Class 11 Economics (Statistics for Economics) Chapter 4 Presentation of Data

Key Concept: Component Conversion

[b) 30%]

[Solution Description] The percentage can be found by dividing the angle by 3.6°. Thus, $\frac{108^\circ}{3.6^\circ/%} = 30%$.

Key Concept: Histogram Basics

b) Class Interval

[Solution Description] The base of each rectangle in a histogram represents a class interval on the X-axis. This is a key aspect of histograms as they are used to display the distribution of continuous variables.

Key Concept: Bar vs Histogram

b) Bar diagrams have spaces between bars

[Solution Description]

Bar diagrams typically have spaces between the bars, indicating that the data is categorical or discrete. In contrast, histograms do not have spaces between their bars, as they represent continuous data.

Key Concept: Column-Row Relationship

c) December

[Solution Description] The column heading that corresponds to seasonal data for specific conditions such as temperatures in different months like December, January, and February can represent winter. So, the correct heading could be one of these typical winter months.

Key Concept: Comparative Analysis

c) Qualitative classification uses categories or attributes; quantitative involves numerical measurement.

[Solution Description] Qualitative classification is based on attributes or categories such as social status, nationality, etc., without focusing on measurable characteristics like height or income. Quantitative classification, on the other hand, focuses on numerical data which can be measured.

Key Concept: Time Scale

c) Kilograms

[Solution Description] Typical scales of time include hours, days, weeks, months, and years. Kilograms are not a time scale.

Key Concept: Bar Diagram Variants

d) Frequency distribution

[Solution Description]

A geometric bar diagram includes types such as simple bar diagrams, multiple bar diagrams, and component bar diagrams. A frequency distribution is generally shown using histograms or other forms of frequency diagrams.

Key Concept: Basic Concepts

b) Because data points are buried within the narrative

[Solution Description] In textual presentation, important data and conclusions are interwoven within the text, requiring readers to go through the whole document to fully comprehend the information presented and understand the context or emphasis.

Key Concept: Basic Definition

b) Two-dimensional diagram

[Solution Description] A histogram is characterized as a two-dimensional diagram, where the X-axis represents class intervals and the Y-axis represents frequency.

Key Concept: Table Parts

b) Caption

[Solution Description] Part of a statistical table includes various elements such as the table number, title, captions or column headings, stubs or row headings, body of the table, unit of measurement, source, and note.

Key Concept: Purpose Understanding

b) It allows emphasis on detailed points

[Solution Description] Textual presentation is most suitable for small quantities of data because it allows specific details to be emphasized through narrative, making it easier to understand without overwhelming the reader with too much information.

Key Concept: Adjusting Heights

d) By using frequency density

[Solution Description] To adjust for differing class widths in a histogram, we use frequency density instead of absolute frequency. This means the height of each rectangle is determined by dividing the class frequency by its width.

$\text{Height of Rectangle} = \frac{\text{Class Frequency}}{\text{Width of Class}}$

Key Concept: Histogram Basics

d) It is a two-dimensional diagram.

[Solution Description] A histogram is a two-dimensional diagram where rectangles represent class intervals on the X-axis and frequencies on the Y-axis.

Key Concept: Data Trend

d) All of the above

[Solution Description]

Arithmetic line graphs help interpret long-term trends, cyclicity, and seasonality in data by visually representing changes over time.

Key Concept: Row Heading Location

d) Left column

[Solution Description] Row headings, or stubs, are typically located in the complete left column of a table, known as the stub column.

Key Concept: Basic Concept

c) Bar chart

[Solution Description] Diagrammatic data presentation methods include visual representations such as bar charts, pie charts, and line graphs.

Key Concept: Pie Chart Calculation

c) $90^\circ$

[Solution Description] To find the angle for a sector in a pie chart, use the formula: Angle $= \frac{\text{Percentage}}{100} \times 360^\circ$. For 25%, the calculation is:

$\text{Angle} = \frac{25}{100} \times 360^\circ = 90^\circ$

Key Concept: Frequency Curve Purpose

d) To smooth out the frequency polygon

[Solution Description]

A frequency curve is drawn to smooth out the frequency polygon into a continuous curve. It provides a visual representation of how the frequencies are distributed across different classes, making it easier to identify trends and patterns in the data.

Key Concept: Data Calculation

b) 43.75%

[Solution Description] To find the percentage of males who were non-workers, we use the formula:

$\text{Percentage} = \left(\frac{\text{Non-worker males}}{\text{Total population}}\right) \times 100$

Substituting the given values:

$\text{Percentage} = \left(\frac{35}{80}\right) \times 100 = 43.75%$

Thus, 43.75% of the total population were male non-workers.

Key Concept: Pie Chart Basics

c) 360°

[Solution Description] A pie chart represents data as parts of a whole circle. The total angle of a complete circle is $360^\circ$, representing 100% of the data.

