Types of Graphs:There are several types of graphs. The choice depends on the type of data collected and the information you want to transmit. Each has a set of advantages and disadvantages. There are various types of graphs available that you will learn in this article. The knowledge of each one of them is fundamental for a correct reading of the information they contain.
Students must understand the types of graphs in data structures to understand the concept and score high in the exam. Popular graph types include bar graphs, line graphs, pie charts, histograms, and scatter plots. Graphs are an excellent way to visualise data. It can display statistics. For example, a bar graph or chart is utilized to display numerical data independent of one another. Students interested to know the types of graphs in detail can check out the article below.
Types of Graphs in Data Structures
Definition: The term graph is a pictorial representation of data in an organised way. Charts are usually formed from different data points that represent the link between two or more things.
We hear a saying that a picture says so many stories. But, on the other hand, a graph says a thousand words and tells so many stories.
Each point, stroke, colour or shape on a graph has various meanings that help in reading a diagram. The charts are of multiple types and vary in structure, with some having just points, others having topics joined together by lines, etc. Students usually look for pie chart making, the example of pie chart, bar graph example, column chart etc.
Types of Graphs
A graph that uses points and lines to represent change over time is defined as a line graph. In other words, it is the chart that shows a line joining multiple points or a line that shows the link between the points.
The diagram illustrates the quantitative data between two changing variables with the straight line or the curve that joins a series of successive data points. Linear charts compare two variables on the vertical and the horizontal axis.
The bar graph is the way to represent the qualitative data visually. The information is displayed horizontally or vertically and compares items like amounts, characteristics, times, and frequency.
The bars are arranged in order of frequency, so more critical categories are emphasised. By looking at all the bars, it is easy to tell which types in a set of data dominate the others. Bar graphs can be single, stacked, or grouped in many ways.
The pie chart is used to represent the numerical proportions of a dataset. This graph involves dividing a circle into different sectors, where each of the sectors represents the proportion of a particular element as a whole. Thus, it is also known as a circle chart or circle graph.
The histogram is another kind of graph that uses bars in its display. The histogram is used for quantitative data, and ranges of values known as classes are listed at the bottom, and the types with greater frequencies have the taller bars.
A histogram and the bar graph look very similar; however, they are different because of the data level. Bar graphs measure the frequency of the categorical data. A categorical variable has two or more categories, such as gender or hair colour. The other difference is that in a bar graph, there are gaps between the bars, but in a histogram, the bars are continuous. There are no gaps between the bars.
Stem and Leaf Plot
The stem and a leaf plot break the value of the quantitative data set into two pieces: a stem for the highest place value and a leaf for the other place values. It gives a way to list all data values in a compact form.
Example: If you are using this graph to review student test scores of \(10,15,22,25,28,23,31,36,45,45,48,\) the stems would be \(1,2,3\) and \(4\) corresponding to the tens place of the data.
A dot plot is a combination between a histogram and a stem and leaf plot. Each quantitative data value sets off a dot or point that is kept on the appropriate class values. Histograms use rectangles or bars, whereas these graphs use beads/dots.
A scatter plot shows data that is matched by using a horizontal axis (the \(x\)-axis) and a vertical axis (the \(y\)-axis). The statistical tools of correlation and regression are then used to display trends on the scatter plot. A scatter plot looks like a line or a curve moving up or down from left to right along the graph with the points “scattered” along the line. The scatterplot helps us display more information about any data set, including:
An overall trend among variables
Outliers from the overall trend.
The shape of any trend.
The strength of any trend.
The time-series graph exhibit the data at the different points in time, and this is another kind of graph used for certain types of paired data. As its name itself implies, this type of graph measures trends over time. However, the timeframe can be minutes, hours, days, months, years, decades, or centuries.
Exponential graphs represent the exponential functions that use the table of the values and plotting the points on graph paper. You must have noticed that the exponential functions are the inverse of the logarithmic functions.
In exponential charts, the graph can be an increasing or decreasing type of curve based on the function. Below you can see an example that will quickly help you understand the graphing exponential function.
Logarithmic functions are the contrary of the exponential functions. However, the plot method is similar. A table of the values is needed to plot the logarithmic graphs and then plot the points correspondingly on graph paper.
The graph of any log function will be the opposite of an exponential function. The diagram is given below for better understanding.
