StudyOSStudyOS CBSE Study Material, Class 5–12

Presentation of Data

NCERT Class 11 · Economics Based on NCERT Class 11 Economics textbook · Free CBSE study kit

Everything you need to ace this chapter, in one place.
Notes · Mind Map · Quiz · Assertion-Reason · Case Studies · Question Bank · Past Papers

Get Full Study Kit →
Studying with friends? Send them this chapter.

Chapter Notes

Overview
This chapter explains how voluminous data collected and organised can be put into a compact and presentable form. It covers three forms of presentation: textual or descriptive, tabular, and diagrammatic. The one big idea a student must walk away with is that data must be presented clearly and effectively so that it is readily usable, easily comprehended, and suitable for further statistical treatment and decision-making.
Key Concepts (26)
Textual or Descriptive presentation
A form of presentation where data are described within the text, suitable when the quantity of data is not too large.
e.g. In a bandh call, 5 petrol pumps were found open and 17 were closed whereas 2 schools were closed and remaining 9 schools were found open in a town of Bihar.
Tabular presentation
A form of presentation where data are presented in rows (read horizontally) and columns (read vertically).
e.g. Table 4.1 tabulating information about literacy rates with three rows (male, female, total) and three columns (urban, rural, total) — a 3 × 3 table.
Qualitative classification
Classification done according to attributes such as social status, physical status, nationality, etc.
e.g. In Table 4.1, the attributes for classification are sex and location which are qualitative in nature.
Quantitative classification
Classification on the basis of characteristics which are quantitative in nature and can be measured quantitatively, such as age, height, production, income.
e.g. Table 4.2 shows distribution of 542 respondents by their age in an election study in Bihar.
Temporal classification
Classification where time becomes the classifying variable and data are categorised according to time (hours, days, weeks, months, years).
e.g. Table 4.3 shows yearly sales of a tea shop from 1995 to 2000.
Spatial classification
Classification done on the basis of place, which may be a village/town, block, district, state, country, etc.
e.g. Table 4.4 shows export from India to rest of the world in 2013-14 as share of total export (per cent).
Table Number
A number assigned to a table for identification purpose, given at the top or at the beginning of the title of the table.
e.g. Table 4.5 should be read as the fifth table of the fourth chapter.
Title
The part of a table that narrates about the contents of the table; it has to be clear, brief and carefully worded.
e.g. Table 4.5 title: 'Population of India according to workers and non-workers by gender and location, 2001'.
Captions or Column Headings
Column designations given at the top of each column to explain figures of the column.
e.g. In Table 4.5, column headings are 'Workers', 'Non-worker', 'Total'.
Stubs or Row Headings
Headings given to each row of the table; the complete left column is known as stub column.
e.g. In Table 4.5, row headings are 'Male', 'Female', 'Total' under 'Rural', 'Urban', 'All'.
Body of the Table
The main part of a table that contains the actual data; location of any one figure is fixed by the row and column.
e.g. In Table 4.5, data in the second row and fourth column indicate that 25 crore females in rural India were non-workers in 2001.
Unit of Measurement
The unit of measurement of the figures in the table should always be stated along with the title.
e.g. In Table 4.5, the unit is 'Crore'.
Source
A brief statement or phrase indicating the source of data presented in the table, generally written at the bottom.
e.g. In Table 4.5, source is 'Census of India 2001'.
Note
The last part of the table that explains the specific feature of the data content which is not self explanatory.
e.g. In Table 4.5, note: 'Figures are rounded to nearest crore'.
Diagrammatic presentation
The third method of presenting data that provides the quickest understanding of the actual situation; translates abstract ideas into concrete and easily comprehensible form.
e.g. Bar diagram, pie diagram, histogram, frequency polygon, ogive, arithmetic line graph.
Bar diagram
A geometric diagram comprising a group of equispaced and equiwidth rectangular bars for each class or category of data; height or length of the bar reads the magnitude of data.
e.g. Figure 4.1 shows a bar diagram of male literacy rates of major states of India, 2011.
Simple Bar Diagram
A bar diagram where each bar represents a single category or class of data.
e.g. Figure 4.1: Bar diagram showing male literacy rates of major states of India, 2011.
Multiple Bar Diagram
Bar diagrams used for comparing two or more sets of data, e.g., income and expenditure for different years.
e.g. Figure 4.2: Multiple bar diagram showing female literacy rates over two census years 2001 and 2011 by major states of India.
