice. 1.3. Circle chart. The ratio of the cost components for the production of current repairs of vehicles of a motor transport enterprise: 1 - total production costs; 2, 3 - main items of expenditure; 4-7 - components of the costs of the main item 2 (direct costs); 9–12 - cost components for main item 3 (indirect costs); 8 - others

As can be seen from the graph, each component of the total costs can be represented by the ratio of costs to more detailed items of expenditure. For example, the cost of current car repairs consists of the cost of spare parts, materials, depreciation of equipment, the cost of electricity, heat and lighting, salaries and bonuses for repairmen and management personnel, cleaning of the premises, etc.

The whole is taken as 100% and expressed as a full circle. The components are expressed as sectors of a circle and arranged in a circle in the clockwise direction. In this case, they start with the element that has the greatest significance. The last element is "other".

The graph shows the ratio of the components of the cost of production. The stratification by components and comparison of costs for individual periods provides an opportunity to obtain information that can be used to reduce the cost of production.

strip chart

A strip chart is used to visually represent the ratio of the components of a parameter and to track the changes in these components over time. For example: for a graphical representation of the ratio of the cost components for the current repair of equipment, for the presentation of the causes of equipment defects and their changes by months, etc.

When constructing a strip chart, the chart rectangle is divided into zones in proportion to the components, for example, production costs. Sections are marked along the length of the tape in accordance with the ratio of the components for each factor.

The tape chart is systematized so that the tapes are arranged in sequential time order. This makes it possible to evaluate the change in components over time.

Rice. 1.4. Ribbon chart:

1-4 - the ratio of the components of the overall result (costs); 5 - others

The graph shows that the share of costs 3, 4 increases over time. Cost share 1 first increases and then decreases. The share of products 2, 5 decreases. This information can be used to take timely action to improve production efficiency.

Z-plot

The Z-plot is used to assess the overall trend of the analyzed indicators over time.

The graph is built as follows:

1 - the parameter values ​​are plotted by time intervals and connected by straight line segments - a broken line graph is obtained;

2 - the cumulative amount for each month is calculated and the corresponding graph is built;

3 - totals are calculated that change from one period of time to another (changing total). Then the corresponding polyline plot is plotted. The principle of constructing a Z-shaped graph to control the change in the total indicator is shown in fig. 1.5.

The general graph, which includes three graphs constructed in this way, looks like the letter Z, which is why it got its name. By changing the total, you can determine the trend of change over a long period.

Rice. 1.5. Monitoring the trend of process indicators:

1 - change in the process indicator; 2 - cumulative sum of indicators; 3 - the changing total of the sum of indicators for the segments of observations L in comparison with the previous similar period

The graph clearly shows the change in the sum of process indicators and the change in the cumulative sum of indicators. According to the behavior of the changing total sum of indicators, the general trend of change in their sum over the interval is clear.

radiation diagram

The chart is used to visualize data for several factors at once. For example, when attesting the workplace of performers of work on car components, for analyzing enterprise management, for assessing personnel, for assessing the quality of maintenance and repair of vehicles, etc.

An example of a radiation diagram for the analysis of the production management of maintenance and repair of vehicles of a motor transport enterprise is shown in fig. 1.6.

The graph is constructed as follows: from the center of the circle to the circle, straight lines (radii) are drawn according to the number of factors, which resemble rays that diverge during radioactive decay (hence the name of the graph). Graduation divisions are applied to these radii and the data values ​​are plotted. The points that denote the delayed values ​​are connected by straight line segments. The numerical values ​​related to each of the factors are compared with targets, standard values ​​or values ​​achieved by other enterprises.

Rice. 1.6. Radiation diagram of certification of the production site:

1 - production and technical base; 2 - logistics; 3 - staffing; 4 - financial support; 5 - organizational support; 6 - information support; 7 - microclimate; 8 - sanitary conditions

Analyzing the schedule, one can assess the state of the resource support of the engineering and technical service at a given enterprise. Standard values ​​of control indicators are indicated by circles. When compared with the standard lines, it can be seen that problem 6, related to information support, requires special attention. There are difficulties with financial security (factor 4).

