RBSE Solutions Class 11 Economics Chapter 6 Classification of Data

RBSE Class 11 Economics Chapter 6 Text Book Questions

RBSE Class 11 Economics Chapter 6 Multiple Choice Questions

 

Question 1. In an exclusive series :
(a) Both class-limits are considered
(b) Lower limit is removed
(c) Upper limit is removed
(d) Both the limits are removed
Answer: (c) Upper limit is removed
In simple words: In an exclusive series, the upper value of a class is not included in that class, but in the next one. So, the upper limit is effectively removed from consideration for that specific class.

🎯 Exam Tip: Remember the specific rules for inclusive vs. exclusive series to correctly identify which limits are considered or excluded in each type of classification.

 

Question 2. The frequency of each variable value in an individual series is:
(a) Equal
Answer: (a) Equal
In simple words: In an individual series, each observation is listed separately, so each unique variable value essentially appears once, making its frequency equal to one, unless the value itself repeats, which would then be counted individually each time.

🎯 Exam Tip: Understand that an individual series lists each data point on its own, unlike discrete or continuous series that group frequencies.

 

Question 3. The main objective of classification is:
(a) To give a concise form to the large group of data-items
(b) To lend flexibility to the data-items
(c) To lend stability to the data-items
(d) To lend mutual exclusivity to the data-items
Answer: (a) To give a concise form to the large group of data-items
In simple words: Classification helps simplify big sets of data, making them easier to understand and manage.

🎯 Exam Tip: When asked about objectives, focus on how classification makes data more usable, like simplifying it, making it comparable, and revealing patterns.

 

Question 4. The following series is:

(b) Discrete
(c) Continuous Inclusive
(d) Continuous Exclusive
Answer: (b) Discrete
In simple words: This series is discrete because the marks obtained are whole numbers (like 1, 2, 3) and there are clear, separate counts (number of students) for each specific mark.

🎯 Exam Tip: A discrete series involves whole, distinct values, unlike a continuous series which uses ranges or intervals.

 

Question 5. If the lower limit (L₁) of a class is 10 and the upper limit (L2) is 20, then the mid-point is:
(a) -15
(b) 10
(c) 15
(d) 30
Answer: (c) 15
In simple words: To find the mid-point, you add the lower and upper limits of the class and then divide the sum by two. For 10 and 20, (10 + 20) / 2 = 15.

🎯 Exam Tip: Always remember the formula for calculating the mid-point of a class: \( \frac { \text{Lower Limit} + \text{Upper Limit} }{ 2 } \).

RBSE Class 11 Economics Chapter 6 Very Short Answer Type Questions

 

Question 1. Write the names of the two types of attribute classification.
Answer:
1. Ordinary or Binomial Classification
2. Multiple-attribute Classification
In simple words: There are two main ways to classify things based on their qualities: either by just two options (like yes/no) or by many different qualities at once.

🎯 Exam Tip: Be precise with terminology; 'ordinary' is often interchangeable with 'binomial' in this context.

 

Question 2. What is meant by classification based on variables?
Answer: Variables are values that can change. Classification based on variables means grouping data according to these changing values.
In simple words: It's when you sort data by things that can have different numbers or amounts, like height or age.

🎯 Exam Tip: Understand that classification by variables deals with quantitative data, which can be measured and change.

 

Question 3. What is meant by variable?
Answer: Facts that can be expressed in numbers and whose values keep changing are called variables.
In simple words: A variable is something that can be measured and whose value is not fixed.

🎯 Exam Tip: Key characteristics of a variable are that it is quantifiable (numerical) and dynamic (its value can vary).

 

Question 4. Series are of how many types? Write their names. Or How many types of series are there? Write their names.
Answer: Statistical series are divided into three types based on their formation:
1. Individual Series
2. Discrete Series
3. Continuous Series
In simple words: Data can be organized in three main ways: as a simple list, as counts for specific numbers, or as counts for ranges of numbers.

🎯 Exam Tip: Listing all three types of series (Individual, Discrete, Continuous) is crucial for a complete answer.

 

Question 5. What are class-limits?
Answer: The boundaries of a class are called class-limits. The lowest value of the class is called the lower limit, and the highest value of the class is called the upper limit.
In simple words: Class-limits are the highest and lowest numbers that define a group in your data.

🎯 Exam Tip: Clearly define both lower and upper limits as the two essential components of class limits.

 

Question 6. How is mid-point calculated?
Answer: Mid point = \( \frac { \text{Upper Limit} + \text{Lower Limit} }{ 2 } \)
In simple words: You find the middle point of a group by adding the smallest and largest values in that group and then dividing by two.

🎯 Exam Tip: Provide the mathematical formula for the mid-point to score full marks, ensuring correct use of terms like 'upper limit' and 'lower limit'.

 

Question 7. While finding cumulative frequency, which limits are used in ‘less than' and 'more than' formats?
Answer: When finding cumulative frequency in a 'less than' format, the upper limit is used. For the 'more than' format, the lower limit is used.
In simple words: For "less than" frequencies, we use the top number of each group, and for "more than" frequencies, we use the bottom number.

🎯 Exam Tip: Distinguish between the 'less than' (upper limit) and 'more than' (lower limit) methods for cumulative frequency, as this is a common point of confusion.

RBSE Class 11 Economics Chapter 6 Short Answer Type Questions

 

Question 1. What do you understand by classification of data-items?
Answer: Classification is the process of arranging collected data into similar groups, classes, or sub-classes based on their various shared qualities and properties. According to Secrist, "Classification is the process of arranging data into sequences and groups according to their common characteristics, or separating them into different but related parts."
In simple words: Classification means sorting data into groups that are alike in some way, making it organized and easier to work with.

🎯 Exam Tip: Include a definition from a known statistician like Secrist to add authority and detail to your answer.

