ICMA Foundation- FBMS- Booster Test-NCERT-Class 11 Statistics for Economics- Test 1- Organisation of Data_Frequency Distribution
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QUESTION 1 OF 20
What is the primary purpose of classifying raw data in statistics?
QUESTION 2 OF 20
In statistical organisation, grouping based on some criteria means:
QUESTION 3 OF 20
What is the primary characteristic of unclassified or raw data?
QUESTION 4 OF 20
How does summarising raw data by classification resolve the difficulty of handling large datasets?
QUESTION 5 OF 20
When data are classified either in ascending or descending order with reference to time, such as years or months, it is known as:
QUESTION 6 OF 20
The yield of wheat classified across different countries like Canada, China, France, and India is an example of which type of classification?
QUESTION 7 OF 20
Characteristics such as nationality, literacy, religion, and gender that cannot be measured quantitatively are called:
QUESTION 8 OF 20
A classification based on whether a population is married or unmarried represents data grouped by the:
QUESTION 9 OF 20
When collected data regarding characteristics like height, weight, age, or income are grouped into classes, this is known as:
QUESTION 10 OF 20
When the frequency of a class is expressed as a proportion or percentage of the total frequency, it is referred to as:
QUESTION 11 OF 20
A variable that is capable of taking any numerical value, including exact fractions and values like 1.414, is defined as a:
QUESTION 12 OF 20
Which statement correctly describes a continuous variable's ability to manifest values?
QUESTION 13 OF 20
A variable that changes its value only by finite jumps and does not take any intermediate value between them is called a:
QUESTION 14 OF 20
Suppose a variable takes values like 1/8, 1/16, and 1/32, but it cannot take any value in between these adjacent fractional values. This variable is:
QUESTION 15 OF 20
Which of the following is defined as a comprehensive way to classify raw data of a quantitative variable, showing how different values are distributed in different classes?
QUESTION 16 OF 20
In a frequency distribution, the number of values or observations that fall into a particular class is referred to as the:
QUESTION 17 OF 20
The lowest and highest values that bound each class in a frequency distribution are called:
QUESTION 18 OF 20
The difference between the upper class limit and the lower class limit of a particular class is known as the:
QUESTION 19 OF 20
Once raw data are grouped into classes, which of the following is used to represent the class in further statistical calculations?
QUESTION 20 OF 20
How is the class mark or mid-value of a class calculated?
Test Complete!
Answer Review
1 What is the primary purpose of classifying raw data in statistics?
The purpose of classifying raw data is to bring order to it, making it manageable and easier to subject to statistical analysis. (NCERT Page 23)
Classification inherently brings order to raw, unorganized data, which is essential for any statistical analysis.
A) To make data collection more time-consuming: Classification saves time and effort; it does not make the process more time-consuming. C) To increase the chaotic nature of the variables: Classification removes chaos by organising data, not increasing it. D) To avoid using statistical methods completely: Classification is a preparatory step for using statistical methods, not a way to avoid them.
Contextual or Tonal Matching: The word "classifying" implies organization and structure. Option B matches the positive, constructive tone of organizing data, whereas the other options describe negative or counterproductive outcomes.
Classify = Clarify.
2 In statistical organisation, grouping based on some criteria means:
Classification is the process of arranging or organising things into groups or classes based on some criteria, similar to how a kabadiwallah groups junk according to the markets for reused goods. (NCERT Page 23)
Grouping requires a specific criterion or characteristic to effectively organize different items into distinct classes.
A) Arranging items randomly without any specific purpose: Grouping is deliberate and based on criteria, not random. C) Collecting only one type of data to avoid confusion: Grouping deals with sorting multiple types of data, not just limiting collection to one type. D) Putting unrelated subjects together in the same group: Putting unrelated subjects together defeats the entire purpose of grouping.
Elimination: Options A and D describe actions that create disorder, which contradicts the concept of "grouping." Option C refers to data collection, not grouping. Option B correctly defines the process.
Criteria = Characteristics.
3 What is the primary characteristic of unclassified or raw data?
Like a kabadiwallah's junk, raw data are highly disorganised, large, and cumbersome, making it difficult to draw meaningful conclusions directly from them. (NCERT Page 24)
Raw data is the initial, unprocessed collection of observations, which naturally lacks organization.
