Ch19 GRAPHIC PRESENTATION OF DATA

CHAPTER-19 

GRAPHIC PRESENTATION OF DATA

INTRODUCTION

Graphic presentation of data is a visual method used to represent and communicate information effectively. It involves the use of graphs, charts, maps, and other visual elements to present data in a clear and concise manner. Graphic presentation helps to simplify complex data, identify patterns and trends, and facilitate better understanding and analysis of the information.

By using visual aids, graphic presentation enhances the audience's ability to interpret and absorb the data quickly. It allows for easy comparison, identification of outliers, and visualization of relationships between variables. Graphic presentation is widely utilized in various fields, including statistics, research, business, marketing, education, and journalism.

The choice of the appropriate graphic representation depends on the type of data, the objectives of the presentation, and the target audience. Different types of graphs and charts, such as line graphs, bar charts, pie charts, scatter plots, and maps, offer diverse ways to represent and analyze data visually.

Overall, graphic presentation of data plays a crucial role in effectively conveying information, making data-driven decisions, and communicating insights to a wider audience. It helps to transform raw data into meaningful visual representations that facilitate understanding, analysis, and decision-making processes.

DIFFERENCE BETWEEN DIAGRAMS AND GRAPHS

Diagrams and graphs are both visual representations used to present data and information, but there are some differences between the two:

Nature of Data: Diagrams are typically used to represent qualitative or categorical data, while graphs are used for quantitative or numerical data. Diagrams often depict the relationships or connections between different elements or concepts, whereas graphs primarily show the numerical values and relationships between variables.

Visual Format: Diagrams often utilize shapes, symbols, and connections to represent concepts or entities, whereas graphs use axes, points, lines, or bars to represent quantitative data. Diagrams may focus on the structural or conceptual aspects, while graphs focus on the numerical or quantitative aspects of the data.

Purpose: Diagrams are commonly used for illustrating processes, hierarchies, relationships, or flowcharts. They help in understanding complex systems, organizing information, or visualizing concepts. On the other hand, graphs are used to analyze and display numerical data, showing patterns, trends, comparisons, or distributions.

Data Representation: Diagrams represent data in a non-numerical or symbolic manner, whereas graphs represent data using numerical values or measurements. Diagrams may involve labeling, descriptions, or annotations to explain the relationships or connections, while graphs typically use scales, axes, and legends to represent the quantitative data accurately.

Interpretation: Diagrams require subjective interpretation as they often involve qualitative or conceptual information. The understanding and meaning of diagrams can vary based on individual perspectives. Graphs, on the other hand, provide a more objective representation of numerical data, allowing for quantitative analysis and comparison.

It's important to note that the terms "diagram" and "graph" can sometimes be used interchangeably, and the distinction between the two may vary depending on the context. The specific purpose, nature of data, and visual format used may influence whether a visual representation is considered a diagram or a graph.

MERITS AND DEMERITS OF GRAPHIC PRESENTATION

Graphic presentation of data offers several merits and advantages, as well as some limitations or demerits. Let's explore them:

Merits/Advantages of Graphic Presentation:

Visual Representation: Graphics make data more visually appealing and easier to understand compared to raw data or text-based presentations. They help to convey complex information in a simplified and concise manner.

Clarity and Conciseness: Graphics provide a clear and concise representation of data, allowing for quick and easy interpretation. Patterns, trends, and relationships between variables can be easily identified, aiding in data analysis and decision-making.

Comparison and Contrast: Graphics enable effective comparison and contrast between different data sets, variables, or categories. They allow for quick identification of differences, similarities, and relative magnitudes, facilitating better data analysis and understanding.

Data Summarization: Graphics condense large amounts of data into a compact form, allowing for effective data summarization. They provide an overview of the information, highlighting key points and eliminating unnecessary details.

Insights and Interpretation: Graphics help to reveal insights, patterns, and trends that may not be immediately apparent in raw data. They aid in data exploration and interpretation, facilitating a deeper understanding of the information.

Demerits/Limitations of Graphic Presentation:

Simplification and Loss of Detail: Graphics often simplify complex data, potentially leading to a loss of detailed information. They may not capture all nuances or intricacies present in the raw data, limiting the depth of analysis.

