NCERT Solutions for Class 11 Economics Chapter 3: Organisation of Data (NCERT 2026–27)

These Class 11 Economics Chapter 3 solutions cover Organisation of Data from Statistics for Economics, updated for the 2026–27 session. The chapter explains how raw, unorganised data are brought into order through classification and a frequency distribution. You will learn quantitative vs qualitative classification, continuous vs discrete variables, how to form classes (range, class interval, class limits, class mark), the difference between inclusive and exclusive methods, tally marking, the frequency array, and bivariate frequency distribution. Below you get every NCERT Exercises question reproduced verbatim and solved step by step — with all frequency-distribution tables computed and verified — plus extra practice, MCQs, Assertion–Reason and FAQs.

Class: 11 Subject: Economics Book: Statistics for Economics Chapter: 3 – Organisation of Data Topic: Classification & Frequency Distribution Session: 2026–27
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Class 11 Economics Chapter 3 – Overview

Chapter 3, Organisation of Data, follows the collection of data and explains the next step — arranging it for analysis. Just as a kabadiwallah sorts his junk into groups, classification arranges data into groups or classes based on some criterion. Data may be classified chronologically (by time), spatially (by location), qualitatively (by attributes such as gender or literacy) or quantitatively (by measurable variables such as marks, height or income). The heart of the chapter is the frequency distribution, which shows how the values of a quantitative variable are spread across classes along with their class frequencies. The chapter teaches how to form classes (deciding the range, number of classes, class interval, class limits and class mark), how to count frequencies using tally marks, the difference between the exclusive and inclusive methods (and the adjustment that restores continuity), the frequency array for discrete variables, and finally the bivariate frequency distribution of two variables. It also notes the inherent loss of information when raw data are grouped.

Key Concepts & Terms

Raw data: unclassified data exactly as collected — disorganised, large and cumbersome, not yielding to statistical methods until arranged.

Classification: arranging or organising data into groups or classes on the basis of some criterion, so that comparisons and inferences can be drawn easily.

Types of classification: Chronological (by time, e.g. years), Spatial (by geographical location), Qualitative (by attributes like gender, literacy that cannot be measured) and Quantitative (by measurable variables like height, weight, income, marks).

Variable: a characteristic that can take different values. A continuous variable can take any value within a range (height, weight, time); a discrete variable takes only certain values, changing by finite “jumps” (number of students, number of cell phones).

Frequency distribution: a comprehensive way to classify the raw data of a quantitative variable, showing how its values are distributed in different classes along with their class frequencies.

Class frequency: the number of observations (values) falling in a particular class.

Class limits: the two ends of a class — the lowest is the lower class limit, the highest the upper class limit.

Class interval (class width): the difference between the upper and lower class limits of a class.

Class mark (mid-point): the middle value of a class, used to represent it once data are grouped.

Exclusive vs inclusive method: in the exclusive method one limit (usually the upper) is excluded from the class (e.g. 0–10, 10–20); in the inclusive method both limits are included (e.g. 0–10, 11–20). The inclusive method needs an adjustment of ±0.5 to restore continuity for a continuous variable.

Tally marks: the technique of counting frequencies, placing four tallies as //// and the fifth across them, then counting in groups of five.

Frequency array: the classification of a discrete variable, where each integral value has its own frequency.

Bivariate frequency distribution: the frequency distribution of two variables together (e.g. sales and advertisement expenditure of firms).

Loss of information: once data are grouped, individual observations lose significance — all values in a class are treated as equal to the class mark, so some detail is lost.

Important Formulas

Range = Largest observation − Smallest observation

Class Mark (Mid-point) = (Upper Class Limit + Lower Class Limit) ÷ 2

Class Interval (Width) = Upper Class Limit − Lower Class Limit

Number of Classes = Range ÷ Size of class interval (for equal class intervals)

Adjusted Class Limit (inclusive→exclusive): Lower limit − 0.5 and Upper limit + 0.5, where 0.5 = (lower limit of next class − upper limit of previous class) ÷ 2

NCERT “Exercises” — Full Solutions

All questions below are reproduced verbatim from the NCERT textbook’s end-of-chapter Exercises. Answers are original; all frequency tables have been computed and verified.

1. Which of the following alternatives is true?

(i) The class midpoint is equal to: (a) The average of the upper class limit and the lower class limit. (b) The product of upper class limit and the lower class limit. (c) The ratio of the upper class limit and the lower class limit. (d) None of the above.

