Collection, Organisation and Presentation of Data: ISC Class 11

What Collection, Organisation and Presentation of Data is about

Weightage: Collection, Organisation and Presentation of Data is part of the unit Statistics of the ISC Class XI Economics syllabus. CISCE gives no Class XI unit weightage for Economics: Paper I (Theory) carries 80 marks, and the school sets the paper.Source: CISCE ISC Economics syllabus, examination year 2028, Class XI paper pattern

Key concepts

Primary and secondary data; sources of secondary data

Primary data are collected for the first time by the investigator for a specific purpose: original, first-hand. Example: a survey of household spending in your town.

Secondary data have already been collected by someone else and are used by the investigator: second-hand. Example: population figures from the Census.

Basis	Primary data	Secondary data
Originality	Original	Already collected by others
Purpose	Suited to the investigator's purpose	May not exactly suit it
Cost and time	High	Low
Accuracy	Under the investigator's control	Depends on the original collector

Important sources of secondary data in India:

1. Census of India: population, literacy, occupations; conducted every ten years by the Office of the Registrar General and Census Commissioner.
2. National Statistics Office (NSO) (Ministry of Statistics and Programme Implementation): National Sample Surveys on consumption, employment (Periodic Labour Force Survey), and the national accounts (GDP).
3. Reserve Bank of India: RBI Bulletin, Handbook of Statistics on the Indian Economy (money, banking, prices).
4. Ministry of Finance: Economic Survey (annual), Union Budget.
5. Office of the Economic Adviser: Wholesale Price Index.
6. Labour Bureau: Consumer Price Index for industrial workers, wages.
7. Directorate General of Commercial Intelligence and Statistics: foreign trade data.
8. International sources: World Bank, IMF, UNDP reports.

Precautions in using secondary data: check the reliability of the source, suitability for the purpose (definitions, units, coverage) and adequacy.

Worked example

Classify as primary or secondary data: (i) a student surveys 50 shops to find tea prices; (ii) a researcher uses literacy rates from the Census. [1 mark]

Try it first, then show the solutionSolution

1. (i) Collected first-hand by the student: primary.
2. (ii) Already collected by the Census office: secondary.

Answer: (i) Primary; (ii) secondary.

Methods of collecting primary data; census and sample

Methods:

1. Direct personal investigation: the investigator meets respondents personally. Accurate and flexible, but costly and suited to small areas.
2. Indirect oral investigation: information obtained from third parties (witnesses) who know the facts; used when respondents are unwilling or cannot be reached (for example, an inquiry into an accident).
3. Information through local correspondents: agents in different areas send information regularly (used by newspapers).
4. Mailed questionnaire: questionnaires posted or e-mailed to respondents. Cheap for wide areas, but needs literate respondents and often has a low response rate.
5. Schedules filled by enumerators: trained enumerators ask questions and fill in a schedule; used in the Census. Accurate but costly.
6. Telephone interviews: quick and cheap; limited to people with phones.

A good questionnaire: short; simple, clear language; no leading or personal questions; logical order; questions that can be answered with yes/no or options where possible; with instructions.

Census vs sample:

• Census (complete enumeration): every item of the population is studied. Accurate and detailed, but costly and slow.
• Sample method: a representative part is studied and results generalised. Cheaper and faster; reliable if the sample is representative.
• Random sampling: every item has an equal chance of selection (lottery or random numbers). Non-random sampling: chosen by judgement or convenience (purposive, quota, convenience).
• Sampling errors arise from studying only a part; non-sampling errors (measurement, non-response, recording) occur in both census and sample.

Worked example

Suppose you want to know the average daily screen time of the 1,800 students of your school. Suggest a method and explain your choice. [2 marks]

Try it first, then show the solutionSolution

1. A census of 1,800 students is costly; a random sample (say 180 students chosen by lottery from the school register) saves time.
2. A short questionnaire filled in class (direct personal method) ensures a high response.

Answer: A random sample of about 10% (180 students) with a short questionnaire administered in person: cheaper and quick, yet representative.

Organisation of data: variables and frequency distributions

Variable: a characteristic that can take different values (height, income, marks). An attribute is a qualitative characteristic (gender, religion) that is counted, not measured.

Types of variables:

• Discrete variable: takes only certain separate values, usually whole numbers (number of children, number of rooms).
• Continuous variable: can take any value within a range, including fractions (height, weight, temperature, income).

Frequency: the number of times a value or class occurs.

Frequency distribution: a table showing values or classes of a variable with their frequencies.

1. Individual series: each item listed separately.
2. Discrete series: values of a discrete variable with their frequencies.
3. Continuous series: classes (class intervals) with frequencies.