1.1.2.7. Map of planned and actual indicators

The map is a table in which the planned and actually achieved indicators are entered in two vertical lines, and the date of receipt of the data is placed horizontally.

The table clearly shows the progress of the plan. Such a map is used, for example, in the case of monitoring the implementation of a car maintenance plan or changing the technical readiness factor of a fleet of cars, etc. An example of a map comparing planned and actual indicators for monitoring a production task is Table. 1.1.

The table makes it easy to compare planned and actual indicators and make a decision on the degree of backlog from the plan. The table shows that, in accordance with the plan, work is carried out only in the third convoy. It is necessary to find out the reasons for the delay in the implementation of plans in the first and second convoys and take measures to eliminate the backlog.

Table 1.1

convoy	Type of maintenance	the date
08.09.08	09.09.08	10.09.08	11.09.08	12.09.08	13.09.08
Mon.	Tue	Wed	Thu.	Fri.	Sat.
	TO-1	Plan
Fact
TO-2	Plan
Fact
…	…	…	…	…	…	…	…	…
N	TO-1	Plan
Fact
TO-2	Plan
Fact

bar graph

Quality indicators always have a certain spread. The scatter is subject to certain patterns. The analysis of indicators of the causes of faults subject to dispersion is carried out using histograms.

A histogram is a tool that allows you to visually evaluate the distribution of statistical data grouped by the frequency of falling into a certain, predetermined interval. It is a bar graph built on the basis of data received over a certain period, which are divided into several intervals; the number of data falling into each of the intervals (frequency) is expressed by the height of the bar (Fig. 1.7).

The histogram provides a lot of information when comparing the obtained distribution with the control standards.

The histogram is built in the following order.

Systematize the data collected, for example, for 10 days or for a month. The number of data should be at least 30–50, the optimal number is about 100. If there are more than 300 of them, the time spent on processing them turns out to be too large.

The next step is to determine the intervals between the largest and smallest values. The width of each section can be determined using the formula:

.

The number of patches should roughly correspond to the square root of the number of data. When the number of data is 30–50, the number of segments is 5–7; when the number of data is 50–100, it is 6–10); with the number of data 100–200, 8–15.

The last step is to plot the histogram plot. The values ​​of quality parameters are plotted along the abscissa axis, the frequency along the ordinate axis. For each section, a rectangle (column) is built with a base equal to the width of the section interval; its height corresponds to the frequency of data falling into this interval (Fig. 1.7).

Analysis of the histogram makes it possible to draw a conclusion about the state of the process at the moment, however, if process control conditions or time changes are unclear, other tools must also be used in combination with the histogram. The information obtained as a result of the analysis of the histogram can be used to build and study a cause-and-effect diagram, which will increase the validity of the measures planned to improve the process.

Since the histogram expresses the process conditions over the period over which the data were collected, the shape of the distribution of the histogram compared to the control limits can provide important information.

There are modifications of the histogram shape: with bilateral symmetry, the histogram is elongated to the right, the histogram is elongated to the left, a two-hump diagram, histograms in the form of a cliff, a histogram with a separate island, a histogram with a flat top, etc. The shape of the histograms is used to judge violations of the rules for their construction.

Histogram with bilateral symmetry (normal distribution). A histogram with this distribution is the most common. It indicates the stability of the process (Fig. 1.7).

Rice. 1.7. Histogram with bilateral symmetry (normal distribution)

When comparing the histogram with the norm or with the planned values, different cases may occur.

1. The average value of the distribution is in the middle between the control standards, the spread does not go beyond the norm.

2. The histogram is completely within the interval limited by the control standards, but the spread of values ​​is large, the edges of the histogram are almost at the limits of the norm (the width of the norm is 5–6 times greater than the standard deviation). In this case, there is the possibility of marriage, so measures are needed to reduce the spread.

