Organisation of Data Class 11: Classification, Variables and Frequency Distribution

What Organisation of Data is about

Weightage: This chapter is part of Unit 2, Collection, Organisation and Presentation of Data. The syllabus groups Unit 2 with Unit 1, Introduction: together they carry 15 of the 80 theory marks in the school annual exam.Source: CBSE Economics (030) syllabus 2026-27, Class XI course structure, Unit 2 Collection, Organisation and Presentation of Data

Key concepts

Raw data and the need for classification

NCERT section 2 and 3

Raw data are data in the form in which they were collected, not yet arranged in any order. They are hard to read and use. For example, the marks of 40 students:

23, 37, 12, 45, 31, 28, 19, 41, 33, 26, 8, 35, 29, 22, 47, 38, 16, 30, 27, 34, 24, 39, 31, 18, 42, 25, 36, 11, 29, 33, 21, 44, 32, 27, 14, 38, 26, 30, 35, 49

Classification is the process of arranging data into groups or classes according to their common characteristics. Objectives: to make data simple and brief; to bring out similarities and differences; to make comparison easy; to prepare data for tabulation and further analysis.

From the list above, even the highest (49) and lowest (8) marks take time to find; a classified table shows at once how many students scored in each range.

Worked example

Find the range of the 40 marks above and say why raw data are inconvenient.

Try it first, then show the solutionSolution

1. Highest = 49, lowest = 8
2. Range = 49 − 8 = 41
3. Even this needs scanning every figure; patterns are not visible

Answer: Range 41; raw data hide patterns and make comparison slow.

Types of classification

NCERT section 3

1. Chronological (temporal) classification: by time (years, quarters, months), in ascending or descending order. A variable shown over time is a time series. Example: India's population in 1951, 1961, ... 2011.
2. Spatial (geographical) classification: by place (countries, states, cities). Example: wheat yield in different countries.
3. Qualitative classification: by an attribute that cannot be measured (gender, literacy, religion, marital status), based on its presence or absence. It can be simple (male/female) or manifold (male-married, male-unmarried, female-married, female-unmarried).
4. Quantitative classification: by a measurable characteristic (income, marks, height, age) grouped into classes. This gives a frequency distribution.

Worked example

Name the type of classification: (a) rainfall in Mumbai for each month of 2025; (b) literacy rate of five states; (c) workers grouped as skilled and unskilled; (d) families grouped by monthly income ₹0-10,000, ₹10,000-20,000 and so on.

Try it first, then show the solutionSolution

1. (a) By time: chronological
2. (b) By place: spatial
3. (c) By attribute: qualitative
4. (d) By size of a measurable variable: quantitative

Answer: (a) Chronological; (b) spatial; (c) qualitative; (d) quantitative.

Variables: continuous and discrete

NCERT section 4

A variable is a characteristic that takes different values (income, height, number of children).

• Continuous variable: can take any value within a range, including fractions: height (152.37 cm), weight, time, temperature, income, rainfall, age. Between any two values there is always another possible value.
• Discrete variable: can take only certain separate values; it jumps from one value to the next: number of students, number of cars, the number on a dice, population of a town. A discrete variable can take fractional values too (1/8, 1/16, 1/32...), as long as it cannot take values between two adjacent ones.

Continuous variables are usually grouped in exclusive classes; discrete variables are often shown value by value or in inclusive classes.

Worked example

Classify as continuous or discrete: area, number of cars on a road, temperature, crop yield, number appearing on a dice, age, population.

Try it first, then show the solutionSolution

1. Can take any value in a range: area, temperature, crop yield, age
2. Only separate values: number of cars, number on a dice, population

Answer: Continuous: area, temperature, crop yield, age. Discrete: number of cars, dice number, population.

Frequency distribution and its parts

NCERT section 5

A frequency distribution classifies raw data of a quantitative variable: it shows the classes and the number of observations (frequency) in each.