Key Concept: Class Mark Usage

c) To plot frequencies on the X-axis

[Solution Description] Class marks are used in plotting a frequency polygon to represent the midpoint values on the X-axis, which allows frequencies to be plotted correctly as they correspond to these central values of the class intervals.

Key Concept: Frequency Density Calculation, Comparative Analysis Using Graphs

b) Plants in Dataset Y grew taller on average than those in Dataset X.

[Solution Description] To find frequency densities for Dataset X, divide each frequency by its class interval width:

$\text{Density for first class} = \frac{8}{4} = 2$

$\text{Density for second class} = \frac{12}{4} = 3$

$\text{Density for third class} = \frac{10}{4} = 2.5$

Since Dataset Y’s frequency polygon lies above Dataset X’s, it indicates generally higher frequencies in Dataset Y.

Key Concept: Unit Measurement Role

c) To clarify the data represented

[Solution Description] Including units of measurement in a table helps to clearly communicate what each number represents, ensuring accurate understanding and interpretation of the data.

Key Concept: Data classification

c) Quantitative classification

[Solution Description] Quantitative classification involves organizing data based on numeric values, such as height, weight, age, etc.

Key Concept: Note Purpose

c) To provide explanations for complex data

[Solution Description] A note in a table provides additional information that may not be immediately clear from the data itself. It helps to explain non-self-explanatory data, ensuring clarity and aiding readers’ understanding.

Key Concept: Axis Identification

b) Variable values

[Solution Description] In a time series graph, the y-axis usually represents the variable values or time series data which shows how these values change over time.

Key Concept: Basic Definition

d) Time series graph

[Solution Description] An arithmetic line graph is commonly referred to as a time series graph because it represents data points in time order.

Key Concept: Data Representation

b) Multiple bar diagram

[Solution Description] A multiple bar diagram allows comparison between two or more sets of data by using adjacent bars for each category, making it easy to visually interpret differences among datasets.

Key Concept: Basic Definition

b) A circle divided into proportional parts

[Solution Description] A pie chart is defined as a circle divided into proportional parts, representing different categories or components of the data.

Key Concept: Geometric Diagrams

b) Pie diagram

[Solution Description] Geometric diagrams include bar diagrams such as simple, multiple, component, and pie diagrams. Among the options provided, “Pie diagram” is a type of geometric diagram.

Key Concept: Advanced Calculation, Real-World Problem Solving

b) 90°

[Solution Description]

To find the angle for the East region, we need to multiply its percentage share by the full circle:

The formula to calculate the angle for a given percentage in a pie chart is:

$\text{Angle} = (\text{Percentage}) \times 3.6^\circ$

For the East region with a 25% share:

$\text{Angle for East} = 25% \times 3.6^\circ = 90^\circ$

Therefore, the angle for the East region is $90^\circ$.

Key Concept: Basic Definition

b) A circle divided into proportional parts

[Solution Description] A pie chart is a circular statistical graphic, which is divided into slices to illustrate numerical proportions. Each slice represents a component of the total dataset, shown as a percentage of the whole circle.

Key Concept: Table Parts

b) To uniquely identify each table

[Solution Description] The table number serves as a unique identifier for tables within a document, distinguishing one table from another.

Key Concept: Basic Definition

b) Cumulative frequency curve

[Solution Description] An ogive is a graphical representation of the cumulative frequency distribution. It is also known as a cumulative frequency curve.

Key Concept: Diagram Characteristics

b) Uniform width of bars

[Solution Description] In a bar diagram, it is essential that the width of all bars be uniform to ensure accurate comparison. The length of the bars represents the data values.

Key Concept: Ogive Interpretation

c) It always increases

[Solution Description] A ‘less than’ ogive always shows an increasing trend since it plots cumulative frequency, which either increases or remains constant as more data values accumulate.

Key Concept: Definition Recall

d) A circle divided proportionally among components

[Solution Description]

A pie diagram is a type of chart that represents data in circular format where the circle is divided into proportional segments or slices to illustrate numerical proportions. Each slice’s size is calculated based on its value as part of the total.

Key Concept: Histogram Basics

d) Frequency density

[Solution Description] When class intervals are unequal, the height of rectangles in a histogram is represented by frequency density. Frequency density is calculated using the formula $\text{Frequency Density} = \frac{\text{Frequency}}{\text{Class Interval Width}}$. Hence, the correct answer is frequency density.

Key Concept: Comparative Analysis

a) Spatial classification categorizes data based on place, whereas quantitative classification categorizes data based on numbers.

[Solution Description] Spatial classification is based on geographical locations such as village, town, or country, while quantitative classification is based on numerical data like population count or percentage.

