Worksheet Solutions: Presentation of Data- 1 | Economics Class 11 - Commerce PDF Download

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Q1: The textual/descriptive presentation of data refers to presenting data in the form of ________.
Ans: text
Textual or descriptive presentation involves describing data using words and written explanations rather than visual elements like charts or graphs.

Q2: Tabular presentation is the method of displaying data in the form of a ________.
Ans: table
Tabular presentation involves organizing and displaying data in a structured table format, typically with rows and columns, to make it easier to read and comprehend.

Q3: The objective of tabulation is to facilitate easy ________ and interpretation of data.
Ans: comparison
Tabulation is used to summarize data in a way that makes it simpler to compare different values and draw meaningful interpretations from the data.

Q4: The main parts of a table include the title, table number, column captions, row stubs, ________, headnote, source note, and footnote.
Ans: body
In a table, the title provides an overall description, the table number identifies it uniquely, column captions describe the data columns, row stubs describe the rows, the body contains the data, headnote provides additional context, source note indicates data sources, and footnotes offer additional explanatory information.

Q5: Qualitative classification is based on ________ such as social status and nationality.
Ans: qualities
Qualitative classification categorizes data based on non-numerical qualities or attributes like characteristics, categories, or descriptors.

Q6: Quantitative classification is based on characteristics that are ________ in nature.
Ans: numerical
Quantitative classification organizes data based on numerical attributes or values, which can be measured and expressed with numbers.

Q7: Temporal classification categorizes data according to ________.
Ans: time.
Temporal classification organizes data based on time-related attributes, such as dates, days, months, or years.

Q8: Spatial classification is based on ________.
Ans: space
Spatial classification arranges data according to geographical or spatial attributes, such as location, area, or coordinates.

Q9: A bar diagram is also known as a ________ or bar chart.
Ans: bar graph
A bar diagram, bar graph, and bar chart all refer to the same type of visual representation that uses rectangular bars of varying lengths to represent data values.

Q10: A histogram is a visual representation of a grouped ________ distribution.
Ans: frequency
A histogram displays the distribution of data in the form of bars or bins, with each bar representing a range or group of data values, showing the frequency of data within those groups.

Assertion and Reason Based

Q1: Assertion: Tabular presentation conserves space and time.
Reason: Tabulation allows for easy understanding and interpretation of data.
(a) Both assertion and reason are true, and the reason is the correct explanation of the assertion.
(b) Both assertion and reason are true, but the reason is not the correct explanation of the assertion.
(c) Assertion is true, but the reason is false.
(d) Assertion is false, but the reason is true.
Ans: (a)
Both the assertion and the reason are true, and the reason is indeed the correct explanation of the assertion. Tabular presentation, in the form of tables, is an effective way to conserve space while presenting data in an organized manner. It also facilitates easy understanding and interpretation of data, which is why the reason correctly supports the assertion.

Q2: Assertion: A pie chart is useful for finding out the composition of something.
Reason: Pie charts can replace other types of graphs, such as bar graphs and line plots.

(a) Both assertion and reason are true, and the reason is the correct explanation of the assertion.
(b) Both assertion and reason are true, but the reason is not the correct explanation of the assertion.
(c) Assertion is true, but the reason is false.
(d) Assertion is false, but the reason is true.
Ans: (a)
Both the assertion and reason are true, and the reason is the correct explanation of the assertion. A pie chart is indeed useful for visualizing the composition of a whole in terms of its parts. While pie charts are valuable for showing proportions, they are not meant to replace other types of graphs entirely. The reason correctly explains why pie charts are used.

Q3: Assertion: A histogram uses rectangles to show the frequency of a variable.
Reason: The width of each rectangle in a histogram equals the class interval.
(a) Both assertion and reason are true, and the reason is the correct explanation of the assertion.
(b) Both assertion and reason are true, but the reason is not the correct explanation of the assertion.
(c) Assertion is true, but the reason is false.
(d) Assertion is false, but the reason is true.
Ans: (a)
Both the assertion and reason are true, and the reason is the correct explanation of the assertion. A histogram represents the frequency distribution of a variable using rectangular bars. The width of each rectangle corresponds to the class interval, and this relationship is explained correctly in the reason.