Terms:

• Class: a group, e.g. 20-30.
• Class limits: the lowest (lower limit) and highest (upper limit) values of a class: 20 and 30.
• Class interval (width): upper limit − lower limit: 30 − 20 = 10.
• Class frequency: number of observations in the class.
• Class mark (mid-point): (lower limit + upper limit) ÷ 2: (20 + 30) ÷ 2 = 25. It represents the class in later calculations.
• Relative frequency: class frequency ÷ total frequency (often as a percentage).

Frequency distribution of the 40 students' marks (each IIII/ is a bundle of five tally marks):

Marks (class)	Tally	Frequency	Class mark	Relative frequency
0-10	I	1	5	2.5%
10-20	IIII/ I	6	15	15%
20-30	IIII/ IIII/ II	12	25	30%
30-40	IIII/ IIII/ IIII/	15	35	37.5%
40-50	IIII/ I	6	45	15%
Total		40		100%

Worked example

For the class 30-40 in the table, give the lower limit, upper limit, class interval, class mark, frequency and relative frequency.

Try it first, then show the solutionSolution

1. Lower limit 30; upper limit 40
2. Class interval = 40 − 30 = 10; class mark = (30 + 40) ÷ 2 = 35
3. Frequency = 15; relative frequency = 15 ÷ 40 = 37.5%

Answer: 30, 40, 10, 35, 15, 37.5%.

Forming classes: number, width, equal or unequal, exclusive or inclusive

NCERT section 5

How many classes? Usually 6 to 15; too few hide detail, too many defeat the purpose of summarising.

Width of each class: Class interval = Range ÷ Number of classes, rounded to a convenient figure.

Equal or unequal classes? Equal classes are easy to compare and draw. Unequal classes are used when data are very unevenly spread (for example, incomes where most people are in low classes and a few are very high).

Exclusive method: the upper limit of one class is the lower limit of the next, and a value equal to the upper limit is excluded from that class (it goes to the next): 0-10, 10-20, 20-30; a mark of 20 goes in 20-30. Used for continuous variables.

Inclusive method: both limits are included in the class: 0-9, 10-19, 20-29. Used mainly for discrete variables.

Adjustment (inclusive to exclusive): find the gap between the upper limit of one class and the lower limit of the next, halve it, deduct it from every lower limit and add it to every upper limit.

Inclusive class (daily wage, ₹)	Adjusted (exclusive) class	Workers	Class mark
100-199	99.5-199.5	6	149.5
200-299	199.5-299.5	14	249.5
300-399	299.5-399.5	22	349.5
400-499	399.5-499.5	10	449.5
500-599	499.5-599.5	8	549.5

Worked example

Mid-points of a distribution are 15, 25, 35, 45 and 55. Find the classes.

Try it first, then show the solutionSolution

1. Difference between mid-points = 10, so half = 5
2. Lower limit = mid − 5; upper limit = mid + 5

Answer: 10-20, 20-30, 30-40, 40-50, 50-60.

Tally marks, cumulative frequency and loss of information

NCERT section 5

Tally marking is the quick way to count class frequencies from raw data: go through the list once and put a stroke against the class of each value; every fifth stroke is drawn across the previous four, so tallies are counted in bundles of five.

Cumulative frequency adds frequencies class by class. A less than cumulative frequency shows how many values are below each upper limit; a more than cumulative frequency shows how many are at or above each lower limit. They are used to draw ogives (Presentation of Data) and to find the median.

Marks	Cumulative frequency (less than)	Marks	Cumulative frequency (more than)
Less than 10	1	0 and above	40
Less than 20	7	10 and above	39
Less than 30	19	20 and above	33
Less than 40	34	30 and above	21
Less than 50	40	40 and above	6

Loss of information: once data are grouped, individual values are no longer used; every value in a class is treated as if it were the class mark. For example, the six marks in 10-20 (19, 16, 18, 11, 14, 12) are all treated as 15. Classification gains clarity but loses detail.

Worked example

From the cumulative frequency table, how many students scored less than 30, and how many scored 30 or more?