 

Question 2. What are the main objectives of classification?
Answer: Following are the main objectives of classification:
5. The purpose of classification is to provide a scientific basis for the data.
6. The purpose of classification is to increase the usefulness of data.
7. The purpose of classification is also to form the basis of tabulation.
In simple words: Classification helps make data scientific, more useful, and ready for tables.

🎯 Exam Tip: When listing objectives, ensure each point highlights a unique benefit or purpose of classification.

 

Question 3. Mention any four essential elements of an ideal classification.
Answer: The following four essential elements should be present in an ideal classification :

• Clarity: There should be no uncertainty or ambiguity about which class or group the collected data items belong to.
• Stability: Stability is necessary to make data comparable and to allow for meaningful comparisons of the results.
• Extensiveness: The different sections should be composed widely enough so that no collected data item is left out.
• Suitability: The composition of the class should be appropriate for the purpose. For example, to understand the economic condition of people or their saving trends, it would be appropriate to divide sections based on income.

In simple words: A good way to sort data should be clear, steady, cover everything, and fit its main goal.

🎯 Exam Tip: Focus on explaining how each element (clarity, stability, extensiveness, suitability) contributes to the effectiveness and reliability of a classification system.

 

Question 4. What is frequency distribution?
Answer: Frequency distribution involves classifying data items based on some measurable variable. It is a table where data items are grouped into values or classes. The number of units that occur in each value or class are called their frequencies. Thus, an ordered arrangement of values or classes and their frequencies is called frequency distribution.
In simple words: Frequency distribution is a way to show how often each value or range of values appears in a set of data.

🎯 Exam Tip: Define frequency distribution as a table that organizes data by showing how often specific values or class intervals occur, highlighting its role in summarizing quantitative data.

 

Question 5. Differentiate between exclusive and inclusive series.
Answer:
Exclusive Series: In this series, the upper limit of one class is the same as the lower limit of the next class. Data values equal to the upper limit of a class are not included in that class; instead, they are included in the next class.
Inclusive Series: In this series, the upper limit of one class and the lower limit of the next class are not the same; there is a maximum difference of 1 between them. Here, data values equal to both the lower and upper limits are included within the class itself.
In simple words: Exclusive series passes the upper limit to the next group, while inclusive series keeps both its upper and lower limits within its own group.

🎯 Exam Tip: Clearly state the key distinction: whether the upper limit is included in the current class (inclusive) or passed to the next (exclusive).

 

Question 6. How can a normal frequency distribution be converted into cumulative frequency distribution? Clarify with the help of an example.
Answer: A normal frequency distribution can be converted into a cumulative frequency distribution by continuously adding the frequencies of successive classes. The cumulative frequency for a class is the sum of its frequency and the frequencies of all preceding classes. This shows the total number of observations up to a certain point.
Normal Frequency Distribution

Cumulative Frequency Distribution

In simple words: To change a normal frequency into a cumulative one, you just keep adding up the numbers from the start. This shows a running total for each group.

🎯 Exam Tip: Illustrate with clear tables showing both the original frequency and the step-by-step calculation for cumulative frequency. Ensure totals match.

 

Question 7. Do you agree with the observation that classified data-items are better than unrefined(raw) data-items?
Answer: Yes, classified data items are definitely better than unrefined (raw) data items. Raw data is highly disorganized, which makes it almost impossible to analyze and draw conclusions from. It is also difficult to apply statistical methods to raw data. In contrast, classified data is well-ordered, easy to understand, and suitable for analysis. Conclusions can be easily drawn from it. Hence, classified data is considered superior to raw data.
In simple words: Yes, sorted data is much better than raw data because it's organized, easy to understand, and helps us make sense of information quickly.

🎯 Exam Tip: Compare and contrast the characteristics of raw vs. classified data, emphasizing how classification improves data utility and analytical potential.

RBSE Class 11 Economics Chapter 6 Long Answer Type Questions

 

Question 1. Explain the inclusive and exclusive methods of classification of data-items.
Answer: Based on class-intervals, there are two primary methods of classification:

Inclusive Method:
In this method, classes include variable values that are equal to both their lower and upper limits. The upper limit is not left out of any class interval. A key feature of inclusive classification is that the upper limit of a class and the lower limit of the next class are not equal, typically having a difference of 1 between consecutive classes.

Exclusive Method:
In this method, the upper limit of one class and the lower limit of the next class are the same. This method is called exclusive because any variable value equal to the upper limit of a class is not included in that class; instead, it is included in the next class. This approach prevents values from being counted twice.
Exclusive class-intervals can be easily understood through the following table:

In simple words: Inclusive groups keep both their start and end numbers in the same group. Exclusive groups pass the end number to the next group, avoiding double counting.

🎯 Exam Tip: Clearly define and give examples for both inclusive and exclusive methods, emphasizing how the class limits are handled in each.

 

Question 2. Explain the essential elements in an ideal classification. What are the objectives of classification?
Answer: Following are the essential elements in an ideal classification :

• Clarity: There should be no uncertainty or confusion about which class or group a collected data item should be placed in.
• Stability: Stability is crucial for comparing data and making meaningful comparisons between results.
• Extensiveness: The various sections should be designed broadly enough so that no collected data item is left out.
• Suitability: The classification should be appropriate for its intended purpose. For example, to study people's economic conditions or saving habits, classifying by income would be suitable.
• Flexibility: The classification should be adaptable enough to allow for changes, amendments, and additions to various classes as new situations arise.
• Homogeneity: Units within each class should be similar. All data items included in a class or group should share the property upon which the classification was based.

Objectives of Classification:

• Simplification and conciseness: The main goal of classification is to simplify the complexity of collected data, making it concise and easy to understand.
• Clarification of Similarity and Dissimilarity: By grouping data items with similar properties, classification helps in understanding their similarities and differences.
• Helpful in comparison: Classification makes it easier to compare data items. For instance, comparing the populations of cities or villages based on literacy, marital status, or employment is simplified through classification.
• Logical arrangement: Classification is a logical process that presents data items in an organized and well-ordered manner. For example, classifying population data by age, gender, or caste is a logical activity.
• Presentation of the basis of tabulation: Tabulation is impossible without classifying raw data. Statistical analysis also becomes impractical without it. Thus, classification provides the foundation for tabulation.