Subjectivity and Misinterpretation: Graphics can be subject to interpretation and may be perceived differently by different individuals. The use of certain design elements or scaling choices can influence how data is interpreted, leading to potential misinterpretation.

Limited Contextual Information: Graphics may not provide comprehensive contextual information about the data. Additional textual explanations or annotations may be necessary to provide a complete understanding of the data being presented.

Limited Data Types: Certain types of data may not be suitable for graphic representation. For example, textual or qualitative data may not lend itself well to graphical presentation, requiring alternative methods of representation.

Overemphasis on Visual Appeal: There is a risk of focusing too much on visual appeal rather than accuracy and clarity of the data. Excessive decoration or unnecessary design elements can distract from the main message or compromise the integrity of the information being presented.

It's important to carefully consider these merits and demerits when using graphic presentation methods and to use them appropriately based on the nature of the data, audience, and the specific objectives of the presentation.

RULES OF CONSTRUCTING A GRAPH

When constructing a graph, there are certain rules and guidelines that you should follow to ensure clarity, accuracy, and effective communication of data. Here are some general rules of constructing a graph:

Choose the appropriate type of graph: Determine the most suitable graph type to represent your data accurately. Common types include bar graphs, line graphs, pie charts, scatter plots, and histograms.

Define the purpose: Clearly identify the purpose of your graph and what you want to convey. Are you comparing values, showing trends, or illustrating proportions? This will guide your design choices.

Determine the axes: Label and scale the axes appropriately. The x-axis usually represents the independent variable, while the y-axis represents the dependent variable. Make sure the axes are labeled clearly and units are specified.

Select appropriate intervals: Choose suitable intervals for the tick marks on each axis to represent the range of values accurately. Ensure the intervals are evenly spaced and clearly labeled.

Title and labels: Provide a descriptive title for the graph that summarizes its content. Label each axis with a concise description and include units of measurement, if applicable.

Plotting the data accurately: Plot the data accurately on the graph. Use the designated symbol or shape consistently for each data point. If necessary, include a key or legend to explain different data series or categories.

Use appropriate scales: Select the appropriate scale for each axis to avoid distorting the data. You can use linear or logarithmic scales, depending on the nature of the data and the patterns you want to highlight.

Maintain clarity: Keep the graph clean and uncluttered. Avoid unnecessary decorations, excessive gridlines, or distracting elements that can confuse or mislead the viewer. Use colors, patterns, or different line styles sparingly and purposefully.

Provide context and annotations: Add any necessary context or annotations to enhance the understanding of the graph. This may include captions, notes, or additional information that helps interpret the data.

Review and revise: Before finalizing the graph, carefully review it for accuracy, consistency, and clarity. Check for any errors in data entry, labeling, or scaling. Make revisions as needed to improve its overall effectiveness.

Remember, the rules may vary slightly depending on the specific type of graph and the data being represented. It's important to always consider the principles of clear communication and data integrity when constructing a graph.

TYPES OF GRAPHS

There are several types of graphs commonly used to represent different types of data. Here are some of the most frequently used types:

Bar Graph: A bar graph uses rectangular bars to represent data. It is suitable for comparing discrete categories or groups. The height or length of each bar represents the quantity or value associated with each category.

Line Graph: A line graph displays data points connected by lines. It is used to show the relationship or trend between two continuous variables over time or any other ordered sequence.

Pie Chart: A pie chart represents data as sectors of a circle. Each sector represents a proportion or percentage of the whole, making it useful for illustrating proportions or composition of a categorical variable.

Scatter Plot: A scatter plot shows individual data points as dots on a graph. It is used to visualize the relationship between two continuous variables and to identify patterns, clusters, or outliers in the data.

Histogram: A histogram represents the distribution of a continuous variable. It consists of bars that represent the frequency or count of data falling within specific intervals, providing a visual depiction of the data's frequency distribution.

FREQUECY DISTRIBUTION GRAPHS

Frequency distribution graphs are used to visualize the distribution of data, particularly for continuous variables. Here are some common types of frequency distribution graphs:

Histogram: A histogram is a bar graph that represents the frequency or count of data falling within specific intervals, also known as bins. The height of each bar corresponds to the frequency of data falling within that interval. Histograms provide a visual representation of the frequency distribution and can reveal patterns such as skewness, peaks, or gaps in the data.