Q4: Assertion: An ogive plots the cumulative frequencies on the vertical axis against data values on the horizontal axis.
Reason: The ogive helps find the popularity or likelihood of data that fall within a certain frequency range.
(a) Both assertion and reason are true, and the reason is the correct explanation of the assertion.
(b) Both assertion and reason are true, but the reason is not the correct explanation of the assertion.
(c) Assertion is true, but the reason is false.
(d) Assertion is false, but the reason is true.
Ans: (a)
Both the assertion and reason are true, and the reason is the correct explanation of the assertion. An ogive is a graphical representation that plots cumulative frequencies against data values. This allows you to determine the popularity or likelihood of data values falling within a specific frequency range. The reason supports the assertion correctly.

Q5: Assertion: Arithmetic line graphs are commonly used to display time series data.
Reason: Arithmetic line graphs are referred to as time series graphs.
(a) Both assertion and reason are true, and the reason is the correct explanation of the assertion.
(b) Both assertion and reason are true, but the reason is not the correct explanation of the assertion.
(c) Assertion is true, but the reason is false.
(d) Assertion is false, but the reason is true.
Ans: (b)
Both the assertion and reason are true. However, the reason is not the correct explanation of the assertion. Arithmetic line graphs are indeed used for time series data, but they are not typically referred to as "time series graphs." The reason is a correct statement but does not directly explain why arithmetic line graphs are used for time series data, so option (b) is the correct choice.

Very Short Answer Type Questions

Q1: What is the purpose of textual/descriptive presentation of data?
Ans: The purpose of textual/descriptive presentation of data is to provide a written explanation or summary of the data, allowing readers to understand the information without having to interpret charts or graphs.

Q2: How does tabular presentation facilitate easy understanding and interpretation of data?
Ans: Tabular presentation organizes data into rows and columns, making it easier to compare and analyze different variables. It provides a structured format that allows for easy understanding and interpretation of data.

Q3: What are the main parts of a table?
Ans: The main parts of a table include the title, column headers, row headers, body cells, and footnotes. These elements help in organizing and presenting the data effectively.

Q4: What is the difference between qualitative and quantitative classification?
Ans: Qualitative classification involves categorizing data based on non-numerical characteristics or qualities, while quantitative classification involves categorizing data based on numerical values or quantities.

Q5: Give an example of qualitative classification.
Ans: An example of qualitative classification is classifying animals into different species or categorizing colors into different groups (e.g., red, blue, green).

Q6: Give an example of quantitative classification.
Ans: An example of quantitative classification is grouping students based on their test scores, such as classifying them into different grade ranges (e.g., A, B, C, D).

Q7: What is temporal classification based on?
Ans: Temporal classification is based on time or chronological order. It involves organizing data according to specific time periods, such as days, months, or years.

Q8: What is spatial classification based on?
Ans: Spatial classification is based on space or location. It involves categorizing data based on geographic regions, areas, or positions.

Q9: What is another name for a bar diagram?
Ans: Another name for a bar diagram is a bar chart.

Q10: What is the advantage of using a bar graph to display data?
Ans: The advantage of using a bar graph to display data is that it allows for easy visual comparison of different categories or variables. The length or height of the bars represents the quantitative values, making it simple to understand the relative magnitudes of the data points.

Short Answer Type Questions

Q1: Explain the objectives of tabulation.

Ans: The objectives of tabulation are as follows:

• To condense and present data: Tabulation helps in summarizing large quantities of data in a systematic and organized manner, making it easier to understand and analyze.
• To facilitate comparison: Tabulation provides a clear and concise representation of data, allowing for easy comparison between different categories or variables.
• To identify patterns and trends: By tabulating data, patterns and trends can be observed more easily, enabling researchers to make meaningful interpretations and draw conclusions.
• To aid in decision-making: Tabulation helps in presenting data in a structured format, which assists in making informed decisions based on the analysis of the data.
• To support statistical analysis: Tabulation is an essential step in statistical analysis as it provides a foundation for further calculations and computations.

Q2: Discuss the main parts of a table in detail.
Ans: The main parts of a table are as follows:

• Title or Table Heading: It provides a brief description of the content of the table.
• Stub or Row Heading: It represents the categories or variables along the vertical axis of the table.
• Body: It consists of the numerical data arranged in rows and columns. The body of the table contains the actual information.
• Caption: It provides additional information about the table, such as the source of data, units of measurement, or any other relevant details.
• Footnotes: These are additional explanations or comments that are placed below the table to provide further clarification or context.

