Class 11 Economics Chapter 3 — Organisation of Data (ASSEB, English Medium)
Welcome to HSLC Guru! This page offers a complete English-medium guide to Class 11 Economics Chapter 3 — Organisation of Data, prepared as per the latest ASSEB (Assam State School Education Board) syllabus for Statistics for Economics. After raw data are collected, they must be arranged systematically before any meaningful interpretation is possible. In this chapter, we learn how to classify data, build frequency distributions, decide between exclusive and inclusive class intervals, and read frequency curves. The page provides a clear chapter summary, full textbook question and answer practice (1-mark, 2–3 mark, and 5–6 mark with numerical problems), additional MCQs, fill-in-the-blanks, true/false items, and a short glossary table.
Chapter Summary
Raw data and the need for classification. When a statistical investigator collects information from the field, the figures appear in an unorganised form. Such unprocessed figures are called raw data. Raw data are usually scattered, repetitive, and difficult to read. Before drawing any inference, the investigator must arrange these figures into a compact and intelligible form. The process of arranging data into homogeneous groups according to common characteristics is called classification. A good classification is unambiguous, stable, flexible, exhaustive, and mutually exclusive — every observation should fit into one and only one class.
Bases of classification. Data may be classified on four common bases. Qualitative classification is based on attributes that cannot be measured numerically, such as sex, religion, literacy, or marital status; here data are sorted into categories. Quantitative classification is based on numerical characteristics like income, age, marks, or height. Geographical (spatial) classification arranges data according to location — state, district, region, or country. Chronological (temporal) classification arranges data according to time, such as production figures by year, month, or day. The choice of basis depends on the purpose of the study.
Variables: discrete and continuous. A characteristic that takes different numerical values is called a variable. Variables are of two types. A discrete variable takes only certain isolated values — for example the number of children in a family (0, 1, 2, 3 …) or number of cars in a household. A continuous variable can take any value within a given range — for example weight, height, temperature, or income. The choice between discrete and continuous classification governs the way the frequency table is built.
Frequency distribution, class intervals and frequency curves. A frequency distribution is a table that shows how observations are distributed over different classes along with their frequencies (the number of times each class occurs). For continuous data, the range is divided into class intervals with a chosen class width (i). The interval can be written in two ways. In the exclusive method (e.g., 10–20, 20–30) the upper limit of one class becomes the lower limit of the next, and an observation equal to that boundary is included in the higher class. In the inclusive method (e.g., 10–19, 20–29) both limits are included in the same class, but for calculation it must be converted to exclusive form by adjusting half the gap. The mid-point of a class is its class mark = (lower limit + upper limit) ⁄ 2. Frequency distributions can be displayed using histograms, frequency polygons, frequency curves, and ogives (cumulative frequency curves of the “less than” and “more than” types). Whenever individual observations are merged into groups, identity is lost — this is called loss of information; the price we pay for compactness and easier handling.
Textbook Questions and Answers
A. Very Short Answer Type Questions (1 Mark)
Q1. What is meant by raw data?
Answer: Raw data are the figures collected directly from the field in their original, unorganised form, before any classification or processing.
Q2. Define classification of data.
Answer: Classification is the process of arranging data into homogeneous groups or classes according to some common characteristic so that the data become compact, comparable and intelligible.
Q3. Name the four common bases of classification.
Answer: Qualitative, quantitative, geographical (spatial) and chronological (temporal).
Q4. What is a variable?
Answer: A variable is a characteristic that takes different numerical values from one observation to another, e.g., income, age, height.
Q5. Distinguish in one line between a discrete and a continuous variable.
Answer: A discrete variable takes only specific (usually whole-number) values, whereas a continuous variable can take any value within a given range.
Q6. Define frequency.
Answer: Frequency is the number of times a particular value or class of values occurs in a given set of data.
Q7. What is meant by class mark?
Answer: Class mark is the mid-point of a class interval, calculated as (lower limit + upper limit) ⁄ 2.
Q8. Give one example of a chronological classification.
Answer: Annual production of rice in Assam from 2015 to 2024 — arranged year by year.