Component Bar Diagram
Bar diagrams that show the bar and its sub-divisions into two or more components; also called sub-diagrams.
e.g. Figure 4.3: Enrolment at primary level in a district of Bihar showing enrolled and out of school components.
Pie Diagram
A component diagram in the form of a circle whose area is proportionally divided among the components; also called a pie chart.
e.g. Figure 4.4: Pie diagram for different categories of Indian population according to working status 2011.
Frequency Diagram
Diagrams used to represent data in the form of grouped frequency distributions, e.g., histogram, frequency polygon, frequency curve, ogive.
e.g. Histogram for distribution of daily wage earners (Table 4.9).
Histogram
A two-dimensional diagram consisting of a set of rectangles with base as the intervals between class boundaries (along X-axis) and with areas proportional to the class frequency.
e.g. Figure 4.5: Histogram for the distribution of 85 daily wage earners in a locality of a town.
Frequency Polygon
A plane bounded by straight lines, usually four or more lines; an alternative to histogram derived from histogram itself.
e.g. Figure 4.6: Frequency polygon drawn for the data given in Table 4.9.
Frequency Curve
A smooth freehand curve passing through the points of the frequency polygon as closely as possible.
e.g. Figure 4.7: Frequency curve for Table 4.9.
Ogive
A cumulative frequency curve; there are two types: 'less than' ogive and 'more than' ogive.
e.g. Figure 4.8(b): 'Less than' and 'More than' ogive for data given in Table 4.10.
Arithmetic Line Graph
A graph also called time series graph where time is plotted along x-axis and the value of the variable along y-axis; helps in understanding trend, periodicity, etc.
e.g. Figure 4.9: Arithmetic line graph for time series data of exports and imports of India (Table 4.11).
Formulas & Equations (3)
Angle of component = (Percentage of component / 100) × 360°
Reads as: Angle of component equals percentage of component divided by 100 multiplied by 360 degrees
Variables: Percentage of component: the percentage share of a category in the total; Angle of component: the angle in degrees that the sector subtends at the centre of the pie chart
Use when: When constructing a pie diagram to convert percentage values into angular components
⚠ Students often forget that a circle has 360° and directly multiply the percentage by 3.6 without understanding the derivation, or they use absolute values instead of percentages.
Each 1% = 3.6° (since 360°/100 = 3.6°)
Reads as: Each one percent corresponds to three point six degrees
Variables: 1%: one percent of the total; 3.6°: the angle representing one percent in a pie chart
Use when: When converting percentages to angles for a pie diagram
⚠ Students sometimes use 360° directly without dividing by 100, leading to incorrect angles.
Frequency density = Class frequency / Width of the class interval
Reads as: Frequency density equals class frequency divided by width of the class interval
Variables: Class frequency: the number of observations in a class; Width of the class interval: the difference between the upper and lower class boundaries
Use when: When constructing a histogram with unequal class intervals, to adjust the heights of rectangles for comparability
⚠ Students use absolute frequency instead of frequency density when class intervals are unequal, making the histogram misleading.
How It Works
Construction of a Simple Bar Diagram
  1. Step 1: Draw a base line (X-axis) and a vertical axis (Y-axis).
  2. Step 2: Mark the categories or classes along the X-axis at equal intervals.
  3. Step 3: Draw equiwidth rectangular bars for each category, with height proportional to the magnitude of data.
  4. Step 4: Ensure the lower end of each bar touches the base line, starting from zero unit.
  5. Step 5: Space the bars equally; do not leave gaps between bars in a histogram but leave gaps in a bar diagram.
💡 Bars are equispaced and equiwidth; height reads magnitude; the lower end touches the base line from zero.
Construction of a Multiple Bar Diagram
  1. Step 1: Identify two or more sets of data to be compared.
  2. Step 2: Draw bars for each category, grouping bars for different data sets side by side.
  3. Step 3: Use different colours or shading to distinguish the data sets.
  4. Step 4: Provide a legend or key to identify the bars.
💡 Multiple bar diagrams are used for comparing two or more sets of data; bars are grouped together for each category.
Construction of a Component Bar Diagram
  1. Step 1: Construct a bar on the X-axis with height equivalent to the total value of the bar (for percentage data, height is 100 units).
  2. Step 2: Divide the bar into components proportional to their values using the unitary method.
  3. Step 3: Give priority to smaller components when partitioning the bar.
  4. Step 4: Shade or colour the components suitably.
💡 The total bar height represents the total; components are drawn in proportion; smaller components are given priority in partitioning.