A) They yield to statistical methods easily and quickly: Raw data do not yield to statistical methods easily; they must be organised first. C) They are already grouped according to specific variables: Grouped data is classified data, not raw data. D) They consist only of small, manageable sets of numbers: Raw data are often very large, not just small sets.
Contextual or Tonal Matching: The term "raw" implies something unprocessed or unrefined. Option B aligns with this by describing the data as disorganized and cumbersome.
Raw = Rough and Random.
4 How does summarising raw data by classification resolve the difficulty of handling large datasets?
Raw data are summarised and made comprehensible by classification. Placing facts of similar characteristics in the same class enables one to locate them easily, make comparisons, and draw inferences. (NCERT Page 25)
Classification simplifies large datasets by grouping similar observations together, allowing for efficient analysis.
A) By reducing the number of variables observed during data collection: Classification happens after data collection, not by changing what is observed. B) By eliminating the highest and lowest values to shrink the dataset: Classification organizes all data; it does not delete extreme values. D) By converting all numerical values into qualitative attributes: Classification groups data but does not change the fundamental nature (quantitative to qualitative) of the numbers.
Elimination: Options A, B, and D suggest altering or deleting the actual data collected. Option C correctly describes organizing the existing data without losing its core characteristics.
Similar Facts = Same Class.
5 When data are classified either in ascending or descending order with reference to time, such as years or months, it is known as:
When data are grouped according to time, such as years, quarters, months, or weeks, the classification is known as a Chronological Classification. (NCERT Page 25)
Time-based arrangement of data is by definition chronological.
A) Spatial Classification: This refers to classification based on geographical locations, not time. B) Qualitative Classification: This is classification based on attributes or qualities, not time. D) Quantitative Classification: This is classification based on numerical values or magnitudes, not time periods.
Odd One Out: The word "chrono" means time. Therefore, chronological uniquely aligns with time-based classification like years or months.
Chrono = Clock (Time).
6 The yield of wheat classified across different countries like Canada, China, France, and India is an example of which type of classification?
In Spatial Classification, data are classified with reference to geographical locations such as countries, states, cities, or districts. (NCERT Page 26)
Geographical data points (countries, states) are defined as spatial classifications.
B) Chronological Classification: This is based on time, whereas countries are geographical locations. C) Attribute Classification: While countries have names, geographical grouping specifically falls under spatial classification in statistical terms. D) Continuous Classification: This refers to numerical continuous variables, not geographical locations.
Contextual or Tonal Matching: The word "space" relates to geography and location. "Spatial" classification perfectly matches data categorized by countries.
Spatial = Space/Location.
7 Characteristics such as nationality, literacy, religion, and gender that cannot be measured quantitatively are called:
Sometimes characteristics cannot be expressed quantitatively (e.g., nationality, literacy). Such characteristics are called Qualities or Attributes. (NCERT Page 26)
Non-measurable, descriptive characteristics in statistics are formally termed attributes.
A) Continuous variables: Continuous variables can take any numerical value and are quantitatively measured. B) Discrete variables: Discrete variables take specific numerical values (finite jumps) and are quantitatively measured. D) Class marks: Class marks are numerical mid-points of quantitative class intervals.
Elimination: Options A, B, and D all relate strictly to numbers and mathematics. Option C relates to non-numerical descriptors, which fits the question.
Attributes = Words, not numbers.
8 A classification based on whether a population is married or unmarried represents data grouped by the:
Attributes can be classified on the basis of either the presence or the absence of a qualitative characteristic. For example, population grouped into married or unmarried. (NCERT Page 26-27)
Qualitative classification divides data based on whether an attribute exists in the subject or not.
A) Exact numerical magnitude of the attribute: Attributes cannot be measured by exact numerical magnitudes. C) Infinite gradations of a continuous variable: Marital status is a quality, not a continuous variable with infinite gradations. D) Class width of a spatial variable: Marital status is not a spatial (geographical) variable and does not have a class width.
Contextual or Tonal Matching: Being married or unmarried is a binary state (yes/no). This directly aligns with the concept of "presence or absence" of a trait.
Qualitative = Present or Absent.
9 When collected data regarding characteristics like height, weight, age, or income are grouped into classes, this is known as:
Characteristics like height, weight, age, and income are quantitative in nature. When data of such characteristics are grouped into classes, it becomes a Quantitative Classification. (NCERT Page 27)
Measurable numerical variables form the basis of quantitative classification.
