The statistical chart is based on the statisticsGeometry, object images and maps.It hasvisual、image、vivid、specificEtc.Statistical charts can simplify, popularize and visualize complex statistics, make people clear at a glance, and facilitate understanding and comparison.Therefore, the statistical chart isData sortingAnd analysis plays an important role and is widely used.When answering the questions about statistical charts in the data analysis test, we should not only examine the visual image of the chart, but also check the data, so as not to be confused by the superficial image.
statisticsAndData analysisThe process can be roughly divided into two parts: quantitative techniques and graphical techniques.The quantitative analysis method refers to the set of statistical operating procedures that produce numerical or tabular outputs;For example, including hypothesis testing, analysis of variancePoint estimation, confidence interval andleast square methodRegression analysis.These means and other similar technical methods are all valuable and belong to the mainstream of classical analysis.
On the other hand, there is also a large set of statistical tools that we generally call graphical analysis methods.These tools include scatter plot, histogram, probability plot, residual plot, box plot, block plot and double plot.Exploratory data analysis (EDA) is closely dependent on these means and other similar technical methods.The graphical analysis operating procedure is not only a tool used in the context of EDA;In terms of hypothesis testing, model selection, statistical model verification, estimator selection, relationship determination, factor effect determination andOutlierIn terms of detection, such graphical analysis tools can also be used as the best shortcut for in-depth understanding of data sets.In addition, high-quality statistical graphics can also be used as a convincing means of communication to convey basic information existing in data to others.
The graphical statistical method has four objectives: ⑴ Exploredata setContent of; ⑵Used to discover the structure in the data; ⑶Check the assumptions in the statistical model; ⑷Communicate and convey the analysis results.[1]
Without the use of statistical graphs, opportunities to gain insight into one or more aspects of the data infrastructure will be lost.
history
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The origin of statistical graphs can be traced back to the earliest attempt to analyze data, and now this technical method has becomescienceOne of the key means of development.As early as the 18th century, people used many statistical mapping methods and forms that we are familiar with at present, such as two-dimensional maps, schematic maps, bar mapsCoordinate paper。People's attention to the following four issues has promoted the development of statistical graphic technology:[2]
Space organization during the seventeenth and eighteenth centuries
Discrete comparison between the 18th century and the early 19th century
Continuous distribution during the nineteenth century
Multivariate distribution and related problems during the nineteenth and twentieth centuries
Since the 1970s, withcomputer graphicsWith the renaissance of related technologies and methods, statistical graphs have now made a comeback and become an important analytical tool again.
brief introduction
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Figure 1 Statistical Chart
Statistical chart is a tool that uses points, lines, surfaces, volumes, etc. to draw geometric figures to show the relationship between various quantities and their changes.A general term for various graphs representing the size and variation of statistics.Among them arebar chart、Sector chart、broken lineStatistical chart, pictogram, etc.In statistics, the method of using statistical graphs to represent statistical data is called statistical graphical method.Its characteristics are: concrete, concise and vividEasy to understand、stick out a mile。Its main uses are: to show the contrast between phenomena;Reveal the overall structure;Check the implementation of the plan;Reveal the interdependence between phenomena and reflectOverall unitThe distribution of;Explain the spatial distribution of the phenomenon.Generally adoptedRectangular coordinate system．AbscissaIt is used to indicate the group or independent variable x of things, and the ordinate is often used to indicate the number of times things appear ordependent variabley；Or use angular coordinates (such as circular map), geographical coordinates (such as topographic map), etc.According to the digital nature of the ruler, there are real number graphs, cumulative number graphspercentageGraphs, logarithmic graphs, exponential graphs, etc;Its structure includes drawing name, drawing title (title in Figure 1), drawing ruler (coordinate unit), various drawing lines (baseline, contour line, guide line, etc.), annotation (legend description, data source, etc.), etc.
Basic use
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Statistical charts are generally composed of graphs, drawing numbers, drawing headings, drawing annotations, etc.Common in the administrative vocational ability test arebar chart, sector statistical chartbroken lineStatistical charts and mesh statistical charts.