Construction of a Pie Diagram
  1. Step 1: Express each category value as a percentage of the total value.
  2. Step 2: Multiply each percentage by 3.6° to find the angle each component will subtend at the centre.
  3. Step 3: Draw a circle of any radius.
  4. Step 4: Divide the circle into sectors using the calculated angles, drawing straight lines from the centre to the circumference.
  5. Step 5: Label each sector or provide a legend.
💡 Pie charts are drawn using percentages, not absolute values; each 1% equals 3.6°.
Construction of a Histogram
  1. Step 1: If class intervals are not continuous, convert them into continuous classes.
  2. Step 2: Mark class boundaries on the X-axis.
  3. Step 3: For equal class intervals, draw rectangles with height equal to the frequency of the class.
  4. Step 4: For unequal class intervals, calculate frequency density (frequency/width) and use that as the height.
  5. Step 5: Ensure rectangles are adjacent with no open space between them.
💡 Histogram is drawn only for continuous variables; width is as important as height; no space between rectangles.
Construction of a Frequency Polygon
  1. Step 1: Plot the midpoints of class intervals on the X-axis.
  2. Step 2: Plot the frequencies (as ordinates) against the midpoints.
  3. Step 3: Join the plotted points by a series of short straight lines.
  4. Step 4: Join the two end points to the base line at the mid-values of the two classes with zero frequency immediately at each end of the distribution.
💡 Frequencies are always plotted against the mid-point of class intervals; broken lines join the ends to the base line.
Construction of a Frequency Curve
  1. Step 1: Draw a frequency polygon for the data.
  2. Step 2: Draw a smooth freehand curve passing through the points of the frequency polygon as closely as possible.
  3. Step 3: The curve may not pass through all points but should pass through them as closely as possible.
💡 It is a smooth freehand curve, not necessarily passing through all points of the frequency polygon.
Construction of an Ogive (Cumulative Frequency Curve)
  1. Step 1: For 'less than' ogive, plot cumulative frequencies against the respective upper limits of the class intervals.
  2. Step 2: For 'more than' ogive, plot cumulative frequencies against the respective lower limits of the class intervals.
  3. Step 3: Join the plotted points with a smooth curve.
  4. Step 4: The intersection point of the two ogives gives the median of the frequency distribution.
💡 'Less than' ogive is never decreasing; 'more than' ogive is never increasing; their intersection gives the median.
Construction of an Arithmetic Line Graph (Time Series Graph)
  1. Step 1: Plot time (hour, day, week, month, year) along the X-axis.
  2. Step 2: Plot the value of the variable along the Y-axis.
  3. Step 3: Plot the data points for each time period.
  4. Step 4: Join the plotted points with straight lines to form a line graph.
💡 Time is always on the X-axis; the graph helps in understanding trend, periodicity, and long-term patterns.
Exam Traps — Don't Make These Mistakes
⚠ Confusing Bar Diagram and Histogram
✗ Bar diagram and histogram are the same method of presentation of data.
→ They are different: in a bar diagram, bars are equispaced with gaps, width is arbitrary, and it can be used for discrete and continuous variables. In a histogram, rectangles are adjacent with no gaps, width is as important as height, and it is drawn only for continuous variables.
✓ Bar diagram and histogram are different. Bar diagram has gaps between bars, width is arbitrary, and it is used for both discrete and continuous variables. Histogram has no gaps, width matters, and it is used only for continuous variables.
⚠ Using Absolute Values in Pie Diagram
✗ Students directly use absolute values of categories to draw the pie chart without converting to percentages.
→ Pie charts are drawn using percentages of the total, not absolute values. The circle represents 100%, and each sector's angle is calculated from the percentage.
✓ First convert each category value to a percentage of the total, then multiply each percentage by 3.6° to get the angle for the sector.
⚠ Incorrect Histogram for Unequal Class Intervals
✗ Students draw rectangles with height equal to the frequency even when class intervals are unequal.
→ When class intervals are unequal, the area of the rectangle must be proportional to the frequency. Using frequency directly as height distorts the comparison. Instead, frequency density (frequency/width) should be used as the height.
✓ For unequal class intervals, calculate frequency density = class frequency / width of class interval, and use that as the height of the rectangle.
⚠ Confusing 'Less than' and 'More than' Ogive
✗ Students plot 'less than' cumulative frequencies against lower limits and 'more than' against upper limits.
