Graphical Representation

Have you ever realized how messy it is to make anything meaningful from large data?

Get started

Millions of flashcards designed to help you ace your studies

Sign up for free

Review generated flashcards

Sign up for free
You have reached the daily AI limit

Start learning or create your own AI flashcards

StudySmarter Editorial Team

Team Graphical Representation Teachers

  • 9 minutes reading time
  • Checked by StudySmarter Editorial Team
Save Article Save Article
Contents
Contents
Table of contents

    Jump to a key chapter

      Consider how much time it will take to sort out data manually to try and identify patterns and trends.

      Did you know that data could be represented visually so that meaning could be easily drawn from just a glance at it?

      In this article, we are going to discuss the many ways data can be graphically represented, which we call Graphical representation.

      Graphical representation definition

      Graphical representation is the way of visually representing numerical data.

      Representing data in a visual form is an effective and useful way of understanding the given data.

      When collected data over a sample or population for the purpose of research is visualized, using one of the many ways possible, it becomes way easier to compare the data and analyze it. Some of the ways data can be represented graphically are through media such as plots, graphs, and lines.

      Graphically, horizontal and vertical lines in a graph are called the coordinate axes. The horizontal line is known as the x-axis, whilst the vertical line is known as the y-axis. These two lines intersect perpendicularly at a point O called the origin.

      On the left-hand side of the Origin of the x-axis are the negative values of the x-axis. The right side of the origin is for the positive values of the x-axis. On the y-axis, the above of the origin values are the positive values. Below the origin are the negative values.

      Consequently, this means that the two axes divide the graph into four parts, called quadrants, Quadrant I, Quadrant II, Quadrant III, and Quadrant IV. We can take a look at the illustration below to see what we mean.

      Rules for graphical representation of data

      To represent data effectively on a graph, one must follow certain rules and these are being discussed in this section.

      1. Title. The title of the graph should be appropriate enough to depict what the graph is really about.
      2. Measurement unit. The graph should indicate the measuring unit.
      3. Proper scale. To have an accurate graph, a proper scale will need to be chosen.
      4. Index. Index the various components of the graph for clarity and easy understanding.
      5. Data sources. Include data sources at the bottom of the graph.
      6. Simplicity. The graph should be simple enough to be easily understood.
      7. Neatness. Construct the graph neatly with regard to font size and style such that it is easily readable.

      Graphical representation types

      There are several ways data can be represented on graphs. Some of these are through plots, diagrams, and pies. Let us discuss the types of graphical representation below.

      Bar graph

      A bar graph uses rectangular bars that represent the values of categorical data on a graph. The rectangular bars are drawn either horizontally or vertically. It is one of the most commonly used types of graphical representations, hence used by quite a number of industries. Bar graphs are an effective way to compare data since they can be easily read.

      The bar graph below represents data collected on people's favorite movie types. We can see here that the graph is basically saying that the more watched sample is comedy, followed by sci-fi, and so on.

      Histogram

      Histograms are very similar to bar graphs. The significant difference here is that it groups the data values into ranges. This means that each bar's height is determined by what range it falls into.

      The below histogram represents the time taken in minutes for 2 PE classes of 30 students to complete a cross country course. This means there are 60 students all here going to be accounted for. The x-axis shows the range of time used to complete the exercise. The y-axis also accounts for the range of the frequency density.

      Pie chart

      Pie charts are graphs that are in a circle sliced proportionately to represent data. The circle is a whole, which has bits of it sliced such that when all the data values come together, it makes the whole circle. It is also a pretty good way of visualizing data.

      The pie chart below shows data on the type of pets owned by the people in London. Blue is used to represent dogs, and this means that a number of people out of the whole circle have dogs as pets and so on.

      Line graph

      Line graphs are graphs that are used to represent data collected over time. They are used to visualize data in a series. For example, it is most appropriate to represent the price of a stock over a period of time on a line graph compared to a pie chart.

      The line graph below represents the sales of umbrellas over specific seasons in the year. Summer 2001 records the least sales of umbrellas according to the graph. It sold 300 as opposed to the Autumn right after it where it sold a little over 600.

      Scatter plot

      Scatter plots are an extremely useful way to represent bivariate data. They visualize data such that you can see almost instantly how one variable correlates with the other.

      The values of each variable are displayed on each of the axes. This means that if we are looking at data talking about the sales of umbrellas against seasons again, the seasons could be displayed on the x-axis, as the sales are displayed on the y-axis. Scatter plots use points to display recorded data values.

      The scatter plot below is a representation of the heights of toddlers and their corresponding ages. The graph makes it a lot easier to notice that there is some extent of correlation between the two variables.

      Frequency table

      Frequency tables are used to organize data in a table form after they are collected. Frequency basically tells about how often a thing occurs. This means that we could collect data on a quiz taken by students in grade 11 for example, and structure this such that we want to see how many students scored 80, how many scored 79, and so on.

      The table below displays the scores of grade 11 students who took a math test that was marked over 10.

      Test marksFrequency
      101
      93
      87
      714
      69
      54

      Graphical representation examples

      In this section, we are going to discuss a few examples of how some of the types of graphical representation types are being applied.

      A research was conducted to check the relationship between rainfall and atmospheric humidity. The table below is the outcome of the data collected.

      Temperature (Degree Fahrenheit)Humidity
      4560
      6248
      7740
      9730
      11820
      12218

      Represent this on a scatter plot.

      Solution

      Firstly, we assign each variable to an axis. Let the temperature be on the x-axis, and the humidity be on the y-axis.