(ii) The frequency distribution of two variables is known as (a) Univariate Distribution   (b) Bivariate Distribution   (c) Multivariate Distribution   (d) None of the above

(iii) Statistical calculations in classified data are based on (a) the actual values of observations   (b) the upper class limits   (c) the lower class limits   (d) the class midpoints

(iv) Range is the (a) difference between the largest and the smallest observations (b) difference between the smallest and the largest observations (c) average of the largest and the smallest observations (d) ratio of the largest to the smallest observation

ANSWER (i) (a) The average of the upper class limit and the lower class limit. (Class mark = (Upper + Lower) ÷ 2.) (ii) (b) Bivariate Distribution — the frequency distribution of two variables together. (iii) (d) The class midpoints — once data are grouped, the class mark represents the class and is used in further calculations. (iv) (a) The difference between the largest and the smallest observations.

2. Can there be any advantage in classifying things? Explain with an example from your daily life.

ANSWER Yes. Classification arranges things into groups based on common characteristics, which saves time and effort, brings order, and makes it easy to locate, compare and draw inferences. It removes the confusion of dealing with a large, mixed mass of items. Example: When I arrange my school books subject-wise — History, Geography, Mathematics, Science — I can instantly pick up the book I need instead of searching through the whole pile. Similarly, a grocery shop keeps pulses, spices and toiletries on separate shelves so any item can be found quickly. In the same way, the raw data of a census becomes meaningful only when classified by gender, age, education and occupation.

3. What is a variable? Distinguish between a discrete and a continuous variable.

ANSWER A variable is a quantity or characteristic that can take different values — for example marks, height, income or the number of students. Its value “varies” from one observation to another. Variables are of two types: discrete and continuous. Discrete variable: takes only certain values; its value changes by finite “jumps” and it does not take intermediate values. For example, the number of students in a class can be 25 or 26 but not 25.5, because “half a student” is absurd. Continuous variable: can take any value within a range — whole numbers, fractions, and even irrational values. For example, a student’s height growing from 90 cm to 150 cm passes through every value in between (90.85 cm, 102.34 cm, etc.). Other examples are weight, time and distance.

4. Explain the ‘exclusive’ and ‘inclusive’ methods used in classification of data.

ANSWER Exclusive method: here an item equal to a class limit (usually the upper limit) is excluded from that class and placed in the next class. The classes are written in a continuous form such as 0–10, 10–20, 20–30. A value of 10 goes into the class 10–20, not 0–10. This method is used very often for continuous variables because continuity is automatically maintained. Inclusive method: here both the lower and upper limits of a class are included in that class. The classes are written with a gap, such as 0–10, 11–20, 21–30. A value of 10 is included in the class 0–10 and 11 in the class 11–20. This method is commonly used for discrete variables. Difference: the inclusive method shows a “gap” between the upper limit of one class and the lower limit of the next (e.g. between 10 and 11). To make a continuous distribution from it, an adjustment is made — subtract 0.5 from each lower limit and add 0.5 to each upper limit (so 0–10 becomes −0.5–10.5, etc.), restoring continuity.

5. Use the data in Table 3.2 that relate to monthly household expenditure (in Rs) on food of 50 households and

(i) Obtain the range of monthly household expenditure on food. (ii) Divide the range into appropriate number of class intervals and obtain the frequency distribution of expenditure. (iii) Find the number of households whose monthly expenditure on food is (a) less than Rs 2000 (b) more than Rs 3000 (c) between Rs 1500 and Rs 2500.

ANSWER (i) Range. From Table 3.2, the highest monthly expenditure is Rs 5090 and the lowest is Rs 1007.
Range = Largest − Smallest = 5090 − 1007 = Rs 4083. (ii) Frequency distribution. Taking a convenient class interval of Rs 500 (exclusive method), the 50 observations are tallied as below. (Number of classes = 4083 ÷ 500 ≈ 9 classes.)
Expenditure on food (Rs)TallyNo. of households (Frequency)
1000–1500//// //// //// ////20
1500–2000//// //// ///13
2000–2500//// /6
2500–3000////5
3000–3500//2
3500–4000/1
4000–4500//2
4500–5000—0
5000–5500/1
Total50
(iii) Number of households (counted directly from the raw data of Table 3.2): (a) Less than Rs 2000: 20 + 13 = 33 households. (b) More than Rs 3000: households with expenditure above 3000 are 3473, 3676, 3222, 4439, 4248 and 5090 = 6 households. (c) Between Rs 1500 and Rs 2500 (i.e. 1500 to under 2500): 13 + 6 = 19 households.