→ For 'less than' ogive, cumulative frequencies are plotted against the respective upper limits of the class intervals. For 'more than' ogive, cumulative frequencies are plotted against the respective lower limits.
✓ For 'less than' ogive: plot cumulative frequencies against upper class limits. For 'more than' ogive: plot cumulative frequencies against lower class limits.
⚠ Omitting Source and Note in a Table
✗ Students present a table without mentioning the source of data or any explanatory notes.
→ A good statistical table must include the source (to indicate where data came from) and a note (to explain any specific features not self-explanatory). Omitting them makes the table incomplete.
✓ Always include the source at the bottom of the table and a note if needed, e.g., 'Source: Census of India 2001' and 'Note: Figures are rounded to nearest crore'.
⚠ Drawing Histogram for Discrete Data
✗ Students draw a histogram for discrete variables like family size or number of children.
→ Histogram is drawn only for continuous variables. For discrete variables, a bar diagram is appropriate.
✓ Use a bar diagram for discrete variables and a histogram only for continuous variables.
Compare & Contrast
Nature of data and construction
Bar Diagram
Histogram
Bar diagram is used for both discrete and continuous variables, bars are equispaced with gaps, width is arbitrary, and height represents magnitude. Histogram is used only for continuous variables, rectangles are adjacent with no gaps, width is as important as height, and area represents frequency.
Method of drawing
Frequency Polygon
Frequency Curve
Frequency polygon is drawn by joining the midpoints of the topside of consecutive rectangles of the histogram with straight lines, and the ends are joined to the base line. Frequency curve is a smooth freehand curve that passes through the points of the frequency polygon as closely as possible, not necessarily through all points.
Exam Focus
Marks pattern: 2 MCQs (1 mark each), 1 SA (3 marks) on parts of table or types of classification, 1 LA (5 marks) on diagrammatic presentation (e.g., draw histogram/frequency polygon/ogive or interpret a given diagram)
Most asked: Parts of a table (table number, title, captions, stubs, body, unit, source, note) · Types of classification (qualitative, quantitative, temporal, spatial) · Difference between bar diagram and histogram · Construction and interpretation of histogram, frequency polygon, ogive · Pie diagram and conversion of percentages to angles · Multiple bar diagram and component bar diagram · Arithmetic line graph (time series graph)
Don't skip: Draw a histogram/frequency polygon/ogive for a given frequency distribution and find mode/median graphically.; Construct a pie diagram from given data showing steps of percentage and angle calculation.; Explain the difference between bar diagram and histogram with examples.; Identify and label parts of a statistical table from a given table.
One-Line Revision (read aloud before the exam)
  1. There are three forms of presentation of data: textual, tabular, and diagrammatic.
  2. Textual presentation is suitable when the quantity of data is not too large.
  3. Tabular presentation presents data in rows and columns, with parts including table number, title, captions, stubs, body, unit, source, and note.
  4. Classification in tabulation can be qualitative, quantitative, temporal, or spatial.
  5. Qualitative classification is based on attributes like sex, nationality; quantitative classification is based on measurable characteristics like age, income.
  6. Temporal classification uses time as the classifying variable; spatial classification uses place.
  7. Bar diagrams are one-dimensional, equispaced, equiwidth rectangles; height reads magnitude.
  8. Multiple bar diagrams compare two or more sets of data; component bar diagrams show sub-divisions of a total.
  9. Pie diagram is a circle divided into sectors; each 1% corresponds to 3.6°.
  10. Histogram is a set of adjacent rectangles for continuous data; area proportional to frequency.
  11. For unequal class intervals in histogram, use frequency density = frequency/width.
  12. Frequency polygon joins midpoints of tops of histogram rectangles with straight lines; ends are joined to base line.
  13. Frequency curve is a smooth freehand curve through the frequency polygon points.
  14. Ogive is a cumulative frequency curve; 'less than' ogive uses upper limits, 'more than' ogive uses lower limits.
  15. The intersection of 'less than' and 'more than' ogives gives the median.
  16. Arithmetic line graph (time series graph) plots time on X-axis and variable value on Y-axis.
  17. Diagrams are less accurate but more effective than tables in presenting data.
  18. A good table must have a clear title, proper captions and stubs, and indicate source and unit of measurement.
  19. Bar diagrams are suitable for both frequency and non-frequency data; histogram is only for continuous variables.
  20. Component bar diagrams are also called sub-diagrams; smaller components are given priority in partitioning.