Q9. What is an ogive?
Answer: An ogive is the graph of a cumulative frequency distribution; it can be drawn as a “less than” ogive or a “more than” ogive.
Q10. What is loss of information in classified data?
Answer: When individual observations are grouped into class intervals, their separate identity is lost; only the frequency of each class is retained. This is known as loss of information.
B. Short Answer Type Questions (2–3 Marks)
Q1. State any three objectives of classification of data.
Answer: (i) To present data in a compact and intelligible form. (ii) To bring out the points of similarity and dissimilarity between groups. (iii) To facilitate comparison and statistical analysis. Classification also helps in highlighting the salient features of the data and prepares them for further treatment such as tabulation and graphic presentation.
Q2. Distinguish between qualitative and quantitative classification.
Answer: In qualitative classification, data are grouped on the basis of attributes that cannot be measured numerically — for example sex, religion, literacy. In quantitative classification, data are grouped on the basis of measurable numerical characteristics — for example income, marks, height. Qualitative classification produces categories; quantitative classification produces class intervals and frequencies.
Q3. Differentiate between exclusive and inclusive methods of forming class intervals.
Answer: In the exclusive method, the upper limit of one class is the lower limit of the next (e.g., 10–20, 20–30). The upper-limit value is excluded from that class and counted in the next class, so the classes are continuous. In the inclusive method, both limits are included in the same class (e.g., 10–19, 20–29); there is a gap of one unit between successive classes. For calculation, inclusive classes are converted to exclusive form by subtracting half the gap from each lower limit and adding half the gap to each upper limit.
Q4. What is a frequency distribution? State its two main types.
Answer: A frequency distribution is a table showing values (or class intervals) of a variable along with the corresponding frequencies. Its two main types are: (a) Discrete (ungrouped) frequency distribution, prepared for a discrete variable where each value has its own frequency, and (b) Continuous (grouped) frequency distribution, prepared for a continuous variable where data are grouped into class intervals.
Q5. What do you understand by a frequency curve?
Answer: A frequency curve is a smooth free-hand curve drawn through the mid-points (or top corners) of a frequency polygon or histogram. It represents the general shape of the frequency distribution and is useful for visual comparison. Common shapes are symmetrical, positively skewed, negatively skewed, J-shaped and U-shaped curves.
Q6. Why is loss of information considered a limitation of classified data?
Answer: When raw data are grouped into class intervals, the individual values disappear inside the classes; we only know how many observations fall in each class, not their exact magnitudes. As a result, statistical computations made from grouped data (mean, median, etc.) are based on the assumption that all values in a class are equal to the class mark. This approximation introduces an unavoidable error and is called loss of information.
C. Long Answer Type / Numerical Questions (5–6 Marks)
Q1. Explain the main characteristics of a good classification.
Answer: A good classification should satisfy the following characteristics: (i) Unambiguous — each class must be clearly defined so that there is no doubt regarding the placement of any item. (ii) Mutually exclusive — the classes must not overlap; an observation should fit only one class. (iii) Exhaustive — the classes together must cover the entire range of the data so that no item is left out. (iv) Stable — the same basis of classification should be followed throughout the study to permit valid comparison. (v) Flexible — the classification should be capable of adjusting to small changes in the nature of data. (vi) Suitable for the purpose — the basis chosen must serve the objective of the investigation. (vii) Homogeneous — the items inside a class should be similar with respect to the chosen attribute. A classification meeting these criteria yields tables that are easy to interpret and that lend themselves to further statistical analysis.
Q2. Construct a discrete frequency distribution from the following data showing the number of children per family in 30 households: 2, 1, 3, 2, 0, 4, 2, 1, 3, 2, 1, 0, 2, 3, 1, 4, 2, 3, 0, 1, 2, 3, 2, 1, 4, 3, 2, 1, 2, 0.