A) Spatial Classification: Based on locations, not measurable numerical data. B) Chronological Classification: Based on time, not general numerical data like height or weight. C) Qualitative Classification: Based on non-measurable attributes, not numbers.
Substitution: Substitute the examples (height, weight, age) with their core trait: they are all measured in numbers (quantities). Therefore, it must be Quantitative Classification.
Quantity = Counting numbers.
10 When the frequency of a class is expressed as a proportion or percentage of the total frequency, it is referred to as:
If the values of frequency are expressed as a proportion or percentage of the total frequency, this frequency is known as relative frequency. (NCERT Page 27)
Relative frequency relates the individual class frequency to the total frequency as a ratio or percentage.
B) Cumulative Frequency: This is the running total of frequencies, not the percentage of the total. C) Absolute Frequency: This is the raw count of observations in a class, not a proportion. D) Class Boundary: This is the limit defining a class, unrelated to frequency proportions.
Contextual or Tonal Matching: A percentage or proportion indicates a relationship relative to the whole. Thus, "Relative Frequency" is the logical term.
Relative = Ratio to total.
11 A variable that is capable of taking any numerical value, including exact fractions and values like 1.414, is defined as a:
A continuous variable can take any numerical value. It may take integral values, fractional values, and values that are not exact fractions. (NCERT Page 27)
A continuous variable can assume an unbroken sequence of numerical values.
A) Discrete variable: Discrete variables take specific, finite values and jump from one value to another without taking intermediate fractions. B) Spatial variable: Spatial relates to geography, not the numerical nature of the variable. D) Qualitative attribute: Attributes are non-numerical qualities.
Elimination: Since the variable takes any numerical value and fractions, it cannot be discrete (which jumps) or qualitative/spatial (which are non-numerical). This leaves continuous.
Continuous = Can be anything (fractions included).
12 Which statement correctly describes a continuous variable's ability to manifest values?
The values of a continuous variable (like height) are capable of manifesting in every conceivable value and can be broken down into infinite gradations. (NCERT Page 28)
Continuous variables measure quantities that can be infinitely subdivided, like weight or time.
A) It can only take whole numbers like 1, 2, and 3: This describes a discrete variable, not continuous. C) It changes only by finite jumps: This is the exact definition of how a discrete variable changes. D) It can only be represented by geographical locations: This relates to spatial classification, not continuous variables.
Extreme Word Filter: Option A ("only take whole numbers") and C ("only by finite jumps") are restricted rules applying to discrete variables. Option B's "infinite gradations" perfectly captures the unbounded nature of continuous variables.
Continuous = Infinite points.
13 A variable that changes its value only by finite jumps and does not take any intermediate value between them is called a:
A discrete variable can take only certain values. Its value changes only by finite "jumps". It jumps from one value to another but does not take any intermediate value between them. (NCERT Page 27-28)
Discrete variables represent countable distinct points (like number of students) rather than measurable scales.
A) Continuous variable: Continuous variables take intermediate and fractional values without jumping. B) Bivariate variable: This refers to two different variables being studied together, not the nature of a single variable's jumps. D) Chronological variable: Refers to time sequence, not numerical jump properties.
Contextual or Tonal Matching: The term "discrete" means distinct or separate. A variable that jumps between distinct, separate values without taking the space between them matches this definition.
Discrete = Distinct Jumps.
14 Suppose a variable takes values like 1/8, 1/16, and 1/32, but it cannot take any value in between these adjacent fractional values. This variable is:
Even though a variable takes fractional values (like 1/8, 1/16), if it cannot take any value between two adjacent fractional values and jumps from one to another, it is a discrete variable. (NCERT Page 28)
The defining trait of a discrete variable is the inability to take intermediate values between its defined steps, regardless of whether those steps are whole numbers or specific fractions.
A) Continuous, because it uses fractions: Using fractions does not make it continuous if it cannot take the intermediate values between those specific fractions. C) Qualitative, because fractions are attributes: Fractions are numerical quantities, not qualitative attributes. D) Spatial, because fractions represent distances: Fractions here represent numerical steps, not necessarily geographical locations.