Trigonometry graphs are plotted for \(6\) different trigonometric functions, and they are:
Cosec function, and
Frequency Distribution Graph
A frequency distribution graph is used to display the frequency of the outcomes in a particular sample. For frequency distribution graphs, the table of values is made by marking the results in one column and the number of times they appear (i.e., frequency) in another column.
An Ogive Chart is the curve of the cumulative frequency distribution or the cumulative relative frequency distribution. When you want to draw such a curve, the frequencies should be shown as the percentage of the total frequency. Then, these types of percentages are cumulated and plotted, in the case of an Ogive.
Types of Graphs in Discrete Mathematics
A graph is represented in the diagrammatic form as dots or circles for the vertices, joined by lines or curves for the edges. Charts are one of the things to study in discrete mathematics. The edges can be directed or undirected. A few of the graphs in discrete mathematics are given below:
Complete Bipartite Graph
Solved Examples – Types of Graphs
Q.1. A survey was carried out of \(30\) students of a class \(VI\) in a school. Data about different modes of transport used by them to travel to school was displayed as a pictograph. What can you conclude from the pictograph?
Mode of Transport
Number of students
Ans: From the pictograph, we find that: The number of students coming by private car is \(4.\) The maximum number of students use the school bus. It is the most popular way. Only three students used cycle. The number of students using other modes can be found similarly.
Q.2. What are the uses of the Bar graph? Ans:The uses of the bar graph and bar graph example are given below: 1. It helps when you want to represent the data that is grouped into nominal or ordinal categories. 2. A bar graph is easier to compare the data among the various categories. 3. This graph can also help us in displaying the significant data changes over time. 4. The bar graph is perfect for visualising the data distribution when you have more than three categories.
Q.3. Draw a histogram for the following \(100\) people whose daily wages are given below:
\(0 – 50\)
\(50 – 100\)
\(100 – 200\)
\(200 – 250\)
\(250 – 450\)
\(450 – 500\)
Number of people
Ans:The histogram using the above chart is drawn as shown below:
Q.4. The film reported its net worth for the years \(2011 – 2016\) is as follows: Draw the frequency polygon by using the above information.
\(2011 – 2012\)
\(2012 – 2013\)
\(2013 – 2014\)
\(2014 – 2015\)
\(2015 – 2016\)
Net worth (in Lakhs)
Ans:The frequency polygon using the given information is shown below:
Q.5. The given table represents the marks obtained by \(120\) kids of class \(IX\) in a cycle test \( – 1.\) Draw an Ogive curve for the given data:
\(0 – 10\)
\(10 – 20\)
\(20 – 30\)
\(30 – 40\)
\(40 – 50\)
\(50 – 60\)
\(60 – 70\)
\(70 – 80\)
\(80 – 90\)
\(90 – 100\)
No. of kids
Ans:The graph is drawn using the given information shown below:
Types of Graphs: Definition, Diagrams & Examples:Summary
In this given article, we have discussed the term graph. Then, we have also covered some of the types of graphs like bar graphs, line graphs, pie charts, histograms, and many more. Finally, we glanced at types of graphs in discrete mathematics and then covered some of the solved examples and a few FAQs.
Frequently Asked Questionson Types of Graphs, Definition, Diagrams & Examples
Here we have provided some frequently asked questions on Types of graphs, Definitions, Diagrams & Examples:
Q.1. Is the bar graph qualitative or quantitative? Ans: The bar graph is used for the qualitative data, whereas a histogram, which is similar to a bar graph, is used for quantitative data.
Q.2. What is a graph? Ans:A graph is a mathematical representation of data to describe the relationship that the lines and the points have. You can see some points and lines on the chart. The length of the lines and the position of the points does not matter. Each object in a graph is known as a node.
Q.3. What are the \(4\) types of the graph? Ans:There are different types of charts/graphs. The four most common diagrams used are: 1. Line graphs 2. Bar graphs 3. Histograms 4. Pie charts
Q.4. What are the \(3\) main types of graphs? Ans: The three main types of graphs that are used more frequently are bar graphs, circle graphs, or pie charts, and line graphs.
Q.5. What are the different types of graphs? Ans: The different kinds of graphs are given below: 1. Line graphs 2. Bar graphs 3. Pie charts 4. Scatter plots 5. Histograms 6. Dot plots 7. Stem and leaf plots 8. Time-series graphs 9. Exponential graphs 10. Logarithmic graph 11. Trignomentaric graphs 12. Frequency distribution table Graphs are an excellent way to visualise data and display statistics. For example, a bar graph or chart is used to represent numerical data independent of one another.