MCQs — 10 Questions with Answers

Q1. According to Table 4.1, what is the literacy rate for rural females in India?

  • A. 59% ✓
  • B. 65%
  • C. 68%
  • D. 74%

Answer: A — Table 4.1 shows that rural female literacy is at the intersection of 'Female' row and 'Rural' column, which is 59%.

Q2. In Table 4.2, if 542 respondents total and 60-70 age group has 144 respondents, what is the percentage for this group?

  • A. 23.56%
  • B. 26.57% ✓
  • C. 28.24%
  • D. 24.35%

Answer: B — Percentage = (144 ÷ 542) × 100 = 26.57%, calculated using the percentage formula.

Q3. Which classification type is used in Table 4.3 (Yearly sales from 1995 to 2000)?

  • A. Qualitative classification
  • B. Quantitative classification
  • C. Temporal classification ✓
  • D. Spatial classification

Answer: C — Time (years 1995-2000) is the classifying variable, making this temporal classification.

Q4. The main advantage of tabular presentation over textual presentation is that tabulation:

  • A. uses fewer words to describe data
  • B. organizes data for further statistical treatment and decision-making ✓
  • C. makes data more visually appealing
  • D. eliminates the need for data source citation

Answer: B — Tabulation's primary advantage is systematic organization enabling statistical analysis and informed decisions.

Q5. In a two-way table with gender (male/female) and location (rural/urban), how many cells will contain data values if you include row and column totals?

  • A. 4 cells
  • B. 6 cells
  • C. 9 cells ✓
  • D. 12 cells

Answer: C — A 3×3 table (3 gender categories including total, 3 location categories including total) has 9 cells total, as shown in Table 4.1.

Q6. In Table 4.4, India's export to USA is 12.5% of total exports worth $314.40 billion. What is the approximate export value to USA in billions?

  • A. $25.2 billion
  • B. $39.3 billion ✓
  • C. $47.2 billion
  • D. $50.0 billion

Answer: B — Export value to USA = (12.5 ÷ 100) × 314.40 = $39.3 billion, using percentage calculation.

Q7. Which of the following is NOT a correct statement about table elements? (A) Captions are column headings read vertically (B) Stubs are row headings found in the leftmost column (C) Table body contains all calculated totals only (D) Table number identifies individual tables in sequence

  • A. Statement A is incorrect
  • B. Statement B is incorrect
  • C. Statement C is incorrect ✓
  • D. Statement D is incorrect

Answer: C — Statement C is wrong; the table body contains actual data values, not just totals—totals are additional summary rows/columns.