Answer: Using the tally-bar method, we count the occurrences of each value:
| No. of children (x) | Tally bars | Frequency (f) |
|---|---|---|
| 0 | |||| | 4 |
| 1 | |||| || | 7 |
| 2 | |||| |||| | 10 |
| 3 | |||| | | 6 |
| 4 | ||| | 3 |
| Total | 30 |
Hence the most common family size is 2 children, and 0 to 4 covers all observations.
Q3. The marks (out of 50) obtained by 40 students are given below. Prepare a continuous frequency distribution using the exclusive method with class intervals of width 10 starting from 0–10.
23, 7, 14, 36, 41, 19, 22, 28, 30, 11, 5, 18, 25, 33, 47, 12, 27, 35, 9, 21, 16, 29, 40, 13, 24, 31, 6, 17, 26, 34, 42, 15, 20, 32, 8, 22, 38, 10, 28, 45.
Answer: We tally each value into its class. The exclusive method takes 0–10, 10–20, 20–30, 30–40, 40–50; an observation equal to the upper limit goes to the next class.
| Class interval (Marks) | Tally bars | Frequency (f) |
|---|---|---|
| 0 – 10 | |||| | 4 |
| 10 – 20 | |||| |||| | 10 |
| 20 – 30 | |||| |||| || | 12 |
| 30 – 40 | |||| |||| | 9 |
| 40 – 50 | |||| | 5 |
| Total | 40 |
The distribution shows that the largest concentration of students lies in the 20–30 mark range.
Q4. Convert the following inclusive frequency distribution of daily wages (in Rs.) into the exclusive form and find the class marks.
| Wages (Rs.) | No. of workers |
|---|---|
| 100 – 109 | 5 |
| 110 – 119 | 12 |
| 120 – 129 | 20 |
| 130 – 139 | 15 |
| 140 – 149 | 8 |
Answer: Gap between successive classes = 110 − 109 = 1, half the gap = 0.5. Subtract 0.5 from each lower limit and add 0.5 to each upper limit.
| Exclusive class interval | Class mark | Frequency |
|---|---|---|
| 99.5 – 109.5 | 104.5 | 5 |
| 109.5 – 119.5 | 114.5 | 12 |
| 119.5 – 129.5 | 124.5 | 20 |
| 129.5 – 139.5 | 134.5 | 15 |
| 139.5 – 149.5 | 144.5 | 8 |
Now the classes are continuous and ready for graphical work such as a histogram.
Q5. From the frequency distribution given below, prepare a “less than” cumulative frequency distribution and find the number of workers earning less than Rs. 30.
| Daily wage (Rs.) | No. of workers (f) |
|---|---|
| 0 – 10 | 6 |
| 10 – 20 | 10 |
| 20 – 30 | 14 |
| 30 – 40 | 12 |
| 40 – 50 | 8 |
Answer: Adding successive frequencies gives the “less than” cumulative frequencies.
| Wage less than (Rs.) | Cumulative frequency (cf) |
|---|---|
| 10 | 6 |
| 20 | 16 |
| 30 | 30 |
| 40 | 42 |
| 50 | 50 |
Therefore, the number of workers earning less than Rs. 30 is 30, and the total number of workers is 50. A graph of these cumulative frequencies against the upper class limits gives the “less than” ogive.
Additional Multiple Choice Questions (MCQs)
Q1. Unprocessed data collected from the field are called:
(a) Primary data (b) Secondary data (c) Raw data (d) Tabulated data
Answer: (c) Raw data.
Q2. Classification of population by religion is an example of:
(a) Quantitative classification (b) Qualitative classification (c) Geographical classification (d) Chronological classification
Answer: (b) Qualitative classification.
Q3. The number of children in a household is an example of a:
(a) Continuous variable (b) Discrete variable (c) Attribute (d) Constant
Answer: (b) Discrete variable.
Q4. Class mark of the interval 20–30 is:
(a) 20 (b) 25 (c) 30 (d) 10
Answer: (b) 25.
Q5. In the exclusive method, the value equal to the upper limit of a class is included in:
(a) The same class (b) The previous class (c) The next class (d) Both classes
Answer: (c) The next class.