3. The average value of the distribution is in the middle between the control standards, the spread of indicators is also within the normal range, but the edges of the histogram do not reach the control standards much (the distribution width is more than 10 times the standard deviation). If you slightly increase the spread, that is, make the standards for technological operations and norms somewhat less stringent, you can increase productivity and reduce the cost of raw materials and components.

4. The scatter is small compared to the width of the norm, but due to the large shift in the average value towards the lower limit of the norm, marriage appears. Measures are needed to help move the average value to the midpoint between control standards.

5. The average value is in the middle between the control standards, but due to the large scatter, the edges of the histogram go beyond the limits of the norm, i.e., a marriage appears. Measures are needed to reduce spread.

6. The average value is shifted relative to the center of the norm, the spread is large, marriage appears. Measures are needed to move the average to the midpoint between the control limits and reduce the spread.

Thus, comparing the type of distribution of the histogram with the norm or planned values ​​provides important information for process control.

It is advisable to analyze the state of the process by histograms in combination with the use of control maps.

When creating a chart in an Excel worksheet, in a Word document, or in a PowerPoint presentation, you have many options to choose from. Whether you use the chart recommended for your data or choose from a list of all charts, this article will help you learn a little more about each type of chart.

To view a description of a chart type, select it from the drop-down list.

Data in columns or rows of a worksheet can be represented as a histogram. In a bar chart, categories are usually shown on the horizontal (categories) axis and values ​​on the vertical (values) axis, as shown in this chart:

Histogram types

Data arranged in columns or rows of a sheet can be presented as a graph. In graphs, category data is evenly distributed along the horizontal axis, and all values ​​are evenly distributed along the vertical axis. Graphs allow you to show the continuous change in data over time on an evenly distributed axis, so they are ideal for presenting data trends at regular intervals, such as months, quarters, or fiscal years.

Graph types

Pie and donut charts

Data in one column or row of a worksheet can be represented as a pie chart. The pie chart displays the size of the elements of one data series relative to the sum of the elements. data points in a pie chart are displayed as percentages of the entire pie.

only one data series needs to be displayed;

all values ​​of your data are non-negative;

almost all data values ​​are greater than zero;

there are no more than seven categories, each of which corresponds to parts of the general circle.

Types of Pie Charts

Donut charts

Data that is only in the columns or rows of a worksheet can be represented as a donut chart. Like a pie chart, a donut chart displays the relationship of parts to a whole, but can contain multiple data series.

Types of donut charts

Data in columns or rows of a worksheet can be represented as a bar chart. Bar charts are used to compare individual items. In this type of chart, the categories are usually placed on the vertical axis and the values ​​on the horizontal axis.

axis labels are long;

the output values ​​are durations.

Types of bar charts

Data in columns or rows of a worksheet can be represented as an area chart. Area charts can be used to show how values ​​change over time and draw attention to the bottom line following a trend. By displaying the sum of the values ​​of the series, such a chart also clearly shows the contribution of each series.

Types of area charts

Scatter chart with scatter and bubble chart

The data in the columns and rows of a worksheet can be represented as a scatter plot. Place the X-axis data in one row or column, and the corresponding Y-axis data in adjacent rows or columns.

A scatter chart has two value axes: horizontal (X) and vertical (Y). In a scatter plot, x and y values ​​are combined into a single data point and plotted at irregular intervals or clusters. Scatter plots are commonly used to display and compare numerical values, such as scientific, statistical, or technical data.

it is required to change the scale of the horizontal axis;

it is required to use a logarithmic scale for the horizontal axis;

the values ​​are located unevenly on the horizontal axis;

there are many data points on the horizontal axis;

You want to set up independent scatter chart scales to display more information about data that contains pairs of grouped value fields.

it is required to display not differences between data points, but analogies in large data sets;

it is required to compare many data points without regard to time; the more data that is used to build the scatter plot, the more accurate the comparison will be.

Types of Scatter Plots

Like the scatter chart, the bubble chart adds a third column to indicate the size of the bubbles used to represent the data points in the data series.

Bubble chart type

Data arranged in columns or rows of a sheet in a certain order can be represented as a stock chart. As the name suggests, stock charts can show changes in stock prices. But they can also be used to illustrate changes in other data, such as daily precipitation or annual temperature variations. To create a stock chart, you need to properly organize the data.