Q8. Both Statement I and Statement II are given. Statement I: Qualitative classification groups data by measurable characteristics like height and age. Statement II: Quantitative classification groups data by attributes like gender and nationality. Which is true?

  • A. Both statements are correct
  • B. Both statements are incorrect ✓
  • C. Only Statement I is correct
  • D. Only Statement II is correct

Answer: B — Both are reversed: qualitative uses attributes (Statement II describes qualitative), quantitative uses measurable traits (Statement I describes quantitative).

Q9. Table 4.2 shows respondent distribution by age groups. If the 60-70 age group has 144 respondents and the missing 'All' total is 542, which age groups' frequencies must be calculated from the percentage column?

  • A. Only 20-30 and 30-40 groups
  • B. Only 60-70 and 70-80 groups
  • C. Groups whose frequency is blank but whose percentage is given ✓
  • D. All groups by applying percentage formula systematically

Answer: C — The 60-70 group's frequency (144) is already given directly in this question, so it does not need to be derived — its percentage is (144 ÷ 542) × 100 = 26.57%. Any age group whose frequency cell is left blank in the table, but whose percentage is shown, must instead be back-calculated as percentage × total ÷ 100.

Q10. [HOTS] A table titled 'Population by State and Gender (2011 Census)' uses 28 rows (one header + 27 states + total) and 4 columns (state name + male + female + total). To calculate the missing total population if you know state-wise male and female breakdowns, which classification types are being integrated?

  • A. Only spatial classification
  • B. Spatial and qualitative classifications combined ✓
  • C. Temporal and quantitative classifications combined
  • D. All four classification types are used

Answer: B — Spatial classification organizes by state (place), qualitative classifies by gender (attribute); together they form a two-way classification combining place and attribute.

Flashcards

What is textual presentation of data?

Data described within written text, suitable when quantity is small and emphasis on certain points is needed.

Define tabular presentation of data.

Data organized systematically in rows (horizontal) and columns (vertical) format for easy comprehension and statistical analysis.

What is qualitative classification?

Classification based on attributes like gender, nationality, or social status that cannot be measured numerically.

What is quantitative classification?

Classification based on measurable characteristics like age, height, income, or production arranged in class intervals.

Define temporal classification with an example.

Classification where time (years, months, days) is the variable; example: yearly sales data from 1995 to 2000.

What is spatial classification?

Classification based on geographical location (village, district, state, country); used for regional or location-based data.

What is the stub column in a table?

The leftmost column containing row headings that describe what each row represents in the table.

Name the five essential parts of a statistical table.

Table number, title, captions (column headings), stubs (row headings), and body of the table with data source.

What does notation 4.3 mean for a table number?

Table 4.3 indicates the third table in the fourth chapter of the textbook or document.

Why is citing the data source important in a table?

It establishes credibility, allows verification of data, and helps readers trace the original information source.

Important Board Questions

Define tabular presentation of data. Give one advantage of tabulation over textual presentation with an example from Table 4.1. [2 marks]

Define as 'data in rows and columns format.' State one advantage (e.g., enables statistical analysis, compact form, easy comparison). Example: Table 4.1 compares literacy by gender and location in single view vs. reading lengthy text.

Classify the following four tables by type: (1) Sales by Year 1995-2000, (2) Exports by Country/Region, (3) Students by Gender and Class, (4) Income by Occupation and Age Group. Explain what distinguishes one classification from another using specific examples. [5 marks]

Table 1 = temporal (time variable); Table 2 = spatial (geographical places); Table 3 = one qualitative (gender) + one quantitative (class); Table 4 = two qualitative (occupation, age group categorized by intervals). Distinguish by identifying the classifying variable(s) in each.