Q6. The graph of a cumulative frequency distribution is called:
(a) Histogram (b) Frequency polygon (c) Ogive (d) Pie chart
Answer: (c) Ogive.
Q7. Annual rainfall figures of Assam from 2010 to 2020 form a:
(a) Geographical classification (b) Chronological classification (c) Qualitative classification (d) Quantitative classification
Answer: (b) Chronological classification.
Q8. The difference between the upper limit and lower limit of a class is called:
(a) Class mark (b) Class size (width) (c) Frequency (d) Range
Answer: (b) Class size (width).
Q9. Which of the following is NOT a characteristic of a good classification?
(a) Mutually exclusive (b) Exhaustive (c) Ambiguous (d) Stable
Answer: (c) Ambiguous.
Q10. When raw data are grouped into class intervals, individual identity of observations is lost. This is called:
(a) Tabulation (b) Classification (c) Loss of information (d) Sampling error
Answer: (c) Loss of information.
Fill in the Blanks
Q1. Data collected directly from the field in unorganised form are called __________.
Answer: raw data.
Q2. Classification of data by states or districts is called __________ classification.
Answer: geographical (spatial).
Q3. A variable that can take any value within a given range is called a __________ variable.
Answer: continuous.
Q4. The mid-point of a class interval is known as the __________.
Answer: class mark.
Q5. The graph of a cumulative frequency distribution is known as an __________.
Answer: ogive.
True / False
Q1. Raw data are already arranged in ascending order. (True / False)
Answer: False.
Q2. In the exclusive method, both the lower and upper limits are included in the same class. (True / False)
Answer: False.
Q3. Height of students measured in centimetres is a continuous variable. (True / False)
Answer: True.
Q4. Frequency curve is a free-hand smooth curve drawn through the points of a frequency polygon. (True / False)
Answer: True.
Q5. Loss of information increases as the size of class intervals decreases. (True / False)
Answer: False (loss of information increases when class intervals are made wider).
Quick Revision Notes
- Raw data → arrange → classify → tabulate → analyse.
- Bases of classification: qualitative, quantitative, geographical, chronological.
- Variables: discrete (isolated values) vs continuous (any value within a range).
- Frequency distribution: discrete (ungrouped) and continuous (grouped).
- Class width (i) = Upper limit − Lower limit.
- Class mark = (Lower limit + Upper limit) ⁄ 2.
- Exclusive vs inclusive: convert inclusive to exclusive by adjusting half the gap before computation.
- Cumulative frequency: “less than” adds upward; “more than” subtracts from total.
- Graphs: histogram, frequency polygon, frequency curve, ogive.
- Limitation: loss of information increases as class width increases.
Glossary
| Term | Meaning |
|---|---|
| Raw data | Unorganised figures collected directly from the field before any processing. |
| Classification | Arranging data into homogeneous groups according to a common characteristic. |
| Qualitative classification | Classification based on attributes such as sex, religion or literacy. |
| Quantitative classification | Classification based on numerical values such as income or marks. |
| Geographical classification | Classification based on place — state, district, region. |
| Chronological classification | Classification based on time — year, month, day. |
| Variable | A characteristic that takes different numerical values across observations. |
| Discrete variable | A variable that takes only specific (usually whole) values, e.g., number of children. |
| Continuous variable | A variable that can take any value within a range, e.g., height, weight. |
| Frequency | The number of times a value or class occurs in the data. |
| Frequency distribution | A table showing values or class intervals with their corresponding frequencies. |
| Class interval | A range of values forming a single class, e.g., 10–20. |
| Class mark | Mid-point of a class = (lower limit + upper limit) ⁄ 2. |
| Exclusive method | Class formation in which the upper limit of a class becomes the lower limit of the next. |
| Inclusive method | Class formation in which both limits are included in the same class. |
| Cumulative frequency | Running total of frequencies up to a given class limit. |
| Ogive | Graph of cumulative frequency, “less than” or “more than” type. |
| Frequency curve | Smooth free-hand curve representing the shape of a frequency distribution. |
| Loss of information | Loss of individual identity of observations when data are grouped into classes. |
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