Key Concept: Importance of Rounding

d) To simplify data representation

[Solution Description] Rounding figures in a table is significant because it simplifies data representation, making it easier to read and compare. By reducing the number of digits, rounding helps present data in a more understandable format without compromising essential information.

Key Concept: Comparison Utility

c) They allow various distributions to be plotted on the same axes

[Solution Description]

Frequency polygons are particularly useful for comparing multiple distributions since they allow us to plot several datasets on the same axes. By overlapping different frequency polygons, we can easily compare the shapes and spreads of the distributions.

Key Concept: Definition Recall

b) 7

[Solution Description] To find the median, first arrange the numbers in increasing order: 3, 5, 7, 8, 12. The middle number in this ordered list is 7. Therefore, the median is 7.

Key Concept: Textual vs. Tabular

a) Textual presentation

[Solution Description] Textual presentation is best used for small datasets or when the information needs to be presented in narrative form, such as summarizing a report. It does not rely on visual aids and can effectively convey detailed descriptions.

Key Concept: Components Identification

b) Midpoints of class intervals

[Solution Description] In a frequency polygon, frequencies are typically plotted against the midpoints of the class intervals on the X-axis. This allows for an accurate depiction of the distribution pattern across different classes.

Key Concept: Bar Diagram Components

d) Spaces between bars

[Solution Description] The components of a standard bar diagram include axis, bars, and sometimes legends. Spaces between bars are part of the design, not a separate component.

Key Concept: Temporal Data Example

c) Revenue over different months

[Solution Description] Temporal classification involves categorizing data based on time periods such as hours, days, or years. To identify the correct answer, we must look for an option that classifies data according to time.

Key Concept: Basic Definition

b) To show the relative sizes of components within a whole

[Solution Description]

A component bar diagram is primarily used to compare the sizes of different component parts within a whole, making it easy to visualize relationships among these parts.

Key Concept: Table Parts

c) Captions

[Solution Description] The headings at the top of each column in a table are referred to as “captions.”

Key Concept: Plotting Points

c) Lower class limits

[Solution Description] In a ‘more than’ ogive, cumulative frequencies are plotted against the lower class limits as this indicates how many observations are more than the given class limit.

Key Concept: Diagram Purpose

c) To show divisions within a whole

[Solution Description] A pie diagram is used to show the proportional parts of a whole category as sectors of a circle. It helps compare various parts within a dataset visually by showing their relative sizes.

Key Concept: Textual Data

a) Descriptive summary

[Solution Description] Textual data presentation involves describing data using text or descriptive words, explaining trends, patterns, or comparing different data sets in written form.

Key Concept: Purpose Recognition

c) For small quantities of data

[Solution Description] Textual presentation is most suitable for small quantities of data. It allows specific points to be emphasized and is effective when detailed explanations are needed more than visual summaries.

Key Concept: Data Interpretation

c) Product C

[Solution Description] The increase in sales for each product can be calculated by subtracting the number of units sold in year 1 from those sold in year 4:

For Product A: $600 – 400 = 200$ units

For Product B: $350 – 200 = 150$ units

For Product C: $800 – 300 = 500$ units

Therefore, Product C has shown the highest increase in sales by year 4.

Key Concept: Bar Diagram Types

c) Component Bar Diagram

[Solution Description] A component bar diagram is used to represent data where we want to compare different components within several items or entities. This allows the viewer to see the relative size of each component part in relation to one another.

Key Concept: Bar Diagram

b) Equispaced and equiwidth bars

[Solution Description] A key feature of a bar diagram is that the bars are equispaced and of equal width, which allows for easy comparison of different categories based on their magnitude.

Key Concept: Diagrammatic Effectiveness

c) Allows quicker comprehension

[Solution Description]

Diagrams such as bar charts and pie charts provide an immediate visual impact that can make it easier to compare quantities or see trends at a glance compared to tables, which may require more time to interpret the same data points numerically.

Key Concept: Basic Definition

c) Identifying long-term trends

[Solution Description] An arithmetic line graph is used to represent time series data by plotting time on the x-axis and values on the y-axis, helping to identify long-term trends.

Key Concept: Time Axis Interpretation

c) 2007-08

[Solution Description] To find the year when imports first exceeded 3000 crores, locate the point on the x-axis where the y-value surpasses 3000. By examining the data points plotted along the line for each year, the year identified is 2007-08.

Key Concept: Comparison with Other Methods

c) Emphasizing specific points through context

[Solution Description] Textual presentation allows for detailed descriptions and can highlight specific points more effectively than tables or diagrams. This method is particularly advantageous when you wish to provide context and narrative around the data.

Key Concept: Basic Definition

a) A cumulative frequency curve

[Solution Description] A ‘Less than Ogive’ is a type of cumulative frequency curve which represents cumulative frequencies plotted against upper class limits of the intervals. This definition distinguishes it from other types of graphs like histograms which use simple frequencies.