Try it first, then show the solutionSolution

1. Less than 30: 19
2. 30 and above: 21
3. Check: 19 + 21 = 40

Answer: 19 below 30; 21 at 30 or above.

Organisation 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

• Classification of Data and Types of Variables
• Frequency Distribution and Class Formation

Organisation of Data: key facts

Range

Range = Largest value − Smallest value

Used to decide class width.

Class interval

Class interval = Upper limit − Lower limit

Also Range ÷ Number of classes, rounded.

Class mark

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

With adjusted limits for inclusive classes.

Adjustment factor

Adjustment = (Lower limit of next class − Upper limit of a class) ÷ 2

Deduct from lower limits; add to upper limits.

Relative frequency

Relative frequency = Class frequency ÷ Total frequency

As a percentage: × 100.

Classes from mid-points

Limits = Mid-point ± (difference between mid-points ÷ 2)

For equal classes.

How the school exam asks Organisation of Data

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

Tricks to remember Organisation of Data

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

• Four types: "Time, Place, Quality, Quantity"

  Chronological, Spatial, Qualitative, Quantitative: "Clocks, Spaces, Qualities, Quantities".

  Use it when: Types of classification.

• Exclusive vs inclusive

  EXclusive EXcludes the upper limit; INclusive INcludes both.

  Use it when: Placing boundary values.

• Count or measure

  If you count it, it is discrete; if you measure it, it is continuous.

  Use it when: Classifying variables.

Organisation 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 E 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 Organisation of Data

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

• ✗Mistake: Putting the upper limit value in the lower class under the exclusive method

  It looks like it "belongs" to that class.

  Wrong working

  Mark 30 counted in 20-30

  Right working

  Mark 30 counted in 30-40

  ✓Do this: Exclusive: upper limit excluded; the value goes to the next class.

  Usually costs: 1 mark and wrong totals.

• ✗Mistake: Finding class marks from unadjusted inclusive limits after converting

  Using the original limits.

  ✓Do this: Class marks are the same either way for equal gaps, but always state them from the adjusted limits when the question asks for exclusive classes.

  Usually costs: ½ mark.

• ✗Mistake: Frequencies not adding to the total

  A value skipped or counted twice while tallying.

  ✓Do this: Tally in one pass and add the frequencies at the end to check against the number of observations.

  Usually costs: 1-2 marks.

• ✗Mistake: Calling all whole-number variables discrete

  Data are often rounded.

  ✓Do this: Age and income are continuous even if recorded in whole numbers; decide by whether intermediate values are possible.

  Usually costs: 1 mark.

NCERT exercise guide: Organisation of Data

What each exercise in the NCERT chapter tests, how to approach it, and a question of the same kind solved step by step. Questions here are written in our own words.

Practice questions on Organisation 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

   Classification of data by years is:
   (a) spatial
   (b) chronological
   (c) qualitative
   (d) quantitative

   Hint

   Time.

   Answer

   (b) chronological

2. Q2 · 1 mark · MCQExam level

   In the exclusive method, the value 40 in classes 30-40 and 40-50 is placed in:
   (a) 30-40
   (b) 40-50
   (c) both
   (d) neither

   Hint

   Upper limit excluded.

   Answer

   (b) 40-50

3. Q3 · 1 mark · Very short answerExam level

   Define class mark.

   Hint

   Mid-point.

   Answer

   The mid-point of a class: (lower limit + upper limit) ÷ 2.

4. Q4 · 4 marks · Long answerExam level

   Explain the four types of classification with an example each.

   Hint

   Time, place, attribute, size.

   Answer

   Chronological: exports by year. Spatial: rainfall by state. Qualitative: workers by skill (skilled/unskilled). Quantitative: families by income classes.

5. Q5 · 3 marks · Short answerHarder exam level

   Convert into exclusive classes and find class marks: 10-19, 20-29, 30-39, 40-49.

   Hint

   Gap 1, half 0.5.