6. In a city 45 families were surveyed for the number of Cell phones they used. Prepare a frequency array based on their replies as recorded below.
1 3 2 2 2 2 1 2 1 2 2 3 3 3 3 3 3 2 3 2 2 6 1 6 2 1 5 1 5 3 2 4 2 7 4 2 4 3 4 2 0 3 1 4 3

ANSWER “Number of cell phones” is a discrete variable, so its data is classified as a frequency array — each integral value gets its own frequency.
Number of cell phonesTallyNumber of families (Frequency)
0/1
1//// //7
2//// //// ////15
3//// //// //12
4////5
5//2
6//2
7/1
Total45
The frequencies add up to 1 + 7 + 15 + 12 + 5 + 2 + 2 + 1 = 45, confirming all families are accounted for. Most families (15) used 2 cell phones.

7. What is ‘loss of information’ in classified data?

ANSWER ‘Loss of information’ is the inherent shortcoming of classifying raw data into a frequency distribution. When individual observations are grouped into classes, their actual values are no longer used — every value in a class is assumed to be equal to the class mark (mid-value), and all further statistical calculations are based on the class mark, not on the original observations. For example, in the class 20–30 the six observations 25, 25, 20, 22, 25 and 28 are all treated as 25. The distribution then tells us only that the class has 6 values, not what those values actually were. This is the loss of information. However, the gain in making the raw data concise, ordered and comprehensible more than makes up for it.

8. Do you agree that classified data is better than raw data? Why?

ANSWER Yes, classified data is generally better than raw data for the purpose of analysis. Raw data are disorganised, large and cumbersome; it is a tedious task to draw any meaningful conclusion from them because they do not yield easily to statistical methods. Classification places facts of similar characteristics in the same class, which: (i) brings order to the data; (ii) makes it concise and easy to understand; (iii) enables easy comparison; (iv) helps locate any item quickly; and (v) makes it ready for further statistical analysis (averages, dispersion, etc.). Although some ‘loss of information’ occurs because individual values are replaced by class marks, the benefit of comprehensibility and analysability far outweighs this drawback. Hence, classified data is more useful.

9. Distinguish between univariate and bivariate frequency distribution.

ANSWER Univariate frequency distribution: the frequency distribution of a single variable. It shows how the values of one variable are distributed across classes with their frequencies — for example, the marks of 100 students in mathematics classified into the classes 0–10, 10–20, …, 90–100. Bivariate frequency distribution: the frequency distribution of two variables together, shown in a two-way table where one variable is classed in rows and the other in columns. Each cell shows the joint frequency — for example, the sales and advertisement expenditure of 20 firms, where a cell shows that 3 firms had sales of Rs 135–145 lakh and advertisement expenditure of Rs 64–66 thousand.

10. Prepare a frequency distribution by inclusive method taking class interval of 7 from the following data.
28 17 15 22 29 21 23 27 18 12 7 2 9 4 1 8 3 10 5 20 16 12 8 4 33 27 21 15 3 36 27 18 9 2 4 6 32 31 29 18 14 13 15 11 9 7 1 5 37 32 28 26 24 20 19 25 19 20 6 9

ANSWER There are 60 observations. The smallest value is 1 and the largest is 37, so Range = 37 − 1 = 36. With class interval 7 by the inclusive method, we start from 1: classes 1–7, 8–14, 15–21, 22–28, 29–35, 36–42 (both limits included in each class).
Class intervalTallyFrequency
1–7//// //// ////15
8–14//// //// //12
15–21//// //// ////15
22–28//// ////10
29–35//// /6
36–42//2
Total60
The frequencies total 15 + 12 + 15 + 10 + 6 + 2 = 60, confirming every observation is included.

11. “The quick brown fox jumps over the lazy dog”
Examine the above sentence carefully and note the numbers of letters in each word. Treating the number of letters as a variable, prepare a frequency array for this data.

ANSWER Counting the letters in each of the 9 words: The (3), quick (5), brown (5), fox (3), jumps (5), over (4), the (3), lazy (4), dog (3). The number of letters takes only whole values, so it is a discrete variable and is classified as a frequency array.
Number of letters in a wordWordsFrequency (number of words)
3The, fox, the, dog4
4over, lazy2
5quick, brown, jumps3
Total9
The frequencies add up to 4 + 2 + 3 = 9, which equals the number of words in the sentence.