Basic type
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(1) Bar chart: also known as straight bar chart, it represents the situation of independent indicators in different stages. There are two or more dimensions, and the legend is located at the top right.[3]
(2) Percentage bar chart and circle chart: describe the size of percentage (composition ratio), and express different proportions with colors or various graphs.
(3) Line chart: the rise and fall of lines are used to show the development trend of things, mainly formeasurement data, describing the relationship between two variables.
（4）Semilog plotThe vertical axis uses logarithmic scale to describe the change speed and trend of a group of continuous data.
（7）Statistical map: Describe the geographical distribution of a phenomenon.
Bar Chart
A unit length (such as 1 cm) is used to express a certain amount. According to the amount of the quantity, draw a proportional straight bar of length and short, and arrange it in a certain order. Such a statistical chart is calledbar chart。The bar chart can clearly show the number of various quantities.Bar ChartIt is the most commonly used graph in statistical chart data analysis.It can be divided into vertical bar chart andHorizontalBar chart;According to different analysis functions, it can be divided into bar comparison chart and bar structure chart.
(1) It enables people to see the size of each data at a glance.
(2) It is easy to compare differences between data.
(3) Can clearly show the quantity.
Sector chart
Use the area of a circle to represent the whole of thingssectorArea represents the proportion ofpercentageThe statistical chart of is called sector statistical chart.Also called percentage comparison chart.The sector statistical chart can clearly reflect the quantitative relationship between parts and between parts and the whole.
(1) The area of the sector represents the percentage of the part in the total.
(2) It is easy to display the size of each group of data relative to the total number.
Line Chart
Broken line statistical chart
withbroken lineA statistical chart representing the increase or decrease of statistical quantity, calledBroken line statistical chart。Andbar chartBy comparison, the broken line statistical chart can not only represent the quantity, but also reflect the development and change of the same thing at different times.Line ChartIt is widely used in life. Although it does not directly give accurate data, as long as you master certain skills, you can quickly determine a specific data by skillfully using the "coordinate method".
Broken line statistical chartFeatures: (1) It can display the change trend of data and reflect the change of things.
Reticular graph
The characteristics of the network statistical chart are:
The meaning of the mother can be separated from the letter in the specific answer process, which is easier to find the answer.
Meaning of statistical chart:
Indicates the contrast between phenomena;Reveal the overall structure;Check the implementation of the plan;Reveal the interdependence between phenomena and reflect the distribution of the overall unit;Explain the spatial distribution of the phenomenon.
Stem and leaf statistics
Stem leaf diagramAlso known as "branch and leaf map", its idea is toarrayPress the number indigitFor comparison, the bits whose size is basically unchanged or has little change are regarded as a trunk (stem), and the bits whose size changes greatly are regarded as branches (leaves), listed behind the trunk, so that you can clearly see the number behind each trunk and the specific number of each.
The stem leaf graph has three columns: one on the leftStatistics, which is the cumulative value from up (or down) to the center, and the number of centers (with parentheses) represents the maximum number of arrays;The middle column represents the stem, that is, the number of digits with little change;On the right is the change bit in the array. It lists the number of each change in the array one by one at a certain interval, like a leaf pulled from a branch, so people call it a stem leaf graph.
Stem leaf graph is a special tool similar to histogram, but different from histogram, stem leaf graph remainssourceThe histogram loses the information of the original data.takeStem leaf diagramThe stem and leaf rotate 90 degrees counterclockwise, which is actually a histogram, from which you can count the times and calculate the frequency or percentage of each data segment.So we can see whether the distribution isNormal distributionOr unimodalSkewed distributionapproach.
Stem leaf chart is similar to histogram in quality management, but it is usually used as a more detailed analysis stage.Because it is a histogram composed of numbers, we usually use professional software to draw when doing histogram.
Characteristics of stem leaf graph
1. There are two advantages of using stem leaf chart to show data: one is that there is no loss of original data information on the statistical chart, and all data information can be obtained from the stem leaf chart;Second, the data in the stem leaf graph can be recorded and added at any time for convenient recording and representation.
2、Stem leaf diagramIt is only convenient to indicate two digitsSignificant figuresThe stem leaf diagram is only convenient for recording two groups of data. Although more than two data can be recorded, it is not as intuitive and clear as two records.