Terms: class limits (lower and upper); class interval (width) = upper limit − lower limit; class mark (mid-point) = (lower + upper) ÷ 2; tally marks (strokes in groups of five) to count; cumulative frequency (running total), 'less than' and 'more than'.

Exclusive classes (0-10, 10-20): the upper limit is excluded from the class (10 goes in 10-20). Inclusive classes (0-9, 10-19): both limits included. To convert inclusive to exclusive, subtract half the gap between classes from each lower limit and add it to each upper limit (0-9, 10-19 → −0.5-9.5, 9.5-19.5).

Worked example

Convert the inclusive classes 20-29, 30-39, 40-49 into exclusive classes and find their class marks. [2 marks]

Try it first, then show the solutionSolution

1. Gap = 30 − 29 = 1; half = 0.5. Classes: 19.5-29.5, 29.5-39.5, 39.5-49.5.
2. Class marks: (19.5 + 29.5) ÷ 2 = 24.5; 34.5; 44.5.

Answer: 19.5-29.5, 29.5-39.5, 39.5-49.5 with class marks 24.5, 34.5, 44.5.

Tabular presentation

A table is a systematic arrangement of data in rows and columns.

Parts of a table:

1. Table number (for reference).
2. Title: what, where, when (for example, 'Enrolment by gender in schools of District X, 2025').
3. Head-note: units (for example, 'in thousands').
4. Captions: column headings.
5. Stubs: row headings.
6. Body: the figures.
7. Footnote: explanations of any item.
8. Source note: where the data came from.

Types: simple (one-way) tables show one characteristic; two-way tables show two (for example, students by class and gender); manifold tables show more.

Advantages: makes data compact and easy to compare; reveals patterns; is the basis for diagrams and analysis.

Worked example

Suppose a school has 240 students in Class XI (130 boys) and 210 in Class XII (100 girls). Prepare the totals of a two-way table by class and gender. [2 marks]

Try it first, then show the solutionSolution

1. Class XI: boys 130, girls 240 − 130 = 110. Class XII: girls 100, boys 210 − 100 = 110.
2. Totals: boys 240, girls 210, grand total 450.

Answer: XI: 130 boys, 110 girls (240); XII: 110 boys, 100 girls (210); totals 240 boys, 210 girls, 450 students.

Diagrams: bar, pie and line

Bar diagrams use bars of equal width, with length proportional to value.

• Simple bar: one variable (output of rice by year).
• Multiple bar: two or more variables side by side (exports and imports each year).
• Sub-divided (component) bar: a bar split into parts (GDP by sector).
• Percentage bar: each bar is 100%, split into percentage shares.

Pie diagram: a circle divided into sectors, each showing a component's share of the total.

Angle of a sector = Component value ÷ Total × 360° (or percentage × 3.6°).

Line graph (time series graph): values plotted against time and joined by straight lines; shows trends. If values are far from zero, use a false base line (a broken axis) to show it clearly.

General rules: a title, a suitable scale, labelled axes, an index (key) for colours or shading, and a source note.

Worked example

Suppose a family's monthly spending is: food ₹12,000, rent ₹9,000, education ₹6,000, others ₹9,000. Find the pie-chart angles. [2 marks]

Try it first, then show the solutionSolution

1. Total = ₹36,000. Food: 12,000 ÷ 36,000 × 360 = 120°; rent: 90°.
2. Education: 6,000 ÷ 36,000 × 360 = 60°; others: 90°. Check: 120 + 90 + 60 + 90 = 360°.

Answer: Food 120°, rent 90°, education 60°, others 90°.

Frequency diagrams: histogram, polygon and ogive

Histogram: adjacent rectangles for a continuous series. Class intervals on the x-axis, frequencies on the y-axis; no gaps between bars.

• If class intervals are unequal, adjust frequencies: adjusted frequency = frequency ÷ class width × standard (smallest) width (or plot frequency density).
• If classes are inclusive, convert them to exclusive first.
• A histogram can be used to locate the mode graphically.

Frequency polygon: join the mid-points of the tops of the histogram bars with straight lines; extend to the mid-points of the imaginary classes at each end (on the x-axis) so that the area matches the histogram. It can also be drawn directly by plotting class marks against frequencies.

Frequency curve: the polygon smoothed freehand.

Ogive (cumulative frequency curve):

• 'Less than' ogive: plot cumulative frequencies against upper limits; rises from left to right.
• 'More than' ogive: plot cumulative frequencies (from the top) against lower limits; falls from left to right.
• The two ogives intersect at the median. Ogives also give quartiles.