Extra Practice Questions

Short Answer Type Questions

Q1. Define classification of data.

ANSWERClassification is the process of arranging or organising raw data into homogeneous groups or classes on the basis of some common characteristic or criterion. It brings order to data and makes comparison and analysis easy — for example, grouping a census population by gender, age and occupation.

Q2. What is a chronological classification? Give an example.

ANSWERIn chronological (or temporal) classification, data are arranged with reference to time — in ascending or descending order of years, quarters, months or weeks. Such data form a time series. For example, the population of India for the years 1951, 1961, 1971, …, 2011 is a chronological classification.

Q3. Distinguish between class limits and class interval.

ANSWERClass limits are the two ends of a class — the lower class limit (lowest value) and the upper class limit (highest value); for the class 60–70 they are 60 and 70. Class interval (or class width) is the difference between the upper and lower class limits; for 60–70 it is 70 − 60 = 10.

Q4. What is a class mark? Find the class mark of the class 40–50.

ANSWERThe class mark (or mid-point) is the middle value of a class, lying halfway between its lower and upper limits: Class mark = (Upper limit + Lower limit) ÷ 2. For the class 40–50, class mark = (40 + 50) ÷ 2 = 45.

Q5. Why are open-ended classes such as “less than 10” or “70 and over” not desirable?

ANSWEROpen-ended classes have no definite lower or upper limit, so their class mark cannot be determined exactly. This makes it impossible to calculate averages and other statistical measures accurately for those classes. Hence class limits should be definite and clearly stated, and open-ended classes are generally avoided.

Long Answer Type Questions

Q1. What is a frequency distribution? Explain the five questions to be addressed while preparing one.

ANSWERA frequency distribution is a comprehensive way of classifying the raw data of a quantitative variable, showing how its values are distributed in different classes along with their corresponding class frequencies. While preparing one, five questions must be addressed: (1) Should the class intervals be equal or unequal? — equal intervals are used in most cases, but unequal intervals suit data with a very wide range (like income) or with heavy concentration in a small part of the range. (2) How many classes should there be? — usually between six and fifteen; for equal intervals, number of classes = range ÷ class size. (3) What should be the size of each class? — it depends on the range and the chosen number of classes. (4) How should the class limits be determined? — they should be definite, clearly stated, avoid open-ended classes, and be set so that frequencies concentrate near the middle of each class. (5) How should we obtain the frequency of each class? — by counting how many observations fall in each class, usually with the help of tally marks.

Q2. Explain the adjustment needed to convert an inclusive frequency distribution into an exclusive one, with an example.

ANSWERIn the inclusive method (e.g. classes 800–899, 900–999, …) there is a “gap” between the upper limit of one class (899) and the lower limit of the next (900). For a continuous variable this discontinuity must be removed by an adjustment: (1) find the gap between the lower limit of the next class and the upper limit of the previous class (900 − 899 = 1); (2) divide it by two (1 ÷ 2 = 0.5); (3) subtract 0.5 from every lower limit; and (4) add 0.5 to every upper limit. Thus 800–899 becomes 799.5–899.5, 900–999 becomes 899.5–999.5, and so on. After this, the class marks are recalculated using the adjusted limits, and continuity of the variable is restored.

Q3. Distinguish between qualitative and quantitative classification, with examples.

ANSWERQualitative classification is based on attributes or qualities that cannot be measured numerically — such as nationality, literacy, religion, gender or marital status. Data are classified on the basis of the presence or absence of a quality. For example, a population may be classified as male or female, and each then sub-divided as married or unmarried. Quantitative classification is based on characteristics that can be measured and expressed numerically — such as height, weight, age, income or marks of students. The data are grouped into classes of numerical values; for example, the marks of 100 students grouped into 0–10, 10–20, …, 90–100. In short, qualitative classification deals with attributes (no numbers), while quantitative classification deals with measurable variables (numbers), and only quantitative data can form a frequency distribution with class intervals.