   Answer

   9.5-19.5, 19.5-29.5, 29.5-39.5, 39.5-49.5; class marks 14.5, 24.5, 34.5, 44.5.

6. Q6 · 3 marks · Short answerHarder exam level

   The class marks of a distribution are 7, 12, 17, 22 and 27. Find the class limits.

   Hint

   Half of 5.

   Answer

   4.5-9.5, 9.5-14.5, 14.5-19.5, 19.5-24.5, 24.5-29.5.

7. Q7 · 3 marks · Short answerHarder exam level

   Prepare a frequency distribution of the number of children in 20 families: 2, 1, 3, 0, 2, 2, 4, 1, 3, 2, 1, 0, 2, 3, 2, 1, 5, 2, 1, 3.

   Hint

   Discrete: list each value.

   Answer

   0: 2; 1: 5; 2: 7; 3: 4; 4: 1; 5: 1; total 20.

8. Q8 · 3 marks · Short answerHarder exam level

   Distinguish between continuous and discrete variables with two examples each.

   Hint

   Any value vs jumps.

   Answer

   Continuous: any value in a range, e.g. height, income. Discrete: only separate values, jumps from one to the next, e.g. number of children, number of cars.

9. Q9 · 3 marks · Short answerHarder exam level

   What is meant by loss of information in a frequency distribution? Why do we still classify data?

   Hint

   Class mark replaces values.

   Answer

   After grouping, individual values are not used; each is assumed equal to the class mark, so detail is lost. We still classify because the summary shows the pattern clearly and makes analysis and comparison easy.

10. Q10 · 3 marks · Short answerHarder exam level

    From the cumulative frequencies "less than 10: 4; less than 20: 15; less than 30: 33; less than 40: 45; less than 50: 50", find the class frequencies.

    Hint

    Subtract successive values.

    Answer

    0-10: 4; 10-20: 11; 20-30: 18; 30-40: 12; 40-50: 5.

11. Q11 · 4 marks · Long answerHarder exam level

    State the objectives of classification and give two qualities of a good classification.

    Hint

    Simplicity, comparison.

    Answer

    Objectives: condense data, bring out similarities, aid comparison, prepare for tabulation and analysis. Qualities: classes should not overlap and should cover all data (exhaustive and mutually exclusive); classes should be suited to the purpose and stable.

12. Q12 · 4 marks · Long answerHOTS / competency

    Suppose a researcher groups ages of 200 workers into classes 18-30, 30-45, 45-60 and 60 and above. Point out two problems with these classes and suggest corrections.

    Hint

    Overlap and open end.

    Answer

    Problems: (1) unclear treatment of 30 and 45 (overlap) unless the exclusive rule is stated; (2) unequal and open-ended classes make comparison hard. Correction: 18-30, 30-42, 42-54, 54-66 with the exclusive rule stated, or state "18 to under 30" etc.

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.What are raw data?Show answer

   Data in the form collected, not arranged in any order.

2. 2.What is a time series?Show answer

   Values of a variable arranged by time.

3. 3.Formula for class mark?Show answer

   (Lower limit + Upper limit) ÷ 2.

4. 4.Which method suits continuous variables?Show answer

   The exclusive method.

5. 5.What is relative frequency?Show answer

   Class frequency divided by total frequency.

6. 6.How are tallies grouped?Show answer

   In bundles of five, the fifth stroke across four.

7. 7.Is the number of students in a class continuous or discrete?Show answer

   Discrete.

Quick revision checklist

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

• ☐Can you name four types of classification with examples?
• ☐Can you classify ten variables as continuous or discrete?
• ☐Can you define class limits, class interval, class mark and frequency?
• ☐Can you build a frequency distribution with tally marks?
• ☐Can you convert inclusive classes to exclusive?
• ☐Can you find classes from mid-points?
• ☐Can you prepare less than and more than cumulative frequencies?
• ☐Can you explain loss of information?

Organisation of Data: frequently asked questions