For example, to create a simple stock chart (highest price, lowest price, close price), place the data in the columns labeled Highest Price, Lowest Price, and Close Price, in that order.

Stock chart types

Data in columns or rows of a worksheet can be represented as a surface chart. This chart is useful if you want to find optimal combinations of data from two sets. As on a topographic map, areas belonging to the same ranges are highlighted with colors and shading. You can create surface charts to illustrate categories and datasets that represent numeric values.

Types of surface charts

Radar charts

Data in columns or rows of a worksheet can be represented as a radar chart. The radar chart allows you to compare the aggregated values ​​of multiple data series.

Types of Radar Charts

Tree chart (Office 2016 and later only)

Note:

Sunburst chart (Office 2016 and later only)

Note:

Bar charts (Office 2016 and later only)

Histogram types

Area and Whisker Charts (Office 2016 and later only)

Note: There are no subtypes for the box and whisker chart.

Waterfall charts (Office 2016 and later only)

Note:

Funnel charts (Office 2016 and later only)

As a rule, the values ​​gradually decrease, so the chart bars look like a funnel. Learn more about funnel charts

Combo charts (Office 2013 and later only)

Data in columns and rows can be represented as a combo chart. Combo charts combine two or more types of charts to improve the readability of the data, especially when the data is significantly different from each other. Displaying a secondary axis on such a chart further enhances the perception. In this example, a bar chart was used to display the number of homes sold from January to June, and then an easy-to-read chart was used to quickly determine the average sale price for the month.

Types of combo charts

Map chart (Excel only)

With a map chart, you can compare values ​​and display categories by geographic region. Use it if you have geographic regions in your data, such as countries/regions, states, districts, or zip codes.

For example, a map showing countries by population uses values. The values ​​represent the cumulative population of each country and are displayed using a spectrum of two-color gradients. The color for each region is determined depending on which part of the spectrum its value falls in relation to other values.

The following example map of countries by population uses a legend to display categories to show groups or relationships. All data points are represented by completely different colors.

If you already have a chart and you just want to change its type, follow these steps:

Many types of charts are available to help you display data in the most appropriate way for your audience. Below are some examples of the most common chart types and how to use them.

Funnel Diagram

Funnel charts display values ​​related to different steps in the process.

As a rule, the values ​​decrease gradually, which allows the bars to resemble a funnel. See Create a funnel chart for more information.

tree diagram

The tree chart provides a hierarchical view of data and an easy way to compare different levels of classification. A tree chart displays categories by color and close together, and can easily display a large amount of data that is difficult to use with other chart types. A tree chart can be built when empty (empty) cells exist in a hierarchical structure and tree charts are well suited for comparing proportions in a hierarchy.

There are no subtypes for tree chart.

For more information, see Create a tree diagram .

sunburst diagram

The sunburst chart is ideal for displaying hierarchical data and can be built if there are blank (empty) cells in the hierarchical structure. Each level of the hierarchy is represented by a single ring or circle, with the innermost circle at the top of the hierarchy. A sunburst chart without hierarchical data (one level of categories) is similar to a donut chart. However, a sunburst diagram with several levels of categories shows how the outer rings are related to the inner rings. The sunburst diagram most effectively shows how one call is broken down into its component parts.

There are no subtypes for the sunburst chart.

For more information, see Create a sunburst chart.

waterfall chart

The waterfall chart shows the cumulative total of financial data as values ​​are added or subtracted. This is useful for understanding how a series of positive and negative values ​​affects the initial value. The columns are highlighted in color so that you can quickly recognize a negative number.

There are no subtypes for waterfall charts.

See Create a Waterfall Chart for more information.

Histograms and Pareto charts

The data displayed on the histogram shows the frequencies of the distribution. Each column of the chart can be modified for further data analysis.

Histogram types

More information can be found in and Pareto charts.