Q3: Differentiate between qualitative and quantitative classification with examples.
Ans: Qualitative classification refers to the categorization of data based on non-numerical characteristics or attributes. It involves grouping data into distinct categories or classes. For example, classifying animals into mammals, birds, reptiles, etc., is qualitative classification.
On the other hand, quantitative classification involves the grouping of data based on numerical values or measurements. It includes dividing data into intervals or ranges. For example, classifying students' heights into different height ranges like 150-160 cm, 161-170 cm, etc., is quantitative classification.

Q4: Describe the different types of bar diagrams.
Ans: There are three main types of bar diagrams:

• Simple Bar Diagram: It represents data using rectangular bars of equal width. The length of each bar corresponds to the magnitude of the data it represents. Simple bar diagrams are suitable for comparing discrete categories or variables.
• Multiple Bar Diagram: It compares data from multiple categories or variables by using sets of bars side by side. Each set of bars represents a different category or variable, and the height of each bar within the set represents the magnitude of the data.
• Subdivided Bar Diagram: It further subdivides the bars in a multiple bar diagram to represent additional subcategories or components within each category or variable. This allows for a more detailed comparison of data.

Q5: Explain the concept of a histogram and its uses.
Ans: A histogram is a graphical representation of data that uses rectangular bars to represent the frequency or count of data points within specific intervals or ranges. The width of each bar corresponds to the width of the interval, and the height of each bar represents the frequency or count of data points in that interval.
Histograms are primarily used to display the distribution and frequency of continuous data. They help in visualizing the shape, central tendency, and dispersion of data. Histograms also aid in identifying outliers, clusters, and patterns within the data.

Q6: Compare and contrast a frequency polygon and a histogram.
Ans: A frequency polygon and a histogram are both graphical representations of data, but they differ in terms of their visual appearance and the type of data they represent.
A frequency polygon is a line graph that represents the frequency or count of data points plotted against the midpoint of each interval or range. It shows the distribution of data and is particularly useful for comparing multiple data sets. Frequency polygons are suitable for displaying both discrete and continuous data.
On the other hand, a histogram uses rectangular bars to represent the frequency or count of data points within specific intervals or ranges. It displays the distribution and frequency of continuous data. Histograms are ideal for visualizing the shape, central tendency, and dispersion of data.
In summary, frequency polygons use lines to represent data frequencies, while histograms use bars. Frequency polygons are suitable for both discrete and continuous data, while histograms are specifically designed for continuous data.

Q7: What is an ogive and how does it help in analyzing data?
Ans: An ogive, also known as a cumulative frequency curve, is a graphical representation of the cumulative frequency or cumulative relative frequency of data. It displays the running total of frequencies or relative frequencies as a line graph.
An ogive helps in analyzing data by providing information about the distribution and cumulative behavior of the data. It allows for the identification of percentiles, quartiles, and other statistical measures. By studying the shape and pattern of the ogive, one can understand the spread and concentration of the data. It also aids in comparing different data sets and assessing their relative positions within the distribution.

Q8: Explain the concept of an arithmetic line graph and its application.
Ans: An arithmetic line graph, also known as a time series graph, is a graphical representation of data that shows the relationship between two variables over a specific period of time. It uses a line to connect data points, where the x-axis represents time and the y-axis represents the variable being measured.
Arithmetic line graphs are commonly used to analyze and display trends, patterns, and fluctuations in data over time. They are particularly useful for depicting changes in variables such as stock prices, population growth, temperature variations, and sales figures. By studying the line graph, one can identify long-term trends, seasonal variations, and the overall behavior of the data over time.

Long Answer Type Questions

Q1: Explain the process of tabular presentation of data, including the steps involved and the importance of proper formatting.
Ans: Tabular presentation of data involves organizing and presenting data in a structured table format. It is a systematic way to display information, making it easier to analyze and interpret.
The following steps are involved in the process:

• Identify the variables: Determine the different categories or variables that need to be included in the table.
• Design the table structure: Decide on the appropriate number of rows and columns for the table based on the variables identified. Ensure that the table is easy to read and understand.
• Collect and organize the data: Gather the relevant data and organize it according to the identified variables. Ensure accuracy and clarity in data entry.
• Label the table: Provide clear and concise labels for each row and column to indicate what they represent. This helps in understanding the data being presented.
• Format the table: Proper formatting is essential for effective tabular presentation. Use consistent and appropriate units of measurement, align the data properly, and consider using visual aids like borders or shading to improve readability.