Elimination: The prompt explicitly states the variable cannot take values in between. This eliminates "Continuous" immediately. Since they are numerical fractions, they are not qualitative or spatial.
No middle ground = Discrete.
15 Which of the following is defined as a comprehensive way to classify raw data of a quantitative variable, showing how different values are distributed in different classes?
A frequency distribution is a comprehensive way to classify raw data of a quantitative variable. It shows how different values of a variable are distributed in different classes. (NCERT Page 28)
A frequency distribution systematically organizes quantitative data into classes alongside their frequencies.
B) Spatial array: Spatial implies geographic distribution, not general quantitative classification. C) Qualitative classification: This deals with attributes, whereas the question asks about quantitative variables. D) Raw data grouping: This is an informal phrase, whereas the formal statistical term is frequency distribution.
Contextual or Tonal Matching: The question asks about "how different values are distributed." The term "Frequency distribution" directly reflects the concept of distributing quantitative counts.
Distribute values = Frequency distribution.
16 In a frequency distribution, the number of values or observations that fall into a particular class is referred to as the:
The term Class Frequency means the number of values in a particular class. (NCERT Page 28)
Frequency indicates how frequently an observation occurs within a specified class bound.
A) Class limit: These are the boundaries (lowest and highest values) of a class. B) Class interval: This is the width or difference between the upper and lower limits of a class. D) Class mark: This is the middle value or average of the class limits.
Elimination: Limit means boundary, interval means gap/width, and mark means midpoint. Only frequency translates to the "count" or "number of values."
Frequency = How many.
17 The lowest and highest values that bound each class in a frequency distribution are called:
Each class in a frequency distribution table is bounded by Class Limits. The lowest value is called the Lower Class Limit and the highest value the Upper Class Limit. (NCERT Page 29)
Limits define the absolute minimum and maximum parameters of a class interval.
A) Class marks: This represents the exact middle value of the class, not the boundaries. C) Class frequencies: This is the count of observations inside the class. D) Tally marks: These are slashes used to count frequencies during data organization.
Substitution: The word "bound" means to set a limit. Therefore, the lowest and highest bounding values must be the class limits.
Boundaries = Limits.
18 The difference between the upper class limit and the lower class limit of a particular class is known as the:
Class Interval or Class Width is the difference between the upper class limit and the lower class limit. (NCERT Page 29)
Subtracting the lower limit from the upper limit measures the total span or width of the class interval.
A) Class mid-point: This is the average of the limits, not the difference between them. B) Cumulative frequency: This is the running total of frequencies across classes. D) Relative frequency: This is the frequency of a class expressed as a percentage of the total.
Contextual or Tonal Matching: The "difference between" two boundaries describes the size or space of the class. "Width" and "interval" accurately describe this space.
Width = Upper minus Lower.
19 Once raw data are grouped into classes, which of the following is used to represent the class in further statistical calculations?
The Class Mid-Point or Class Mark is the middle value of a class. Once raw data are grouped into classes, individual observations are not used; instead, the class mark is used to represent the class. (NCERT Page 29)
The class mark serves as the statistical proxy for all observations contained within a specific class interval.
A) The upper class limit: The extreme highest point does not represent the whole class accurately. B) The lower class limit: The extreme lowest point does not represent the whole class accurately. D) The actual raw observations in that class: Once grouped, the original raw values are ignored in favor of the class representative to simplify calculations.
Elimination: Using either extreme (upper or lower limit) biases the data. Using raw observations defeats the purpose of grouping. The only balanced representative is the middle point (class mark).
Mark = Middle point.
20 How is the class mark or mid-value of a class calculated?
The class mark lies halfway between the lower and upper limits and is ascertained by the formula: (Upper Class Limit + Lower Class Limit)/2. (NCERT Page 29)
The class mark is the arithmetic mean of the upper and lower class limits.
A) By subtracting the lower class limit from the upper class limit: This calculates the class width/interval, not the mid-point. B) By multiplying the upper class limit and the lower class limit: This has no statistical relevance for finding a mid-point. C) By dividing the upper class limit by the lower class limit: This calculates a ratio, which is not the mid-point.
Substitution: Finding the "mid-point" is mathematically the same as finding the "average" of two numbers. Averaging requires summing the two numbers and dividing by two.
Mid-point = Average of Limits.