Mustache and cell chart

A box and whisker chart shows the distribution of data by quartile, highlighting the mean and outliers. Margins may contain lines, vertically called "whiskers". These lines indicate variation outside of the upper and lower quartiles, and any of the points outside of these lines or whiskers is considered an outlier. Use this chart type if you have multiple datasets that can be related to each other in some way.

For more information, see Create a box and mustache chart.

Data arranged in columns or rows in an Excel worksheet can be visualized as a surface chart. As with a topographic map, colors and patterns indicate areas that are in the same range of values.

A surface chart is useful when you need to find the optimal combination of two sets of data.

Surface charts include the chart subtypes listed below.

Shows trends for values ​​across two dimensions as a continuous curve. The colored bars in the surface chart do not represent data series, but the difference between values. This chart displays a three-dimensional representation of the data, which can be represented as a rubber sheet stretched over a 3D bar chart. Typically this chart is used to show relationships between large amounts of data that would otherwise be hard to see.

Wire surface chart. This chart only displays lines. The wire surface plot is difficult to read, but this type of plot is recommended for quickly displaying large datasets.

Contour diagram. When viewed from above, a surface chart resembles a two-dimensional topographic map. In a contour chart, the colored bars represent specific ranges of values. Lines on a contour plot link interpolated points with the same value.

Wire contour diagram. Surface chart when viewed from above. Without color bars, only lines are displayed on the contour plot surface. Colorless contour diagrams are difficult to read. Surface charts can be used instead.

Like a pie chart, a donut chart shows the relationship of parts to a whole. However, it may contain more than one data series. Each ring in a donut chart represents one data series.

Donut charts include the following subtypes of charts.

Displays data as rings, each representing one data series. If the data labels show percentages, each ring's data will add up to 100%.

Sliced ​​donut chart. Reflects the contribution of each value to the total, highlighting individual values. Such charts can contain more than one data series.

Radar charts are used to compare the aggregate values ​​of multiple data series.

Radar charts include the following subtypes of charts.

Displays changes in values ​​from the origin.

Completed radar chart. Displays changes in values ​​from the origin, filling the area covered by each data series with color.

Introduction

Often it is more convenient for us to re-create information with the help of a card-ti-nok than a set of numbers. To do this, use dia-grams and gra-fi-ki. In the fifth grade, we have already learned one type of diagrams - circles.

Pie chart

Rice. 1. A circle diagram of the area of ​​the ocean-a-nov from the total area of ​​the ocean-a-nov

In figure 1, we see that the Pacific Ocean is not only the largest, but also for-ni-ma-et almost exactly in-lo-vi-well of the whole world oke-a-on.

Let's look at another example.

Che-you-re-nearest planes-you to the Sun on-zy-va-yut-sya plane-not-that-mi-terrestrial group.

You write the distance from the Sun to each of them.

To Mer-ku-riya 58 million km

To Ve-ne-ry 108 million km

150 million km to Earth

Mars 228 million km

We can again build a circle diagram. It will show what contribution the distance for each plane has in the sum of all races. But the sum of all races has no meaning for us. A full circle does not correspond to any value (see Fig. 2).

Rice. 2 Kru-go-vaya dia-gram-ma of distances-to-I-ny to the Sun

Since the sum of all the values ​​\u200b\u200bhas no meaning for us, then there is no point in building a circle diagram.

bar chart

But we can depict all these distances using the simplest geo-met-ri-che-fi-gu-ry - rectangular-coal-ni -ki, or table-bi-ki. Each ve-li-rank will have its own beak table. How many times more is the ve-li-chi-na, so many times the column-beak is higher. The sum of the values ​​\u200b\u200bof us is not in-te-re-su-et.

To make it convenient to see you-with-that every-to-go-table-bi-ka, on-the-dark-time de-car-to-woo si-ste-mu ko-or-di-nat. On the vertical axis, let's make a mark in milli-li-o-nah ki-lo-meters.

And now, in a row-by-them, 4 table-bi-ka you-with-that, with-from-the-st-tu-th-distance from the Sun to the plane-not-you ( see Fig. 3).