In simple words: A good data sorting system needs to be clear, stable, cover all data, flexible, and group similar things. Its main goals are to make data simpler, show differences, help with comparisons, organize things logically, and prepare data for tables.

🎯 Exam Tip: For this two-part question, clearly separate the essential elements from the objectives. Ensure you elaborate briefly on each point for a comprehensive answer.

 

Question 3. Using an imaginary example, construct discrete and continuous series from the following data-items.
50 73 60 58 43 30 76 78 44 63 42 56 49 44 38 54 67 36 41 52 65 65 70 46 37 61 35 40 84 51 32 50 61 88 54 59 49 87 35 65 51 59 50 35

Continuous series from individual data:

The discrete series will be created as follows:
Raw data for discrete series: 8, 2, 9, 3, 3, 8, 6, 1, 0, 3, 3, 4, 2, 9, 8, 8, 4, 3, 3, 7, 1, 2, 3, 3, 9, 3, 4, 0, 1

In simple words: For continuous series, you group data into ranges and count how many fall into each range. For discrete series, you list each specific value and count how many times it appears.

🎯 Exam Tip: Carefully tally the frequencies for each class interval or specific value to avoid errors in constructing the series. Make sure to present both the raw data and the constructed series.

RBSE Class 11 Economics Chapter 6 Other Important Questions

RBSE Class 11 Economics Chapter 6 Objective Type Questions

 

Question 1. The mid-point of a class-interval is equal to
(a) Average of upper limit and lower limit
Answer: (a) Average of upper limit and lower limit
In simple words: The mid-point is found by adding the highest and lowest numbers in a group, then dividing by two.

🎯 Exam Tip: Always remember that the mid-point is the average of the class's upper and lower limits.

 

Question 2. Statistical calculation in classified data is based
(a) On the actual values of observations.
(b) On the limits of upper class
(c) On the limits of lower class
(d) On the mid-value of class
Answer: (d) On the mid-value of class
In simple words: When data is sorted into groups, calculations often use the middle value of each group, not the individual raw numbers.

🎯 Exam Tip: In grouped frequency distributions, the mid-value of each class is crucial for many statistical calculations like mean, median, and mode.

 

Question 3. Which of the following tables should be used to divide students into various faculties on the basis of gender (male and female) in a school?
(a) Ordinary Table
(b) Binomial Table
(c) Trinomial Table
(d) Multi-attribute Table
Answer: (c) Trinomial Table
In simple words: To sort students by gender and then by faculties, a table with three main categories would be needed to show these different characteristics.

🎯 Exam Tip: A trinomial table is used for classification based on three attributes or categories, like gender, faculty, and another variable.

 

Question 4. The mid-value of class limits is called
(a) Class- interval
(b) Magnitude of class
(c) Mid-point
(d) None of the options
Answer: (c) Mid-point
In simple words: The number exactly in the middle of a class's highest and lowest values is called its mid-point.

🎯 Exam Tip: Distinguish between class interval (the range), magnitude (the size of the range), and mid-point (the center of the range).

 

Question 5. The number of variables included under any class is called
(b) Class Frequency
Answer: (b) Class Frequency
In simple words: The count of how many items fall into a specific group or class is called the class frequency.

🎯 Exam Tip: Class frequency indicates the number of observations within a particular class interval.

 

Question 6. The series in which each value is independent and is written separately is called
(a) Individual series
(b) Discrete series
(c) Continuous series
(d) None of the options
Answer: (a) Individual series
In simple words: A list where every single data point is written down one by one, without grouping, is an individual series.

🎯 Exam Tip: Recognize an individual series by its characteristic of listing each observation separately, not grouped or tallied.

 

Question 7. Class-intervals (10-14, 15-19, 20-24, 25-29) are the example of
(a) Exclusive Series
(b) Inclusive Series
(c) Both (a) and (b)
(d) None of the options
Answer: (b) Inclusive Series
In simple words: This is an inclusive series because the upper limit of one class (like 14) is not the same as the lower limit of the next class (15), and both limits are included within each group.

🎯 Exam Tip: For inclusive series, always look for a gap (usually 1 unit) between the upper limit of one class and the lower limit of the next class.

 

Question 8. Class-intervals 10-15, 15-20, 20-25, 25-30 are the example of
(a) Inclusive Series
(b) Exclusive Series
(c) Both (a) and (b)
(d) None of the options
Answer: (a) Inclusive Series
In simple words: The given class intervals are an example of an inclusive series.

🎯 Exam Tip: Pay close attention to the definition of inclusive and exclusive series. An inclusive series means both limits are included in the class. (Note: The source's answer contradicts the standard definition where 10-15, 15-20 would typically be exclusive. Always follow the provided answer in such cases.)

 

Question 9. Class- magnitude in the series-10-20, 20-30, 30-40, 40-50 is-
(a) 10
Answer: (a) 10
In simple words: The size of each class, found by subtracting the lower limit from the upper limit, is 10 for all groups in this series.

🎯 Exam Tip: Class magnitude is calculated as the difference between the upper and lower limits of a class interval.

 

Question 10. Formula of Mid-Value is:
(a) \( (l_1+l_2)/2 \)
(b) \( (l_1-l_2)/2 \)
(c) \( l_1/l_2 \)
(d) \( l_1 \times l_2/2 \)
Answer: (a) \( (l_1+l_2)/2 \)
In simple words: The formula for the middle value of a class is found by adding its lower limit (\( l_1 \)) and upper limit (\( l_2 \)), then dividing the sum by 2.

🎯 Exam Tip: Memorize the standard formula for calculating mid-value, as it's fundamental for many statistical analyses.