Frequency Polygon: A frequency polygon is a line graph that connects the midpoints of the bars in a histogram. It shows the shape of the frequency distribution and is especially useful for comparing multiple distributions on the same graph.

Cumulative Frequency Graph: A cumulative frequency graph (or ogive) represents the cumulative frequency of data up to a certain point. It is constructed by plotting the cumulative frequency against the upper boundary of each interval. The resulting graph shows how the cumulative total increases over the range of values and can help analyze the spread of data or identify percentiles.

Frequency Curve: A frequency curve is a smooth line graph that represents the distribution of data. It is typically constructed by connecting points representing the midpoints of each interval in a histogram. Frequency curves provide a visual representation of the shape and symmetry of the distribution and can be used to identify patterns such as normal distributions or skewed distributions.

Stem-and-Leaf Plot: A stem-and-leaf plot is a graphical representation that displays the distribution of data while retaining the individual data values. The stem represents the highest place value of the data, and the leaves represent the remaining digits. It provides a compact representation of the data and allows for quick identification of the distribution's characteristics.

These frequency distribution graphs help visualize the spread, central tendency, shape, and other characteristics of data distributions. They are useful for exploratory data analysis, identifying outliers, understanding patterns, and making comparisons across different datasets. The choice of graph depends on the nature of the data and the specific insights you want to extract.

TIME SERIES GRAPHS

Time series graphs are used to visualize the changes in data over time. They are particularly useful for analyzing trends, patterns, and seasonality in sequential data. Here are some common types of time series graphs:

Line Graph: A line graph is the most basic and commonly used type of time series graph. It displays data points connected by straight lines, where the x-axis represents time and the y-axis represents the variable being measured. Line graphs are suitable for showing continuous changes over time and identifying trends or patterns.

Area Chart: An area chart is similar to a line graph but with the area below the line filled in. It is used to represent the cumulative or stacked values of multiple variables over time. Area charts are effective for comparing the contributions of different variables to the overall trend.

Scatter Plot: A scatter plot can also be used for time series data. In this case, the x-axis still represents time, while the y-axis represents the variable being measured. Scatter plots are helpful for visualizing the relationship between two variables over time and identifying any correlations or patterns.

Seasonal Subseries Plot: A seasonal subseries plot is a specialized time series graph used to identify seasonal patterns in the data. It involves dividing the data into seasons or periods and creating a subseries plot for each season. Each subseries plot shows the data points within a specific season, allowing for visual inspection of seasonal variations.

Decomposition Plot: A decomposition plot breaks down a time series into its individual components, such as trend, seasonality, and residual (or error). It helps in understanding the underlying patterns and structures within the data and enables further analysis of each component separately.

 

VERY SHORT QUESTIONS ANSWER

Q.1. Give meaning of graphical presentation?

Ans. Representation

Q.2.What is the difference between frequency polygon and frequency curve?

Ans. Shape.

Q.3.What is meant by Histogram?

Ans. Distribution.

Q.4.What is meant by ogive?

Ans. Cumulative.

Q.5. Give meaning of time series graphs?

Ans. Time-based representation

Q.6. When do we use false base line?

Ans. Comparison

 

 

 

 

Q.7.Differentiate between one variable graph and two or more than two variables graph?

Ans. Variables

Q.8. When do we use time series graphs?

Ans. Time trends

 

SHORT QUESTIONS ANSWER

Q.1. Explain with the help of a suitable example the Ogive both in less than and more than form?

Ans. The ogive, also known as a cumulative frequency graph, displays the cumulative frequency of data. It helps visualize how the data accumulates over a range of values. There are two forms of ogives: the less than ogive and the more than ogive.

Less Than Ogive: In a less than ogive, the cumulative frequencies are plotted against the upper boundaries of the corresponding class intervals. This graph shows the cumulative frequency up to and including each upper boundary. It provides information about the accumulation of data values that are less than or equal to a particular value.