To Mer-ku-riya 58 million km

To Ve-ne-ry 108 million km

150 million km to Earth

Mars 228 million km

Rice. 3. Pillar-cha-taya diagram-ma-hundred-I-ny to the Sun

Compare two diagrams (see Fig. 4).

Pillar-cha-thaya diagram is more useful here.

1. On it you can immediately see the smallest-neck and the largest-neck distance.

2. We see that each next-du-th-distance-sto-i-increase-whether-chi-va-et-sya example by the same ve-li-chi- well - 50 million km.

Rice. 4. Comparing types of diagrams

In this way, if you are wondering which diagram is better for you to build - round or column, then you need to answer :

Do you need the sum of all things? Does it make sense? Do you see the contribution of each ve-li-chi-we to the total, to the sum?

If yes, then you need a circle, if not, then a column-cha-thai.

The sum of the area of ​​​​the ocean-a-nov makes sense - this is the area of ​​\u200b\u200bMi-ro-in-the-th ocean-a-on. And we build-and-whether a circle diagram.

The sum of distances from the Sun to different planets did not make sense to us. And for us, it was easier for her eye-for-a-pillar-cha-taya.

Task 1

Build a diagram from me-not-niya average te-pe-ra-tu-ry for each month in those years.

Tem-pe-ra-tu-ra with-ve-de-na in table 1.

If we add everything up to those-pe-ra-tu-ry, then the resulting number will not have any pain-sho-th meaning for us. (It will make sense if we divide it into 12 - we’ll get the average-not-go-to-th-pe-ra-tu-ru, but this is not the topic of our lesson. )

So, we will build a column diagram.

Our mini-small value is -18, max-si-small - 21.

So, on the vertical axis there will be up to a hundred exact values, from -20 to +25 for example.

Now there are 12 bi-tables for each month.

Table-bi-ki, corresponding to-answer-stu-u-schi from-ri-tsa-tel-noy te-pe-ra-tu-re, ri-su-em down (see Fig. 5).

Rice. 5. Pillar-cha-taya diagram-ma from-me-not-niya average temp-pe-ra-tu-ry for each month in those years

What does this diagram say?

It is easy to see the coldest month and the warmest. You can see the specific meaning of those-pe-ra-tu-ry for each month. It can be seen that the warmest summer months are less from each other than autumn or spring.

So, in order to build a column diagram, you need:

1) Draw the axes of co-or-di-nat.

2) Look at the mini-small and max-si-small values ​​​​and make a mark-up of the vertical axis.

3) Draw a bi-table for each ve-li-chi-ny.

Let's see what unexpected data-no-sti can arise when building.

Example 1

Build a column-cha-thuyu chart of distances from the Sun to the nearest 4 planets and the nearest stars.

We already know about the plane, and the nearest star is Prok-si-ma Tsen-tav-ra (see Table 2).

All distances again indicate us in milli-li-o-nas ki-lo-meters.

Build a column diagram (see Fig. 6).

Rice. 6. Pillar-cha-taya diagram of the distance from the sun to the planet of the earth group and the nearest stars

But the distance to the star is so huge that, against its background, the distance to four planes is not one hundred, but we.

Dia-gram-ma in-te-rya-la makes all the sense.

The conclusion is this: you can’t build a diagram according to data that are from-whether they are from each other a thousand or more times.

So what to do?

It is necessary to break the data into groups. For the planet, build one diagram, as we de la li, for the stars - another.

Example 2

Build a column diagram for the temperature of the melting of metals (see Table 3).

Tab. 3. Tem-pe-ra-tu-ry melting metal

If we build a diagram, then we almost do not see the difference between copper and gold (see Fig. 7).

Rice. 7. Pillar-cha-taya diagram-ma tem-pe-ra-tour melt-le-niya metal-lov (gra-di-ditch-ka from 0 deg-du-owls)

All three metals have tem-pe-ra-tu-ra up to a hundred-precise-but you-so-kai. The area of ​​\u200b\u200bthe diagram is below 900 deg-du-owls to us not in-te-res-na. But then this area is better not to depict.