Worked example

Suppose classes 0-10, 10-20, 20-40, 40-80 have frequencies 5, 8, 12, 16. Find the adjusted frequencies for a histogram (taking 10 as the standard width). [2 marks]

Try it first, then show the solutionSolution

1. Widths: 10, 10, 20, 40.
2. Adjusted: 5, 8, 12 ÷ 20 × 10 = 6, 16 ÷ 40 × 10 = 4.

Answer: 5, 8, 6 and 4: bar heights for the histogram.

Collection, Organisation and Presentation of Data in real life

Each concept, met in an everyday situation. Read the situation, answer the question in your own words, then compare with the model answer. The one-line hook is what to remember.

Topics in this chapter

• Frequency Distributions, Class Intervals, Cumulative Frequency and Diagrams
• Collecting Data: Primary and Secondary Data, Methods, Census and Sample

Collection, Organisation and Presentation of Data: key facts

Class mark

Class mark = (Lower limit + Upper limit) ÷ 2

Class interval

Class width = Upper limit − Lower limit

Pie-chart angle

Angle = Component value ÷ Total × 360°

Or percentage share × 3.6°.

Adjusted frequency (unequal classes)

Adjusted frequency = Frequency ÷ Class width × Standard width

Used for histograms with unequal class intervals.

Inclusive to exclusive

Correction = (Lower limit of next class − Upper limit of this class) ÷ 2

Subtract from lower limits; add to upper limits.

Collection, Organisation and Presentation of Data: diagrams to practise

Practise each one on paper: draw it from the checklist, then tick off every label.

How the school exam asks Collection, Organisation and Presentation of Data

The question patterns to expect, and the method that works for each.

Tricks to remember Collection, Organisation and Presentation of Data

Short memory aids. Say each one aloud once, then use it on a question the same day.

• Primary = Personal, Secondary = Shelf

  Primary you collect; secondary you take off the shelf (Census, NSO, RBI).

  Use it when: Types of data.

• Less than → upper; More than → lower

  'Less' and 'Upper' both point to the end of the class.

  Use it when: Drawing ogives.

• Pie: 3.6 per cent

  Each 1% of the total is 3.6°.

  Use it when: Pie-chart angles.

• Unequal widths? Divide first

  Frequency ÷ width × standard width before drawing a histogram.

  Use it when: Adjusting frequencies.

Collection, Organisation and Presentation of Data: exam-level solved questions

Ordered from exam level to HOTS. Cover the solution, write your own, then compare step by step.

Case-study practice (Section C style)

Read the situation, then answer every part. In a school exam set on the board pattern this is a 4-mark question split into 1 + 1 + 2 marks.

Where the marks are

How a typical answer is split into step marks. Show every step: a right final answer alone rarely earns full marks.

Where students lose marks in Collection, Organisation and Presentation of Data

The slips examiners see most often, and what to write instead.

• ✗Mistake: Leaving gaps between histogram bars

  A histogram represents a continuous variable; bars must touch. Gaps make it a bar diagram.

  ✓Do this: Adjacent rectangles; gaps only in bar diagrams.

  Usually costs: 1 mark.

• ✗Mistake: Not adjusting unequal class intervals

  Area must be proportional to frequency; wide classes appear too large otherwise.

  ✓Do this: Adjusted frequency = f ÷ width × standard width.

  Usually costs: 1-2 marks.

• ✗Mistake: Plotting a less-than ogive against lower limits

  'Less than 20' means up to the upper limit 20.

  ✓Do this: Less than → upper limits; more than → lower limits.

  Usually costs: 1-2 marks.

• ✗Mistake: Pie angles that do not total 360°

  Rounding or arithmetic slips distort the circle.

  ✓Do this: Show a working table and check the total.

  Usually costs: 1 mark.

• ✗Mistake: Diagram without title, scale or key

  Presentation marks depend on these.

  ✓Do this: Title, scale, axis labels, key, source: every time.

  Usually costs: 1 mark.

Practice questions on Collection, Organisation and Presentation of Data

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

1. Q1 · 1 mark · MCQExam level

   Which of the following is a continuous variable?
   (a) number of rooms in a house
   (b) number of students in a class
   (c) weight of a student
   (d) number of cars in a parking lot

   Hint

   Can it take fractional values?

   Answer

   (c) weight of a student.

2. Q2 · 1 mark · Very short answerExam level

   Name two important sources of secondary data in India.

   Hint

   Population; surveys.

   Answer

   Census of India; National Statistics Office (National Sample Surveys); also RBI publications and the Economic Survey.

3. Q3 · 2 marks · Short answerExam level

   State four qualities of a good questionnaire.

   Hint

   Short, simple, neutral, ordered.

   Answer

   Few questions; simple, clear language; no leading or offensive personal questions; logical order with options where possible (also clear instructions).