Importance of proper formatting:

• Clarity: Proper formatting ensures that the data is presented in a clear and organized manner, making it easier to comprehend.
• Comparison: Well-formatted tables allow for easy comparison of data across different categories or variables.
• Accuracy: Proper formatting helps in avoiding errors or misinterpretation of data.
• Professionalism: Well-designed and formatted tables enhance the overall professionalism and credibility of the presentation.

Q2: Discuss the various types of geometric diagrams used for the presentation of data, including bar diagrams and pie charts.

Ans: Geometric diagrams are graphical representations used to present data visually. They help in analyzing and understanding complex information more easily.
Some common types of geometric diagrams used for data presentation are:

• Bar diagrams (Bar charts): Bar diagrams represent data using rectangular bars of different lengths. They are suitable for comparing different categories or variables. Vertical or horizontal bars can be used based on the nature of the data.
• Pie charts: Pie charts are circular diagrams divided into sectors, representing different categories or variables. The size of each sector corresponds to the proportion of data it represents. Pie charts are useful for displaying proportions or percentages.
• Line graphs: Line graphs display data points connected by lines. They are effective for showing trends or changes over time. Line graphs are particularly useful for analyzing continuous data.
• Scatter plots: Scatter plots use individual data points plotted on a graph to demonstrate the relationship between two variables. They help in identifying patterns or correlations.
• Histograms: Histograms are graphical representations of frequency distributions. They consist of bars of different heights, where the width of each bar represents a specific range of values. Histograms are used to display grouped continuous data.

Each type of geometric diagram has its own advantages and is suitable for different types of data and purposes. Choosing the right type of diagram depends on the nature of the data being presented and the message intended to be conveyed.

Q3: Describe the different types of frequency diagrams used to represent grouped data.

Ans: Frequency diagrams are used to represent grouped data in a visual format, providing a summary of the distribution of data.
Some common types of frequency diagrams used for grouped data are:

• Histograms: Histograms are bar graphs that represent the frequency of data within specific intervals or ranges. The height of each bar corresponds to the frequency or count of data falling within that interval. Histograms are widely used for displaying continuous data.
• Frequency polygons: Frequency polygons are line graphs that connect the midpoints of the tops of the bars in a histogram. They provide a smooth representation of the distribution and allow for easier comparison between different distributions.
• Cumulative frequency curves (Ogive): Cumulative frequency curves plot the cumulative frequency against the upper or lower class boundaries. They help in analyzing the cumulative distribution of data and identifying percentiles or quartiles.
• Stem-and-leaf plots: Stem-and-leaf plots organize the data in a tabular format, where the leading digits form the "stem" and the trailing digits form the "leaves." They provide a quick visual representation of the distribution of data values.

These frequency diagrams help in understanding the shape, center, and spread of the data distribution. They allow for easy comparison between different groups or categories, aiding in data analysis and decision-making.

Q4: Discuss the characteristics and uses of arithmetic line graphs, with examples.
Ans: Arithmetic line graphs, also known as line charts, are graphical representations that display continuous data points connected by straight lines. They are used to show trends, changes, or relationships over time or across different variables.
Some characteristics and uses of arithmetic line graphs are:
Characteristics:

• Continuous data: Line graphs are suited for representing continuous data, where the variable being measured can take any value within a specific range.
• Time-based representation: Line graphs often depict data over time, with time usually plotted on the x-axis. This allows for the analysis of trends or patterns in the data.
• Connected data points: The data points in a line graph are connected by straight lines, emphasizing the continuity and progression of the data.

Uses:

• Trend analysis: Line graphs are commonly used to analyze and display trends in data over time. This can be useful in identifying patterns, forecasting future values, or understanding the impact of certain factors.
• Comparison of variables: Line graphs enable the comparison of multiple variables or categories on the same graph. This helps in identifying relationships or differences between the variables.
• Visual representation: Line graphs provide a visual representation of data, making it easier to communicate complex information and facilitate understanding.

For example, an arithmetic line graph can be used to show the temperature variations in a city over a year. The x-axis represents the months, and the y-axis represents the temperature. The line connecting the data points indicates the changing temperature trend throughout the year. This graph allows for easy interpretation of seasonal temperature patterns and helps in making informed decisions based on the data.