Start with 880 degrees-doo-and-ditch (see Fig. 8).

Rice. 8. Pillar-cha-taya dia-gram-ma tem-pe-ra-tour melt-le-niya metal-lov (gra-du-i-ditch-ka from 880 deg-du-owls)

This pos-in-li-lo us to more accurately depict a bi-table.

Now we can clearly see these te-pe-ra-tu-ry, as well as how much more and how much. That is, we just from-re-for-whether the lower parts of the table-bi-kov and depict-ra-zi-whether only the top-hush-ki, but in close proximity.

That is, if all the values ​​​​are na-chi-na-yut-sya with up to a hundred-precise-but pain-sho-go, then the city-du-and-ditch-ku can be started from this sign -che-niya, and not from scratch. Then the diagram will turn out to be more visual and useful.

Spreadsheets

Manual ri-co-va-tion of diagrams - up to a hundred-accurate-but long and labor-to-eat-something for-nying. This year, in order to quickly make a beautiful diagram of any type, use Excel or ana electronic spreadsheets -logical programs, for example, Google Docs.

You need to enter the data, and the program itself will build a diagram of any type.

According to the diagram, il-lu-stri-ru-yu-shchy for some number of people which language is native.

Data taken from Wi-ki-ped-dia. We write them down in an Excel table (see Table 4).

You-de-lim tab-li-tsu with data-us-mi. Let's look at the types of pre-la-ha-e-my diagrams.

There are both round ones and pillars here. In a strict way, both of them.

Kru-go-wai (see Fig. 9):

Rice. 9. Kru-go-vaya diagram of the shares of languages

Pillar-cha-taya (see Fig. 10)

Rice. 10. Pillar-cha-thaya diagram, il-lu-stri-ru-yu-shaya, for some number of people which language is native

What kind of diagram do we need - it will be necessary to decide every time. You can sko-pi-ro-vat and insert into any do-ku-ment.

As you can see, this year we’re creating a diagram, we don’t make any labor.

Application of diagrams in real life

Let's see how in real life, the dia-gram-ma-mo-ga-et. Here is information on the number of lessons on 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, but for perception. Below is the image on the diagram (see Fig. 11).

Rice. 11. Number of lessons per year

And here she is, but the given races are in descending order (see Fig. 12).

Rice. 12. Number of lessons per year (in descending order)

Now we see beautifully which lessons are the most, which are the least. We see that the number of English language lessons is two times less than Russian, which is logical, because Russian is our native language and speak, read, write on it, we come a lot more often.

abstract source - 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

Histogram (bar graph)

It is used to visualize the distribution of specific parameter values ​​by repetition frequency over a certain period of time. It can be used when plotting allowable values ​​on a graph. You can determine how often it falls into or out of the acceptable range. The order of plotting the histogram:

• 1. observe a random variable and determine its numerical values. The number of experimental points must be at least 30
• 2. determine the range of the case value, it determines the width of the histogram R and is equal to Xmax - Xmin
• 3. The resulting range is divided into k intervals, the interval width is h = R/k.
• 4. distribute the received data by intervals - the boundaries of the first interval, - the boundaries of the last interval. Determine the number of points that fall into each interval.
• 5. Based on the data obtained, a histogram is built. Frequencies are plotted along the ordinate axis, interval boundaries are plotted along the abscissa axis.
• 6. according to the form of the resulting histogram, they find out the state of the batch of products, the technological process and make management decisions.

Typical types of histograms:

• 1) Typical or (symmetrical). This histogram indicates the stability of the process.
• 2) Multimodal view or comb. Such a histogram indicates the instability of the process.
• 3) Distribution with a break on the left or right
• 4) Plateau (uniform rectangular distribution, such a histogram is obtained in the case of combining several associations, whose average values ​​differ slightly) analyze such a histogram using the stratification method
• 5) Two-peak (bimodal) - two symmetrical with far-standing averages (crowns) are mixed here. Spend stratification on 2 factors. This histogram indicates the occurrence of a measurement error.
• 6) With an isolated peak - this histogram indicates the occurrence of a measurement error