4. Q4 · 2 marks · Short answerHarder exam level

   Suppose a company's sales (₹ crore) by region are: North 45, South 60, East 30, West 45. Find the angles for a pie chart.

   Hint

   Total 180.

   Answer

   Total 180: North 90°, South 120°, East 60°, West 90°.

5. Q5 · 2 marks · Short answerHarder exam level

   Suppose classes 5-14, 15-24, 25-34, 35-44 have frequencies 4, 9, 11, 6. Convert to exclusive classes, find the class marks and the 'more than' cumulative frequencies.

   Hint

   Correction 0.5.

   Answer

   4.5-14.5, 14.5-24.5, 24.5-34.5, 34.5-44.5; class marks 9.5, 19.5, 29.5, 39.5; more than 4.5: 30, more than 14.5: 26, more than 24.5: 17, more than 34.5: 6.

6. Q6 · 4 marks · Short answerHarder exam level

   Explain the merits and demerits of the mailed questionnaire method.

   Hint

   Cost vs response.

   Answer

   Merits: cheap for a large, widely spread population; respondents answer at leisure and without the investigator's influence. Demerits: only literate respondents can reply; response rates are often low; answers cannot be clarified, so incomplete or wrong answers occur; the sample of those who reply may be biased.

7. Q7 · 4 marks · Short answerHOTS / competency

   Suppose the age distribution of 50 workers is: 20-25: 5, 25-30: 12, 30-40: 18, 40-60: 15. Find the adjusted frequencies for a histogram (standard width 5) and explain which class has the greatest concentration of workers.

   Hint

   Widths 5, 5, 10, 20.

   Answer

   Adjusted: 5, 12, 18 ÷ 2 = 9, 15 ÷ 4 = 3.75. The 25-30 class has the greatest concentration (12 per 5 years), although 30-40 has more workers in total.

8. Q8 · 2 marks · Short answerHarder exam level

   Distinguish between a bar diagram and a histogram.

   Hint

   Gaps, area, data type.

   Answer

   A bar diagram shows discrete or categorical data with bars of equal width separated by gaps; length shows value. A histogram shows a continuous frequency distribution with adjacent bars; area shows frequency, and widths equal class intervals.

9. Q9 · 2 marks · Short answerHOTS / competency

   Suppose a researcher uses state-wise literacy data from a report that defines literacy for ages 7 and above, and compares it with another report using ages 15 and above. What precaution has she ignored, and what should she do?

   Hint

   Suitability and comparability.

   Answer

   She has ignored the suitability and comparability of secondary data: the definitions differ, so the figures are not comparable. She should use data with the same definition or adjust them, and state the definition used.

10. Q10 · 6 marks · Long answerHOTS / competency

    Suppose the 'less than' cumulative frequencies of the weights (kg) of 80 students are: less than 40: 8, 45: 22, 50: 46, 55: 66, 60: 80. Derive the class frequencies, the more-than cumulative frequencies, and estimate the median by interpolation.

    Hint

    Differences of cumulative frequencies.

    Answer

    Classes and frequencies: below 40 (35-40 if the lowest class starts at 35): 8; 40-45: 14; 45-50: 24; 50-55: 20; 55-60: 14. More than: 35: 80, 40: 72, 45: 58, 50: 34, 55: 14. N ÷ 2 = 40 lies in 45-50 (cf before 22, f 24): median = 45 + (40 − 22) ÷ 24 × 5 = 48.75 kg; the ogives would intersect here.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1. 1.Primary data means?Show answer

   Data collected first-hand for a specific purpose.

2. 2.Class mark formula?Show answer

   (Lower + upper limit) ÷ 2.

3. 3.Pie-chart angle formula?Show answer

   Value ÷ total × 360°.

4. 4.Less-than ogive is plotted against?Show answer

   Upper limits.

5. 5.Where do the two ogives meet?Show answer

   At the median.

6. 6.Adjusted frequency formula?Show answer

   f ÷ class width × standard width.

Quick revision checklist

The night before the exam: can you do each of these without looking?

• ☐Primary: first-hand, costly, suited; secondary: published, cheap, check suitability.
• ☐Sources: Census, NSO, RBI, Economic Survey, Labour Bureau.
• ☐Methods: direct, indirect oral, correspondents, mailed questionnaire, enumerators, telephone.
• ☐Discrete vs continuous; exclusive vs inclusive classes; class mark = mid-point.
• ☐Pie angle = share × 360°; bars have gaps, histograms do not.
• ☐Ogives: less than (upper limits), more than (lower limits), meet at the median.

Collection, Organisation and Presentation of Data: frequently asked questions