Meaning of statistical chart:
Indicates the contrast between phenomena;Reveal the overall structure;Check the implementation of the plan;Reveal the interdependence between phenomena and reflect the distribution of the overall unit;Explain the spatial distribution of the phenomenon.
The characteristic of the network statistical chart is that there are only some letters in this kind of statistical chart, and the meaning represented by the letters is outside the question. Before answering the question, you must understand the meaning represented by these letters. In the specific process of answering the question, you can break away from the letters and get the answer more easily.
Statistical table is a form of statistical data represented by tables drawn by vertical and horizontal cross lines
According to the Encyclopedia of Primary School Teaching in China, it is a form made of raw data. For practical needs, people often need to sort out and classify the interrelated data obtained in industrial and agricultural production, science and technology and daily work according to certain requirements, and arrange the data in a certain order to form a table,Such tables are called statistical tables
Its functions are: ① to show the relationship between the research objects with quantity; ② to show the change rule between the research objects with quantity; ③ to show the difference between the research objects with quantity, which is convenient for people to analyze and study problems
Statistical tableThe forms ofSingle statistical tableandCompound statistical tableTwo kinds of tables. The tables that only make statistics on the data of a certain item are called single statistical tables or simple statistical tables. The tables with two or more statistical items are called double statistical tables
The contents of statistical tables generally include the general title, horizontal title, vertical title, numerical data, unit, and date of tabulation. The general title refers to the name of the table, which should simply reflect the main contents of the table. The horizontal title refers to the meaning of the data in each horizontal row;Vertical headings refer to the meaning of data in each vertical column;Digital data refers to the numbers filled in the blanks as required;The unit refers to the unit of measurement of the data in the table. When the data unit is the same, the unit is generally placed in the upper left corner of the table. If the data unit of each item is different, it can be indicated in the table. The date of table preparation is placed in the upper right corner of the table, indicating the time of table preparation. All statistical tables should have a column of "for reference" or "notes",In order to fill in the facts or descriptions that do not belong to the items in the table when necessary
histogram
HistogramHistogram、Mass distribution diagram。It is a kind of statistical report chart, and data distribution is represented by a series of vertical stripes or line segments with different heights.GeneralHorizontal axisIndicates the data type, and the vertical axis indicates the distribution.Meaning of histogram method
How to predict and monitor product quality in quality management?How to analyze quality fluctuation?Histogram is to clearly
Tools for diagramming these problems.It processes the seemingly disordered data collected to reflect the distribution of product quality, judge and predict product quality and unqualified rate.
HistogramMass distribution diagramHistogram, which is a main tool to show the change of data.Using the data that can be obtained from the histogram, the regularity can be analyzed, and the distribution state of product quality characteristics can be seen intuitively. The distribution state of resources can be seen at a glance, so that the overall quality distribution can be judged.When making histograms, the concept of science is involved. The first thing to do is to group the data. Therefore, how to group the data reasonably is a key issue.PressGroup spacingThe two key digits for the principle of equality are the number of groups and group spacing.It is a geometric chart, which is collected from the production processQuality dataDistribution, with group spacing as the bottom edge andfrequencyFor a series of high connected squareRectangle。
The purpose of making histogram is to judge whether the production process is stable and predict the quality of the production process by observing the shape of the graph.Specifically, the purpose of making histograms is to:
Histogram classifies data according to differences, which is characterized by clear understanding of differences.Drawing method of histogram
① Collect and record data, and calculate its maximum and minimum values.The number of data shall be more than 100, or at least 50 if the number is not large.We call the number of groupsNumber of groups, two for each groupEndpointThe difference of is calledGroup spacing。
② Divide the data into several groups and mark them.The number of groups is between 6 and 20.
③ Calculate the width of the group spacing.Remove the difference between the maximum value and the minimum value with the number of groups, and calculate the width of group spacing.
④ Calculate the limit of each group.The limit position of each group can be calculated from the first group in turn. The lower limit of the first group is the minimum value minus half of the minimum measurement unitupper boundAdd group spacing to its lower bound value.The lower limit of the second group is the upper limit of the first group, and the lower limit of the second group plus the group spacing is the upper limit of the second group, and so on.