For example, let's consider a dataset of exam scores:

Class Interval Frequency

0-20 5

20-40 12

40-60 20

60-80 15

80-100 8

To construct a less than ogive, we calculate the cumulative frequency by adding up the frequencies in ascending order. Then, we plot the cumulative frequencies against the upper boundaries of each class interval. The resulting graph shows how many scores are less than or equal to a specific upper boundary.

More Than Ogive: In a more than ogive, the cumulative frequencies are plotted against the lower boundaries of the class intervals. This graph represents the cumulative frequency greater than or equal to each lower boundary. It provides information about the accumulation of data values that are greater than or equal to a particular value.

Using the same example dataset, we can construct a more than ogive by calculating the cumulative frequency from the highest class interval to the lowest. We plot the cumulative frequencies against the lower boundaries of the class intervals, showing the cumulative frequencies for values greater than or equal to each lower boundary.

Both forms of ogives are useful for analyzing the distribution of data, identifying percentiles, and understanding the cumulative behavior of the dataset.

Q.2.What is the difference between histograms and bar Diagrams?

Ans. The difference between histograms and bar diagrams lies in the types of data they represent and the way they are constructed:

Histograms:

Histograms are used to represent the distribution of continuous or interval data.

The x-axis represents the range of values or intervals of the continuous variable, while the y-axis represents the frequency or count of data points falling within each interval.

The bars in a histogram are usually touching and have widths that correspond to the intervals of the variable being measured.

Histograms display the frequency distribution and provide insights into the shape, central tendency, and variability of the data.

Bar Diagrams (or Bar Graphs):

Bar diagrams are used to represent discrete or categorical data.

The x-axis represents the categories or groups, while the y-axis represents the frequency or count of data points belonging to each category.

The bars in a bar diagram are usually separated with gaps between them and have equal widths.

Bar diagrams are suitable for comparing different categories or groups and showing the relative frequencies or counts associated with each category.

In summary, histograms are used for continuous data, displaying the distribution of values, while bar diagrams are used for discrete or categorical data, comparing different categories or groups.

Q.3. Write notes on the following and explain by giving examples in each case?

Ans. I apologize for the confusion. To provide accurate notes and examples, I need specific topics or terms you would like me to cover. Please provide the specific subjects or concepts you would like me to explain, and I'll be glad to assist you.

Q.4 Define Histogram frequency polygon frequency curve and plot these from some imaginary data?

Ans. Histogram: A histogram is a graphical representation of the frequency distribution of a continuous or interval variable. It consists of a series of adjacent bars where the area of each bar represents the frequency or count of data falling within a specific interval. Histograms provide insights into the shape, spread, and central tendency of the data.

 

Example: Let's consider the imaginary data of exam scores for a class of students. The scores range from 50 to 100, and we want to create a histogram with five intervals: 50-60, 60-70, 70-80, 80-90, and 90-100. We count the frequency of scores falling within each interval and represent it in the form of a bar graph.

Frequency Polygon: A frequency polygon is a line graph that represents the frequency distribution of a dataset. It is created by connecting the midpoints of the tops of the bars in a histogram using line segments. Frequency polygons provide a smooth visual representation of the distribution and help analyze trends and patterns.

Example: Using the same exam score data, we can construct a frequency polygon by connecting the midpoints of the tops of the histogram bars. The x-axis represents the midpoints of the score intervals, and the y-axis represents the frequency or count of scores falling within each interval. The resulting line graph shows the shape and trend of the data distribution.

Frequency Curve: A frequency curve, also known as a smooth curve or probability density curve, is a line graph that represents the distribution of data. It is created by drawing a smooth curve through the tops of the histogram bars or by fitting a mathematical function to the data. Frequency curves help identify the shape, symmetry, and central tendency of the distribution.

Example: Continuing with the exam score data, we can construct a frequency curve by fitting a smooth curve to the tops of the histogram bars. This curve represents the underlying distribution of the scores and allows for a more detailed analysis of the shape, such as identifying skewness or multimodality.

Note: To provide specific examples and plots, it would be helpful to have the actual values or frequencies of the data. The provided examples are illustrative and not based on specific data.

 

LONG QUESTIONS ANSWER

Q.1What do you mean by tabulation of data Discuss various parts of table?