MCQs & Assertion–Reason

1. Arranging data into groups or classes on the basis of some criteria is called:

(a) tabulation    (b) classification    (c) collection    (d) presentation

2. Classification of data with reference to time (years, months) is called:

(a) spatial    (b) qualitative    (c) chronological    (d) quantitative

3. Which of the following is a discrete variable?

(a) height    (b) weight    (c) number of cell phones    (d) temperature

4. The class interval of the class 50–60 is:

(a) 5    (b) 10    (c) 55    (d) 110

5. In the exclusive method, a value equal to the upper class limit is:

(a) included in the same class    (b) excluded and put in the next class    (c) dropped    (d) counted twice

6. The classification of a discrete variable is known as a:

(a) frequency curve    (b) frequency array    (c) time series    (d) bivariate distribution

7. The number of classes in a frequency distribution is usually between:

(a) 2 and 5    (b) 6 and 15    (c) 16 and 25    (d) 25 and 50

8. Gender and marital status are examples of:

(a) quantitative variables    (b) continuous variables    (c) attributes (qualitative)    (d) discrete numbers

9. The class mark of the class 800–899 (inclusive) is:

(a) 800    (b) 899    (c) 849.5    (d) 850

10. The technique of counting class frequency by putting marks against a class is called:

(a) tally marking    (b) class marking    (c) array    (d) tabulation

Answer key: 1-(b), 2-(c), 3-(c), 4-(b), 5-(b), 6-(b), 7-(b), 8-(c), 9-(c), 10-(a).

For each Assertion–Reason question, choose: (A) Both true and the Reason correctly explains the Assertion; (B) Both true but the Reason is not the correct explanation; (C) Assertion true, Reason false; (D) Assertion false, Reason true.

A-R 1. Assertion: Classification involves a loss of information.

Reason: Once data are grouped, individual observations are replaced by the class mark in further calculations.

A-R 2. Assertion: A continuous variable can take only whole-number values.

Reason: A continuous variable can take any value — whole numbers, fractions and irrational values — within a range.

A-R 3. Assertion: Open-ended classes such as “70 and over” are not desirable in a frequency distribution.

Reason: The class mark of an open-ended class cannot be determined exactly.

A-R 4. Assertion: A bivariate frequency distribution shows the distribution of two variables together.

Reason: It is presented in a two-way table where each cell shows the joint frequency of the row and column values.

A-R 5. Assertion: In the inclusive method an adjustment of 0.5 is made to the class limits.

Reason: The adjustment removes the gap between classes and restores continuity for a continuous variable.

Answer key: 1-(A), 2-(D), 3-(A), 4-(A), 5-(A).

Exam Tips & Common Mistakes

How to score full marks in this chapter

Memorise the three formulas — Range, Class Mark and Class Interval — and the rule that further calculations use the class mark, not actual values. In numericals, always start by writing the range (largest − smallest), choose a sensible class interval, and show the tally column — examiners give marks for the tallies. Check that your frequencies total to the given number of observations (50, 45, 60, 9). Clearly state whether you are using the exclusive or inclusive method, and remember that discrete data (cell phones, letters in a word) need a frequency array, not class intervals. Quote the textbook’s own examples — the kabadiwallah, marks of 100 students, the bivariate sales/advertisement table — to show thorough study.

Common mistakes to avoid

  • Confusing class limits (the two ends of a class) with class interval (their difference) and class mark (their average).
  • Using class intervals for a discrete variable — cell phones and letters per word need a frequency array.
  • Forgetting the 0.5 adjustment when converting an inclusive distribution to an exclusive (continuous) one.
  • Mixing up the exclusive method (one limit excluded; classes 10–20, 20–30) with the inclusive method (both limits included; classes 11–20, 21–30).
  • Frequencies not adding up to the total number of observations — always verify the sum.
  • Saying classification has “no drawback” — remember the loss of information.
  • Confusing univariate (one variable) with bivariate (two variables) frequency distribution.

Frequently Asked Questions

What is Chapter 3 of Class 11 Economics (Statistics for Economics) about?

Chapter 3, Organisation of Data, explains how raw data are organised through classification and a frequency distribution. It covers chronological, spatial, qualitative and quantitative classification, continuous and discrete variables, the formation of classes (range, class interval, class limits, class mark), the exclusive and inclusive methods, tally marking, the frequency array and the bivariate frequency distribution.

What is the difference between the exclusive and inclusive methods?

In the exclusive method one limit (usually the upper) is excluded from the class, so classes are written continuously as 0–10, 10–20, 20–30; a value of 10 goes into 10–20. In the inclusive method both limits are included, so classes are written with a gap as 0–10, 11–20, 21–30. The inclusive method needs a ±0.5 adjustment to become a continuous distribution.

How many questions are there in the Class 11 Economics Chapter 3 exercises?

The end-of-chapter Exercises of Organisation of Data contain 11 questions — including MCQs, theory questions and numerical problems on building frequency distributions and frequency arrays. All 11 are solved step by step on this page, with every frequency table computed and verified.

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