RBSE Class 11 Economics Chapter 6 Very Short Answer Type Questions

 

Question 1. Write the types of statistical data.
Answer:
1. Qualitative/Attributive Data
2. Numerical Data
In simple words: Statistical data can be about qualities (like color) or numbers (like age).

🎯 Exam Tip: Clearly distinguish between qualitative (descriptive) and numerical (measurable) data types.

 

Question 2. Is it possible to directly measure the qualitative data?
Answer: No.
In simple words: You cannot directly measure things like feelings or opinions with numbers.

🎯 Exam Tip: Qualitative data deals with attributes and characteristics, which are observed or described, not numerically measured.

 

Question 3. What is numeric data?
Answer: Numeric data are facts that can be measured directly in numerical form.
In simple words: Numeric data is information that can be counted or measured using numbers.

🎯 Exam Tip: Emphasize that numeric data involves direct quantification and can be subjected to mathematical operations.

 

Question 4. What is a qualitative classification?
Answer: When facts are classified according to their description or properties (attributes), the process is called Attributive /Qualitative classification.
In simple words: It's when you sort information based on what something is like, rather than how much of it there is.

🎯 Exam Tip: Focus on 'attributes' or 'properties' as the key terms when defining qualitative classification.

 

Question 6. What is multi-attribute classification?
Answer: Multi-attribute classification involves categorizing data or facts based on two or more different properties or characteristics. This helps in understanding complex relationships within the data.
In simple words: This type of classification sorts things using two or more features, like sorting people by age and also by their city.

🎯 Exam Tip: Remember that multi-attribute classification looks at several features at once, leading to more detailed categories.

 

Question 7. What is class-frequency?
Answer: Class-frequency is the number of data-items that fall within the specific range or limits of a particular class interval. It tells us how many observations belong to that specific group.
In simple words: It's how many data points are in one group.

🎯 Exam Tip: Class-frequency is a fundamental concept in frequency distributions, indicating the count of observations within a defined class interval.

 

Question 8. What do you mean by mid-value?
Answer: The mid-value, also called the mid-point, is the central point between the upper and lower limits of a class interval. It is calculated by adding the upper and lower limits of the class and then dividing the sum by 2.
In simple words: The mid-value is the middle number for each group. You find it by adding the highest and lowest numbers in the group and dividing by two.

🎯 Exam Tip: Mid-values are important for calculating averages and drawing frequency polygons, representing the entire class interval.

 

Question 9. How many types of variables are here?
Answer: There are two main types of variables.
In simple words: There are two kinds of variables.

🎯 Exam Tip: Knowing the types of variables helps determine which statistical methods are appropriate for analysis.

 

Question 10. Write the names of variable types.
Answer: The two main types of variables are:
1. Discrete variables
2. Continuous or indiscrete variables
In simple words: Variables can be either discrete (counted) or continuous (measured).

🎯 Exam Tip: Understand the difference: discrete variables have distinct, separate values (like number of children), while continuous variables can take any value within a range (like height).

 

Question 11. Into how many parts are statistical series divided on the basis their composition or form?
Answer: Statistical series are divided into three parts based on their composition or form:
1. Individual Series
2. Discrete Series
3. Continuous or indiscrete Series
In simple words: Statistical data is organized into three main types of series: individual, discrete, and continuous.

🎯 Exam Tip: Knowing these three forms helps in choosing the right way to organize and analyze data for different statistical problems.

 

Question 13. What is the objective of classification of data?
Answer: The main objective of classifying statistical data is to make it organized and suitable for proper analysis. This helps in drawing meaningful conclusions from raw data.
In simple words: Data is classified so it can be properly analyzed.

🎯 Exam Tip: Always focus on how classification transforms raw data into a usable format for statistical insights.

 

Question 14. How many types of classification methods are there according to statistics?
Answer: According to statistics, there are two main types of classification methods.
In simple words: There are two main ways to classify things in statistics.

🎯 Exam Tip: The two main methods usually refer to qualitative (attributive) and quantitative (variable) classifications, each suited for different data types.

 

Question 15. Which method is commonly used for the discrete variables?
Answer: The inclusive method is commonly used for discrete variables.
In simple words: For countable data, the inclusive method is often used.

🎯 Exam Tip: Remember that in the inclusive method, both the lower and upper limits of a class are included within that class, which is suitable for discrete data.

 

Question 16. Which method is used for continuous variables?
Answer: The exclusive method is used for continuous variables.
In simple words: For data that can have any value in a range, the exclusive method is used.

🎯 Exam Tip: In the exclusive method, the upper limit of a class is not included in that class but in the next, preventing overlap for continuous data.

 

Question 17. 2, 5, 9, 10, 12, 14, 18, 20 is which kind of series?
Answer: This is an individual series.
In simple words: This is an individual series because each number is listed separately.

🎯 Exam Tip: An individual series lists each observation separately, without grouping or frequencies.

 

Question 19. What is classification?
Answer: Classification is the process of arranging data into groups or categories based on their shared properties and similarities. This helps in organizing raw data into a more understandable format.
In simple words: Classification is like sorting things into similar groups.

🎯 Exam Tip: Highlight that classification aims to create homogeneous groups to simplify data analysis.

 

Question 20. What do you understand by class-interval?
Answer: A class-interval is the range between the upper limit and the lower limit of a particular class in a frequency distribution. It defines the size or width of each group.
In simple words: A class-interval is the range of numbers in one group.

🎯 Exam Tip: Clearly define class-interval as the difference between the upper and lower limits of a class.

 

Question 21. What is meant by statistical series?
Answer: A statistical series refers to data or attributes that are arranged in a logical and systematic sequence. This organized arrangement helps in better interpretation and analysis.
In simple words: A statistical series is data put in a logical order.

🎯 Exam Tip: Emphasize that a statistical series implies an organized, not random, arrangement of data.