Ans. Tabulation of data refers to the systematic arrangement of data in a table format for easy comprehension and analysis. Tables are commonly used to present structured data in a concise and organized manner. The various parts of a table include:

Title: The title of the table provides a brief description of the data presented in the table. It should be clear and concise, conveying the main purpose or focus of the table.

Column Headings: Column headings are placed at the top of each column and describe the content or variables represented in the respective column. They help identify and label the different categories or aspects of the data.

Row Headings: Row headings, also known as stubs, are placed on the leftmost side of the table. They identify and label the different entities or units represented in each row. Row headings provide context and help navigate the table.

Body: The body of the table contains the actual data values. It is organized into rows and columns, with each cell representing a specific data point or value. The body of the table is where the data is tabulated and presented.

Gridlines: Gridlines are horizontal and vertical lines that separate the cells and provide a visual structure to the table. They help in reading and interpreting the data by demarcating the boundaries of rows and columns.

Footnotes: Footnotes are additional explanations or clarifications provided at the bottom of the table. They offer additional context, define terms, or provide information about the data sources or any specific notes regarding the table.

Totals and Summary Statistics: In some cases, tables may include rows or columns for displaying totals, subtotals, or summary statistics. These help summarize the data and provide aggregated information for analysis or comparison.

Units of Measurement: It is essential to include units of measurement or scales alongside the data values to ensure clarity and accuracy. Units help in correctly interpreting the data and understanding the magnitude or scale of the variables.

By utilizing these different parts effectively, a well-constructed table can present data in a structured and organized manner, facilitating data analysis, comparisons, and decision-making.

Q.2. Define tabulation of data Give essential qualities of good table what are the limitations of tabulation of data?

Ans. Tabulation of data refers to the process of arranging and presenting data in a tabular form, usually in rows and columns, to facilitate easy comprehension, analysis, and comparison of information. It involves organizing raw data into a structured format that enhances understanding and supports decision-making.

Essential qualities of a good table include:

Clear and Concise Presentation: A good table should have a clear and concise layout that allows for easy interpretation. The table should be visually appealing and well-organized, with appropriate spacing, font size, and formatting.

Proper Title and Heading: The table should have a descriptive and informative title that summarizes the content or purpose of the table. Clear and meaningful column and row headings should be provided to indicate the variables or categories being presented.

Logical Arrangement: The data in the table should be logically arranged, with a consistent order of variables or categories. The arrangement should make it easy to locate and compare specific data points or patterns.

Accuracy and Precision: The table should accurately reflect the data being presented, with precise numerical values and appropriate units of measurement. Care should be taken to avoid errors, inconsistencies, or misinterpretation of the data.

Adequate Context and Labels: The table should provide sufficient context and labels to ensure understanding and interpretation. This includes providing footnotes, sources of data, definitions of terms, and explanations of any abbreviations or symbols used.

Appropriate Summary Measures: If applicable, the table should include summary measures such as totals, averages, percentages, or other relevant statistics. These measures can provide a quick overview and aid in data analysis.

Limitations of tabulation of data:

Loss of Detail: Tabulating data often involves summarizing or condensing large amounts of information. While this can aid in simplicity and clarity, it may also result in a loss of detailed information that could be relevant in certain analyses.

Limited Contextual Information: Tables may lack contextual information or narrative that could provide a deeper understanding of the data. They often focus on presenting the data itself, without capturing the underlying context or factors that may influence the interpretation.

Inability to Capture Complex Relationships: Tables typically present data in a straightforward format and may not effectively capture complex relationships or interdependencies among variables. Visualizations or other analytical techniques may be more suitable for representing such relationships.

Subjectivity in Classification: Tabulating data requires categorizing or classifying the data into groups or categories. The process of classification can sometimes be subjective, leading to potential biases or limitations in the representation of the data.

It is important to consider these limitations while using tabulated data and supplement it with additional analysis, visualizations, or contextual information to gain a comprehensive understanding of the data.

Q.3. How bar diagrams are useful in presentation of data Discuss various types of bar diagrams?