In Table 4.2, the total respondents = 542. Age group 60-70 shows 28.24% in the percentage column but the frequency is missing. Calculate: (a) the frequency for 60-70 age group, (b) the missing frequency for 80-90 if percentage is 0.37%, and (c) verify your answer by checking if all frequencies sum to 542. Show all steps. [6 marks]

Use formula: Frequency = (Percentage ÷ 100) × Total for both (a) and (b). For (a): (28.24 ÷ 100) × 542. For (b): (0.37 ÷ 100) × 542. Verify in (c) by summing: 3 + 61 + 132 + 153 + [your answer for 60-70] + [your answer for 80-90] + 51 + 2 = 542. This tests understanding of percentage-frequency conversion and table verification.

Assertion-Reason Questions for Presentation of Data

Q1. Assertion (A):

Textual presentation of data is the most suitable method when the quantity of data is large and voluminous.

Reason (R):

Textual presentation requires reading through complete narrative text, making comprehension difficult for large datasets.

Answer: D — A is false but R is true — The assertion is false. Textual presentation is suitable for small quantities of data, not large datasets. The reason correctly explains why textual presentation struggles with volume. Large data require tabular or diagrammatic methods.

Q2. Assertion (A):

A table with subscripted number 4.5 indicates the fifth table in the fourth chapter.

Reason (R):

Subscripted table numbers follow the format chapter.table sequence for systematic identification and reference.

Answer: A — Both A and R are true, and R is the correct explanation of A — Both assertion and reason are true. The subscripted notation (4.5) correctly denotes Chapter 4, Table 5, and the reason accurately explains why this system is used for organisation and referencing in textbooks.

Q3. Assertion (A):

Qualitative classification uses attributes such as social status, gender, or nationality to organise data.

Reason (R):

Qualitative characteristics can be measured and expressed numerically in precise units.

Answer: C — A is true but R is false — The assertion is true; qualitative classification uses non-numerical attributes. However, the reason is false—qualitative characteristics cannot be measured numerically by definition. The reason contradicts the nature of qualitative data.

Unlock more Assertion-Reason questions in Premium — unlock →

Case-Based Questions (CBQ) for Presentation of Data

Case Study:

The Census of India 2011 recorded literacy data across urban and rural regions, further broken down by gender. In rural areas, male literacy stood at 79% while female literacy was 59%, with an overall rural literacy rate of 68%. Urban areas showed higher literacy: males at 90%, females at 80%, and overall urban literacy at 84%. This data was compiled to assess educational disparities across gender and location dimensions and to inform policy decisions regarding educational infrastructure development.

Q1. What type of classification is used in the Census literacy data when separating rural and urban populations?

  • A. Temporal classification
  • B. Spatial classification ✓
  • C. Qualitative classification
  • D. Quantitative classification

Answer: B

Q2. Based on the passage, what is the gender-based literacy gap in rural areas?

  • A. 20 percentage points (male − female) ✓
  • B. 10 percentage points (female − male)
  • C. 9 percentage points (male − female)
  • D. 11 percentage points (male − female)

Answer: A

Q3. Which location-gender combination has the lowest literacy rate, and which has the highest?

  • A. Lowest: rural female (59%); Highest: urban male (90%) ✓
  • B. Lowest: rural male (79%); Highest: urban female (80%)
  • C. Lowest: urban female (80%); Highest: rural male (79%)
  • D. Lowest: rural female (59%); Highest: urban female (80%)

Answer: A

Q4. To present this three-dimensional literacy data (gender, location, and literacy percentage) in a single table systematically, what type of table structure would be most appropriate?

  • A. A one-way table with only location classification
  • B. A two-way table with gender rows and location columns ✓
  • C. A textual presentation within narrative paragraphs
  • D. Three separate one-way tables for each dimension

Answer: B

Unlock more case studies in Premium — unlock →

Class 11 Economics Formula Sheet

Every formula from the Statistics and Microeconomics chapters on one page, checked against the NCERT textbook and the CBSE 2026-27 syllabus. Free PDF download.

View the formula sheet →

Next chapterMeasures of Central Tendency →
Found this useful? Share it with your class group.

You've seen the free preview. Open the full interactive study kit — mind map, instant-graded quiz, progress tracking — free, no sign-in required.

Open Full Study Kit — Free →

Premium unlocks the full Question Bank, Daily Practice Papers, Chapter Quiz and Full Mock Papers for every chapter.