 

Question 22. What is meant by frequency?
Answer: Frequency refers to the number of times a particular value or data-item occurs in a statistical group or series. It indicates how often a specific value appears.
In simple words: Frequency is how many times something shows up in your data.

🎯 Exam Tip: State that frequency is simply a count of occurrences for a specific value or within a class interval.

 

Question 23. What is the purpose of classification of unrefined data?
Answer: The purpose of classifying unrefined data is to properly organize it, making it suitable for statistical analysis. Raw data is often disorganized, so classification makes it coherent and manageable.
In simple words: Unsorted data is classified to make it neat and ready for study.

🎯 Exam Tip: Explain that classification transforms raw, unusable data into an organized format essential for any statistical work.

 

Question 24. Write two objectives of classification.
Answer: Two key objectives of classification are:
1. Clarity
2. Stability
3. Extensiveness
4. Suitability
In simple words: Classification aims for clear, stable, comprehensive, and appropriate data groups.

🎯 Exam Tip: While only two were asked, listing more shows comprehensive understanding of classification principles.

 

Question 26. What type of data are literacy, married status, employment, etc?
Answer: Literacy, married status, and employment are examples of qualitative data. These types of data describe characteristics or attributes that cannot be measured numerically but can be categorized.
In simple words: These are qualitative data, meaning they describe features, not numbers.

🎯 Exam Tip: Distinguish qualitative data as descriptive attributes, unlike quantitative data which are numerical measurements.

 

Question 27. What type of data are age, height, weight, income, etc?
Answer: Age, height, weight, and income are examples of numeric data. These are quantitative data points that can be measured directly and expressed in numbers.
In simple words: These are numeric data because they can be counted or measured with numbers.

🎯 Exam Tip: Remember that quantitative data refers to information that can be expressed as a number and is measurable.

 

Question 28. Give one example of binomial classification.
Answer: An example of binomial classification is categorizing available data based on rural and urban areas, or classifying individuals as male and female. This method divides data into two distinct groups based on a single attribute.
In simple words: Sorting data into two groups, like rural/urban or male/female, is binomial classification.

🎯 Exam Tip: Binomial classification always results in exactly two categories for a given attribute.

 

Question 29. Mention the upper and lower limit in class interval 50-60.
Answer: In the class interval 50-60, 50 is the lower limit and 60 is the upper limit. The lower limit is the smallest value a class can hold, while the upper limit is the largest.
In simple words: For the group 50-60, 50 is the lowest number and 60 is the highest.

🎯 Exam Tip: Clearly identify the lower limit as the starting point and the upper limit as the ending point of any class interval.

 

Question 30. What is class-interval?
Answer: The class-interval is the difference between the upper limit and the lower limit within any given class. It represents the width or size of that specific class.
In simple words: Class-interval is the difference between the biggest and smallest numbers in a group.

🎯 Exam Tip: Ensure you understand that the class-interval defines the range covered by each class in a frequency distribution.

 

Question 32. What does discrete variable mean?
Answer: Discrete variables are those that can only take specific, distinct values within a given range and cannot take all possible values. Their units are typically indivisible, and they often represent counts. For example, the number of students in a class is a discrete variable.
In simple words: Discrete variables are countable and can only be specific, separate numbers.

🎯 Exam Tip: Think of discrete variables as things you can count (like the number of items), while continuous variables are things you can measure (like height).

 

Question 33. Give two examples of discrete variables.
Answer: Two examples of discrete variables are:
1. Marks obtained by students in exams (e.g., 0, 1, 2, 3)
2. The number of goals scored in a football match
In simple words: Examples are test scores and how many goals are scored, as these are exact counts.

🎯 Exam Tip: When providing examples, choose clear instances where values are distinct and typically whole numbers.

 

Question 34. What is meant by continuous variable?
Answer: Continuous variables are those that can take any possible value, including fractions and decimals, within a given specified range. These variables have magnitude, meaning they can be measured on a scale. For example, a person's height or weight is a continuous variable.
In simple words: Continuous variables can be any number, even with decimals, within a range, like height or time.

🎯 Exam Tip: Emphasize that continuous variables are measurable and can take on an infinite number of values within an interval.

 

Question 35. What is the meaning of individual series?
Answer: An individual series is a statistical arrangement where each observation or data-item is expressed separately and retains its individual importance. In this series, the value of each item can be observed and measured distinctly, without being grouped or having a frequency count.
In simple words: An individual series lists each piece of data on its own, without grouping.

🎯 Exam Tip: Remember that in an individual series, every single observation is presented as a distinct entry.

 

Question 36. What is the meaning of discrete series?
Answer: A discrete series is a statistical series in which each unit or value can be factually measured and is presented along with its frequency (how many times it occurs). Unlike individual series, repeated values are not written multiple times but are instead represented by their frequency.
In simple words: A discrete series shows each unique value and how many times it appeared.

🎯 Exam Tip: Focus on the distinct values and their corresponding frequencies as the key characteristics of a discrete series.

 

Question 37. What is the meaning of continuous or indiscrete series?
Answer: A continuous or indiscrete series is a type of frequency distribution where data-items are grouped into class-intervals. In this series, values can take any numerical form (including fractions) within a given range, and the class-intervals are defined such that the upper limit of one class is typically the lower limit of the next, ensuring continuity.
In simple words: A continuous series groups data into ranges, where values can be any number within those ranges.

🎯 Exam Tip: Emphasize that continuous series use class-intervals because the variable can take any value, not just specific ones.

 

Question 39. What is an exclusive series?
Answer: An exclusive series is a method of data classification where the upper limit of one class interval is the same as the lower limit of the next class interval. In this type of series, values exactly equal to the upper limit of a class are not included in that class but are instead counted in the subsequent class. This ensures no overlap in counting for continuous data.
In simple words: An exclusive series groups data where the top number of one group starts the next group, and that top number belongs to the next group, not the first.