Ans. Bar diagrams, also known as bar graphs or bar charts, are widely used for the presentation of data. They are particularly useful for comparing and visualizing categorical or discrete data. Bar diagrams represent data using rectangular bars of varying lengths or heights, where the length or height of each bar corresponds to the value or frequency of the category being represented. Here are various types of bar diagrams:

Simple Bar Diagram: A simple bar diagram displays bars of equal width with varying heights to represent the values or frequencies of different categories. Each bar is independent and does not have any additional subdivisions.

Grouped Bar Diagram: In a grouped bar diagram, multiple bars are grouped together in different clusters, each representing a category or subcategory. This allows for easy comparison of values between different categories or subcategories.

Stacked Bar Diagram: In a stacked bar diagram, bars are stacked on top of one another to represent the total value or frequency of a category, with each segment of the bar representing a subcategory or component. This type of bar diagram is useful for illustrating the composition or proportion of different subcategories within a category.

100% Stacked Bar Diagram: A 100% stacked bar diagram is similar to a stacked bar diagram, but the height of each stacked bar represents the relative percentage rather than the actual value. This allows for the comparison of proportions across categories.

Floating Bar Diagram: A floating bar diagram, also known as a range bar diagram, represents the range of values for different categories or time intervals. Each bar consists of a line segment or bar that extends from a starting point to an ending point, indicating the minimum and maximum values for the category.

Gantt Chart: A Gantt chart is a specialized type of bar diagram used for project management. It represents activities or tasks along a timeline, with bars representing the duration or progress of each activity. Gantt charts are useful for visualizing project schedules, dependencies, and milestones.

These different types of bar diagrams provide versatile options for presenting categorical data and facilitating comparisons, composition analysis, and trend analysis. The choice of the specific type of bar diagram depends on the nature of the data and the insights you want to convey.

Q.4.What is meant by graphic presentation of data Discuss in detail various form of graphs?

Ans. Graphic presentation of data refers to the visual representation of data using graphs or charts. Graphs provide a powerful way to communicate information, patterns, and relationships in a clear and concise manner. Here are various forms of graphs commonly used for data visualization:

Line Graph: A line graph uses lines to connect data points, typically showing the trend or change in a variable over time or across different categories. It is useful for illustrating continuous data and identifying patterns, trends, or fluctuations.

Bar Graph: A bar graph represents data using rectangular bars of varying lengths or heights. It is effective for comparing categorical data or discrete variables. Bar graphs can be simple, grouped, stacked, or 100% stacked, depending on the type of data and the comparison needed.

Pie Chart: A pie chart is a circular graph divided into slices, with each slice representing a proportion or percentage of a whole. It is suitable for displaying the composition or distribution of categorical data, allowing for easy comparison of relative proportions.

Histogram: A histogram displays the frequency distribution of continuous or interval data. It consists of adjacent bars where the area of each bar represents the frequency or count of data falling within a specific interval. Histograms provide insights into the shape, central tendency, and variability of the data.

Scatter Plot: A scatter plot uses individual data points represented by dots to visualize the relationship between two continuous variables. It is useful for identifying correlations, patterns, or clusters in the data. Scatter plots can also include a regression line to show the overall trend.

Area Graph: An area graph represents data using filled-in areas between the lines, typically illustrating the cumulative total or proportion of different variables over time. It is effective for showing the cumulative trend or comparison of multiple variables.

Box and Whisker Plot: A box and whisker plot, also known as a box plot, provides a visual summary of the distribution of continuous data. It displays the median, quartiles, and outliers, allowing for quick understanding of the range, spread, and skewness of the data.

Network Graph: A network graph, also called a network diagram or graph visualization, shows the relationship or connections between entities or nodes. It is used to represent complex networks, such as social networks, communication networks, or interconnected systems.

Heatmap: A heatmap uses color gradients to represent the intensity or density of data across different categories or variables. It is effective for visualizing large datasets and identifying patterns or clusters based on the intensity of the colors.

Treemap: A treemap represents hierarchical data using nested rectangles, with each rectangle representing a category or variable. The size and color of the rectangles reflect the magnitude or proportion of the data, allowing for the visualization of hierarchical structures and comparisons.

These different forms of graphs provide a wide range of options for visually representing and analyzing data. The choice of the appropriate graph depends on the type of data, the message to be conveyed, and the insights sought from the visualization.