      On both axes, let us use the scale where 1 interval = 10 units.

      The results of a quiz conducted by a grade 12 teacher are as follows 14, 20, 15, 5, 20, 15, 15, 20, 15, 14, 10, 5, 10, 20, 15, 5, 18, 14, 18, 18, 15. Represent this on a frequency table.

      Solution

      First, we will draw the table with one column being the marks recorded and the other being the frequency.

      MarksNumber of students (Frequency)
      53
      102
      143
      156
      183
      204
      Total21

      The data of favorite colors of a staff of a school was collected and is displayed in a frequency table below. Draw a pie chart representing the data.

      Colour Frequency
      Green2
      Red5
      Blue7
      Yellow4

      Solution

      The frequency will make a total of 18. Now to represent this on a pie chart, we will have to convert the frequencies into degrees where each color's degrees are proportional to their frequency so that they make a whole circle.

      We know that the total angle in a complete circle is 360°, and since we want to share that by the people, we will first divide 360 by the total number of frequencies.

      36018= 20.

      So each number of the frequencies here is now going to be multiplied by the number we just worked out (20) to give us the corresponding degree that it's going to be in the circle.

      ColourFrequencyAngles
      Green22×20 = 40°
      Red55×20 = 100°
      Blue77×20 = 140°
      Yellow44×20 = 80°

      We can now draw the pie chart using these angles.

      The data below is the recorded waking times of a nurse in two weeks, 7:00, 13:00, 13:00, 8:00, 7:00, 8:00, 9:00, 12:00, 13:00, 9:00, 8:00, 9:00, 8:00, 13:00. Represent this on a bar graph.

      Solution

      We first need to identify what would be represented on the x-axis, and what will be on the y-axis. First of all, we can categorize the times to be on the x-axis, so that their frequencies will be on the y-axis.

      The graph can thus be represented as follows,

      Uses of graphical representation

      Graphical representation is extremely helpful for the following reasons,

      • It is used to understand data by easily identifying patterns and trends in them.
      • Data can easily be compared with others especially when they are in large quantities.
      • Graphical representation helps to easily communicate data.
      • Graphs like the scatter plot display bivariate data so well that they visually analyze the correlation between variables.
      • Graphical representation fundamentally avoids the confusion of information.

      Graphical Representation - Key takeaways

      • Graphical representation is the way of visually representing numerical data.
      • Graphically, there are horizontal and vertical lines in a graph called the coordinate axes. The horizontal line is known as the x-axis, whilst the vertical line is known as the y-axis.
      • To have an accurate graph, a proper scale will need to be chosen.
      • The types of graphical representation include bar graphs, histograms, pie charts, line graphs, frequency tables, and scatter plots.
      • Data can easily be compared with others especially when they are in large quantities using a graphical representation.
      Frequently Asked Questions about Graphical Representation

      What is graphical representation? 

      Graphical representation is the way of visually representing numerical data.

      What is a graphical representation example? 

      A graphical representation example is, a data on the scores of a quiz conducted for students is displayed on a frequency table where the scores are displayed on the first row, and the frequency is displayed on the second row.

      What are the types of graphical representation? 

      Bar graph

      Histogram

      Pie chart

      Line graph

      Frequency table

      Scatter plot

      What are the rules in graphical representation? 

      1. Title: The title of the graph should be appropriate enough to depict what the graph is really about.
      2. Measurement unit: The graph should indicate the measuring unit.
      3. Proper scale: To have an accurate graph, a proper scale will need to be chosen.
      4. Index: Index the various components of the graph for clarity and easy understanding.
      5. Data sources: Include data sources at the bottom of the graph.
      6. Simplicity: The graph should be simple enough to be easily understood.
      7. Neatness: Construct the graph neatly with regard to font size and style such that it is easily readable.

      What is the purpose of graphic representation? 

      Graphical representation helps to easily communicate data.

      Save Article

      Test your knowledge with multiple choice flashcards

      To have an accurate graph, a proper scale will need to be chosen. Is this statement true or false?

      Rectangular bars in the bar graph are drawn only horizontally. Is this statement true or false?

      On the left-hand side of the Origin of the x-axis are the positive values of the x-axis. Is this statement true or false?

      Next

      Discover learning materials with the free StudySmarter app

      Sign up for free
      1
      About StudySmarter

      StudySmarter is a globally recognized educational technology company, offering a holistic learning platform designed for students of all ages and educational levels. Our platform provides learning support for a wide range of subjects, including STEM, Social Sciences, and Languages and also helps students to successfully master various tests and exams worldwide, such as GCSE, A Level, SAT, ACT, Abitur, and more. We offer an extensive library of learning materials, including interactive flashcards, comprehensive textbook solutions, and detailed explanations. The cutting-edge technology and tools we provide help students create their own learning materials. StudySmarter’s content is not only expert-verified but also regularly updated to ensure accuracy and relevance.

      Learn more
      StudySmarter Editorial Team

      Team Math Teachers

      • 9 minutes reading time
      • Checked by StudySmarter Editorial Team
      Save Explanation Save Explanation

      Study anywhere. Anytime.Across all devices.

      Sign-up for free

      Sign up to highlight and take notes. It’s 100% free.

      Join over 22 million students in learning with our StudySmarter App

      The first learning app that truly has everything you need to ace your exams in one place

      • Flashcards & Quizzes
      • AI Study Assistant
      • Study Planner
      • Mock-Exams
      • Smart Note-Taking
      Join over 22 million students in learning with our StudySmarter App
      Sign up with Email