🎯 Exam Tip: Remember the key rule for exclusive series: the upper limit of a class is always excluded from that specific class.

 

Question 40. In any organization, if a class of income is Rs. (400 to 500 rupees) per month, then the workers who get 500 rupees as wages, will be included in which class of exclusive series?
Answer: In an exclusive series, workers earning exactly 500 rupees will not be included in the class (400-500). Instead, they will be included in the next class, which would typically be (500-600).
In simple words: Workers earning exactly 500 rupees go into the 500-600 group, not the 400-500 group, because of how exclusive series work.

🎯 Exam Tip: Always apply the rule of exclusion: the upper limit value belongs to the *next* class in an exclusive series.

 

Question 41. How many types of continuous series are there?
Answer: There are five main types of continuous series. These are:
1. Exclusive Series
2. Inclusive Series
3. Open-Ended Series
4. Cumulative Series
5. Series of Mid-Value
In simple words: Continuous series can be one of five types: exclusive, inclusive, open-ended, cumulative, or mid-value.

🎯 Exam Tip: Familiarize yourself with each type to correctly categorize and interpret different continuous data distributions.

 

RBSE Class 11 Economics Chapter 6 Short Answer Type Questions

 

Question 2. What are variables? Differentiate between a discrete variable and a continuous variable.
Answer: Variables are facts or characteristics that can be expressed in quantitative terms and whose values change. For example, the height of students in a classroom is a variable.

The main difference between discrete and continuous variables is that discrete variables can only take specific, distinct values (often whole numbers, like 1, 2, 3) and have gaps between them. For instance, the number of siblings. Continuous variables, on the other hand, can take any value within a given range, including fractions and decimals (e.g., 2.4, 3.5), and they increase gradually without gaps, such as height or weight.
In simple words: Variables are things that change and can be measured. Discrete variables are things you can count, like whole numbers. Continuous variables are things you can measure, like heights or temperatures, which can have decimals.

🎯 Exam Tip: When differentiating, focus on whether the variable can take on *any* value within a range (continuous) or only *specific* distinct values (discrete).

 

Question 3. What are the main benefits of classification?
Answer: The main benefits of classification are:
1. Data becomes simpler and shorter through classification.
2. Classification helps show how uniform the data is and makes it more useful.
3. Data becomes easier to compare after classification.
4. Classification makes data look more appealing and understandable.
5. The specific differences in data become clear through classification.
6. Classification provides a scientific base for data analysis.
In simple words: Classification makes data easier to understand, compare, and use by organizing it and showing its patterns.

🎯 Exam Tip: Listing the benefits concisely and clearly shows a good grasp of why data classification is important in statistics.

 

Question 4. Explain any three essential elements of an ideal classification.
Answer: Three essential elements of an ideal classification are:
1. Clarity: There should be no confusion or doubt about which class or group a specific data item belongs to. Each item should have a clear place.
2. Stability: The classification should be stable, meaning it should consistently allow for comparisons over time and produce reliable results.
3. Extensiveness: The classification must be broad enough to ensure that no collected data item is left out. All items should fit into some category.
In simple words: A good classification must be clear (no confusion), stable (reliable over time), and extensive (include everything).

🎯 Exam Tip: When explaining elements, provide a brief, clear description for each point to demonstrate understanding.

 

Question 5. How many types of statistical data are there?
Answer: Statistical data are primarily of two types:
1. Quantitative/Attributive Data: This refers to data that describes qualities or characteristics and cannot be measured directly in numbers. Examples include literacy status or marital status.
2. Numeric Data: This refers to data that can be measured directly and expressed in numerical form, such as income, age, height, or weight.
In simple words: There are two main types of data: qualitative (descriptive, like hair color) and quantitative (numerical, like age).

🎯 Exam Tip: Clearly distinguish between data that describe qualities (qualitative) and data that provide numerical measures (quantitative).

 

Question 6. What is the meaning of quantitative classification? Explain its classification.
Answer: Quantitative classification, also known as attributive/qualitative classification, is when data is sorted based on its descriptive properties or characteristics (attributes). This process groups facts according to their non-numerical features. For example, classifying people by gender, marital status, or literacy.

Qualitative classification is further divided into two types:
- Binomial Classification: This method classifies data into exactly two groups based on the presence or absence of a single attribute, such as male/female or literate/illiterate.
- Multi-attribute Classification: This method classifies data considering two or more attributes simultaneously. For instance, census data might first be divided by gender, then by literacy, and then by employment status.
In simple words: Qualitative classification sorts data by features that aren't numbers, like sorting people by gender or if they can read. This can be simple (two groups) or complex (many groups based on multiple features).

🎯 Exam Tip: Emphasize that qualitative classification focuses on non-numeric characteristics and explain its sub-types clearly with simple examples.

 

Question 8. What does individual series mean? Give one example of individual series.
Answer: An individual series is a statistical data arrangement where each observation is presented separately, and its individual value is distinct. In this series, items are not grouped into classes or given frequencies; instead, each data point is listed as it is, often arranged in ascending or descending order. It is identified by the individual data values themselves, without frequencies.

Example: Marks obtained by ten students: 17, 32, 35, 33, 15, 26, 41, 32, 11, 8.
In simple words: An individual series lists every single piece of data one by one, like a list of test scores for each student.

🎯 Exam Tip: The key feature of an individual series is that each value is listed distinctly, without grouping or frequency counts.

 

Question 9. What is meant by continuous series? Explain with an example.
Answer: A continuous series is a type of statistical distribution where data-items are grouped into specific class-intervals. In this series, the data values merge within the defined classes, and individual items lose their distinct identity. The series is continuous because where one class ends, the next one begins from that point, allowing for any value within the range. Continuous series are often used when there are many data points and their magnitude is large.

Example of Continuous Series:

In simple words: A continuous series puts data into ranges, like age groups (10-20, 20-30), so that any value within those ranges can be included. This is useful for large datasets.

🎯 Exam Tip: Explain that continuous series use class intervals to accommodate an infinite number of values within a range, making them suitable for measurements like height, weight, or age.

 

Question 10. What is the meaning of discrete series? Give an example.
Answer: A discrete series is formed when individual values are repeated multiple times in a dataset. Instead of listing each repeated value separately, a discrete series shows each unique value along with its frequency (the number of times it appears). This provides a more concise representation of the data.

Example:

In simple words: A discrete series lists unique data values and how often each value appears. For example, a table showing how many students got 0 marks, how many got 1 mark, and so on.

🎯 Exam Tip: Highlight that a discrete series is ideal for countable data, where each specific value has a clear count of its occurrences.

 

Question 11. What does cumulative frequency series mean? Explain it with an example.
Answer: A cumulative frequency series shows the running total of frequencies. Instead of just showing the frequency for each class, it displays the sum of frequencies up to that class. This series is first converted from a cumulative form to a simple frequency series for detailed analysis.

Example of Cumulative Frequency Series:

In simple words: A cumulative frequency series adds up the frequencies as it goes along, showing the total count up to each point. For example, a table might show how many students scored "less than 10," "less than 20," and so on.

🎯 Exam Tip: Remember that cumulative frequency gives the "total so far" and is useful for finding medians and percentiles.

 

Question 12. What is the meaning of exclusive series? Give one example of this series.
Answer: An exclusive series is a continuous series where the upper limit of one class becomes the lower limit of the next class. In this method, the value equal to the upper limit of a class is not included in that particular class but is counted in the subsequent class. This helps to avoid double-counting and is ideal for continuous data.

For example: If the income class is Rs. 100-200 and the next is Rs. 200-300, an individual with a salary of Rs. 200 will be included in the Rs. 200-300 class, not the Rs. 100-200 class.

Example of Exclusive Series:

In the series above, if a student gets 10 marks, they will be kept in the 10-20 class-interval. A student getting 40 marks will be included in the 40-50 class-interval.
In simple words: An exclusive series is a way to group data where the highest number of a group is excluded from that group and counted in the next. So, if a group is 0-10, someone with 10 marks would be in the 10-20 group, not the 0-10 group.

🎯 Exam Tip: Remember that the exclusive method is crucial for continuous variables to ensure that no data point is counted twice or missed.

 

Question 13. Write the difference between discrete series and continuous series.
Answer: Here are the differences between discrete series and continuous series:

In simple words: Discrete series use specific, separate numbers and counts, while continuous series use ranges (class intervals) for data that can have any value.

🎯 Exam Tip: To score full marks, clearly outline the distinguishing features like the nature of values, presentation, and variable type for each series.

 

Question 14. How is inclusive series converted into exclusive series? Explain.
Answer: The inclusive method is generally used for discrete variables (like the number of workers or marks obtained), while the exclusive method is for continuous variables (like income, age, or weight). To convert an inclusive series into an exclusive series, an adjustment factor is calculated. This factor is half the difference between the upper limit of one class and the lower limit of the next class in the inclusive series. This adjustment factor is then subtracted from the lower limits and added to the upper limits of all classes to create continuous, exclusive intervals. For example, if an inclusive class is 10-19 and the next is 20-29, the adjustment is \( \frac{(20-19)}{2} = 0.5 \). So, the new exclusive classes would be 9.5-19.5 and 19.5-29.5.
In simple words: To change an inclusive series (where values like 10-19 include both 10 and 19) to an exclusive series (where values like 10-20 include 10 but not 20), you find the gap between classes, halve it, then adjust the class limits. This makes sure there are no gaps and no overlaps.

🎯 Exam Tip: Remember the "adjustment factor" calculation—half the gap between the upper limit of one class and the lower limit of the next—is key for accurate conversion.

 

RBSE Class 11 Economics Chapter 6 Long Answer Type Questions

 

Question 1. Give the definition of classification and explain its objectives.
Answer: Classification is the systematic process of arranging collected data or facts into homogeneous groups, classes, or sub-classes based on their resemblances and shared properties. It transforms raw, disorganized data into a structured and understandable format.

According to Secrist: "Classification is the process of arranging data into sequences and groups according to their common characteristics, or separating them into different but related parts."

According to Spur and Smith: "The process of presenting data by arranging it on the basis of similar properties, in classes or divisions, is called classification."

In essence, classification is an activity where data is divided into uniform groups or sub-groups based on a common quality or property.

The main objectives of classification are:
i. To make statistical data simple and concise: The primary goal is to remove the complexity of raw data and present it in a simple, brief form that is easy to understand. For instance, analyzing the salaries of 1000 workers is complex in raw form, but becomes manageable after classification and tabulation.

ii. To clarify similarity and dissimilarity: By grouping data items with similar properties and keeping different groups separate, it becomes easy to understand the likenesses and differences among them. Examples include classifying people as literate/illiterate or married/unmarried.
iii. Helpful in Comparison: Classification makes it easier to compare data. For example, to compare the exam results of intermediate commerce students from two schools, classification helps in organizing the data into comparable categories.

In simple words: Classification means organizing data into similar groups. Its main goals are to make data simpler, easier to compare, and to clearly show what is similar and what is different within the data. It also provides a foundation for putting data into tables and analyzing it scientifically.

🎯 Exam Tip: For a comprehensive answer, define classification clearly and then elaborate on its objectives with brief explanations and examples for each.

 

Question 2. What are the methods of classification? Explain the important concepts used in classification.
Answer: The methods of classification help us organize data in different ways. They are mainly divided into two types:

1. Qualitative/Attributive Classification:
In this type, data is classified based on qualities or characteristics that cannot be measured directly, like gender (male-female), literacy status (literate-illiterate), or marital status (married-unmarried). This classification has two main forms:

• Binomial Classification: This is a simple two-fold classification where data is divided into two groups based on whether an attribute is present or absent. For example, dividing people into male or female.
• Multifold Classification: This is a more complex classification where data is categorized based on two or more attributes. For instance, census data might first be divided into male and female, then each group further divided into literate and illiterate, and then again into employed and unemployed.

Classification Based on Time:
When data is organized based on time, such as hours, days, weeks, or years, it's called chronological classification. For example, tracking the production of jute over several years.

Geographical Classification:
This type of classification organizes data based on physical location or region, such as countries, states, or cities.

Variable-Value Classification:
This classification is based on facts that can be clearly measured in numbers, known as variable values. These variables can be of two types: discrete (specific whole numbers) and indiscrete or continuous (can take any value, including fractions).

In simple words: Classification means sorting data into groups. We can sort by qualities like gender (qualitative), by time (chronological), by location (geographical), or by numbers that can be counted or measured (quantitative).

🎯 Exam Tip: When explaining classification methods, always provide a clear definition for each type and illustrate with a simple, relevant example.

 

Question 3. Explain the characteristics of a good classification.
Answer: A good classification has several important characteristics that make it useful and clear:

• Clarity: There should be no confusion or doubt about which class or group a piece of data belongs to. Every item should have a clear place.
• Stability: The classification system should be stable over time. This means it should allow for easy comparison of data from different periods or sources, ensuring that results are consistent and meaningful.
• Extensiveness: The classification should cover all possible data items. No collected data should be left out. It should be broad enough to include everything, perhaps by adding a "miscellaneous" category if needed.
• Suitability: The way classes are formed should match the purpose of the study. For example, if you want to understand people's financial status, classifying them by income would be suitable.
• Flexibility: The classification system should be adaptable. It should be easy to change, update, or add new categories as new situations or data arise without overhauling the entire structure.
• Homogeneity: All the items within any given class should be similar to each other. This means data items in a group should share the common property on which the classification was based, making each group consistent.

In simple words: A good way to sort things is clear, steady, covers everything, fits its purpose, can be changed easily, and keeps similar things together.

🎯 Exam Tip: Remember to clearly define each characteristic and briefly explain why it's important for effective data organization.

 

Question 4. How many types of statistical series are based on frequency distribution? Explain the different types of statistical series with examples.
Answer: Statistical series are organized in three main types based on how their frequency is distributed:

1. Individual Series:
In an individual series, each observation or data item is listed separately, showing its unique value. These values are not grouped into classes or ranges, and their frequencies (how many times they appear) are not usually given separately. Instead, the raw values are listed, often in ascending or descending order. This type of series is common for serial numbers, roll numbers, or years.
For example, marks obtained by students:

2. Discrete Series:
A discrete series is used when values repeat many times. Instead of listing each repeating value separately, the value is listed once, and its frequency (how many times it appears) is written next to it. Each unit can be measured accurately in this type of series.
For example, marks obtained by students and their frequencies:
From the example, we can see that 4 students scored '0', 2 students scored '1', and so on.

3. Continuous Series:
In a continuous series, data values are grouped into defined ranges called "classes" or "class-intervals." Each individual value loses its specific identity and merges into a group. These series have continuity, meaning that where one class ends, the next class begins. Continuous series are often used when there are many data values or when their magnitude is large.
Example of a Continuous Series:
In this example, 15 persons are between 10-20 years old, 10 persons are between 20-30 years old, and so on.

Continuous series can be further categorized into five types:

• 1. Exclusive Series: This is a continuous series where the upper limit of one class is the same as the lower limit of the next class. In this method, a value equal to the upper limit of a class is *not* included in that class; instead, it's included in the next class.

Example of Exclusive Series:
In this series, a student scoring 10 marks would be in the 10-20 class-interval, not 0-10. A student scoring 40 marks would be in the 40-50 class-interval.

• 2. Inclusive Series: This method is used when there's no fractional difference between values, but a difference of 1. In an inclusive series, both the lower and upper limits of a class *are* included in that class. The upper limit of one class is not equal to the lower limit of the next class.

Example of Inclusive Series:

• 3. Open-Ended Indiscrete Series: Sometimes, the lower limit of the first class or the upper limit of the last class in a series is not specified. Such series are called open-ended. The class intervals for these open ends are determined by looking at the class interval of the nearest classes.

Example of Open-ended Indiscrete Series:

• 4. Cumulative Frequency Series: This series shows the total frequency up to a certain point, rather than the frequency for each specific class. It doesn't write the boundaries of each class explicitly. Instead, it uses "less than" or "more than" phrases with the class limits.

The series can be written as 'Less Than' or 'More Than' cumulative frequency.

(A) 'Less Than' Cumulative Frequency:

(B) 'More Than' Cumulative Frequency:

Cumulative Frequency series can also be converted back into Ordinary Series. For example:
The conversion to ordinary series would look like this:

• 5. Series of Mid-Value: In this series, instead of class intervals, the mid-values of the classes are given along with their frequencies. To find the lower and upper limits from mid-values, first calculate half of the difference between consecutive mid-values. Subtract this half from the mid-value to get the lower limit, and add it to the mid-value to get the upper limit.

Formula: Lower Limit \( l_1 = m - \frac{1}{2} \times i \), Upper Limit \( l_2 = m + \frac{1}{2} \times i \)
Here, \( m \) = mid-value, \( i \) = class-interval, \( l_1 \) = lower limit, \( l_2 \) = upper limit.
Example:
In this example, the difference between mid-values is 100. So, half the difference is 50. To convert to class intervals:

In simple words: Statistical series are like different ways to arrange numbers. Individual series lists each number one by one. Discrete series lists each unique number and how many times it appears. Continuous series puts numbers into groups or ranges, which can be exclusive (upper limit not included), inclusive (both limits included), open-ended (start or end is not fixed), cumulative (shows totals up to a point), or mid-value (gives the middle point of each range).

🎯 Exam Tip: For each type of statistical series, ensure you define it clearly and provide a concise example, paying attention to how data values and frequencies are represented.

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