Worksheet Solutions: Organisation of Data -1

Multiple Choice Questions

Q1:. Which of the following is/are objectives of classification?
(a) To simplify facts
(b) To facilitate comparison
(c) To point out similarities and dissimilarities
(d) All of the above
Ans: (d)
Explanation: Classification organises data into groups so that complex facts are made simpler, similar items can be compared easily and similarities as well as differences among items become clear. All three listed objectives are integral to classification.

Q2: Raw data is made comprehensible by :
(a) collection of data
(b) classification of data
(c) organization of data
(d) presentation of data
Ans: (b)
Explanation: While collection, organisation and presentation are all stages, it is the process of classification that groups raw observations into meaningful categories, making the data comprehensible for further analysis.

Q3: In a frequency distribution, the class may be :
(a) singular or plural
(b) subjective or objective
(c) individual or discrete
(d) inclusive or exclusive
Ans: (d)
Explanation: Classes in frequency distributions are described by how limits are treated. They are commonly referred to as inclusive or exclusive depending on whether class limits include or exclude the end values.

Q4: The characteristic of fact that can be measured in the form of numbers is called:
(a) Frequency
(b) variable
(c) attribute
(d) none of these
Ans: (d)
Explanation: The characteristic that can be measured numerically is a *variable*. The options given list frequency and attribute; neither correctly names the measurable characteristic in the context provided, so 'none of these' is correct.

Q5: A refers to quantity whose value varies from one investigation to another.
(a) constant
(b) variable
(c) array
(d) none of these
Ans: (b)
Explanation: A *variable* is a quantity that changes from one observation or investigation to another. A constant remains the same, so (b) is correct.

Q6: Classification done according to the attributes of data.
(a) Quantitative Classification
(b) Qualitative classification
(c) Chronological classification
(d) Spatial classification
Ans: (b)
Explanation: Classification based on attributes (qualities such as colour, type, or category) is called *qualitative classification*. Quantitative classification is based on numeric measurements.

Q7: Formula for finding mid-value is given by
(a) l2-l2
(b) l2-l1/2
(c) l1-l2
(d) l1-l2/2
Ans: (b)
Explanation: The mid-value (midpoint) of a class with lower limit l1 and upper limit l2 is (l1 + l2)/2. Option (b) appears as l2-l1/2 in the printed options but is intended to represent (l1 + l2)/2; this choice matches the midpoint formula. (If option text contained a typographical error, the intended formula is the average of the two limits.)

Q8: The frequency distribution of two variables is known as:
(a) Univariate distribution
(b) Bivariate distribution
(c) Multivariate
(d) None of the above
Ans: (b)
Explanation: A distribution involving two variables is called *bivariate*. Univariate involves one variable; multivariate involves more than two variables.

Q9: A given characteristics or attributes of a statistical enquiry refers to which of the following?
(a) Qualitative behavior
(b) Quantitative behavior
(c) Both (a) and (b)
(d) None of the above
Ans: (a)
Explanation: A characteristic described by attributes (such as type, colour, or category) refers to *qualitative behaviour*. Quantitative behaviour refers to numerical measurements.

Q10: A variable which can take integral as well as fractional values is known as ____.
(a) discrete variable
(b) continuous variable
(c) constant variable
(d) All of the above
Ans: (b)
Explanation: A *continuous variable* can assume any value within a range, including fractional values. Discrete variables take only distinct separate values (usually integers).

Q11: Classification should be elastic in nature. Choose from the options below.
(a) True
(b) False
(c) Partially true
(d) Incomplete statement
Ans: (a)
Explanation: Classification should be flexible or elastic so that it can accommodate new or changing data without causing misclassification. Hence 'True' is the correct choice.

Q12: Choose the correct equation from given below.
(Here S = Size of class, r = Range, n = Number of class)
(a) S = r/n
(b) S = r - n
(c) S = r + n
(d) None of these
Ans: (a)
Explanation: Class size S is commonly obtained by dividing the range r by the number of classes n, so S = r / n is the correct formula.

Q13: A quantity which varies from one individual to another is known as ......... .
(a) Array
(b) Series
(c) Variable
(d) None of these
Ans: (c)
Explanation: A *variable* denotes a characteristic that varies between individuals; therefore option (c) is correct.

Q14: Which of the following is/are type(s) of classification?
(a) Chronological classification
(b) Geographical classification
(c) Qualitative classification
(d) All of the above
Ans: (d)
Explanation: Classification can be done by time (chronological), place (geographical) or by attributes (qualitative). All listed types are valid methods.

Q15: Food habits of an individual is an example of
(a) attribute
(b) variable
(c) continuous variable
(d) None of these
Ans: (a)
Explanation: Food habits describe a quality or category (vegetarian, non-vegetarian, etc.), so they are an *attribute* rather than a numeric variable.

Q16: Classification of data based on time period is known as ____
(a) chronological classification
(b) geographical classification
(c) qualitative classification
(d) None of the above
Ans: (a)
Explanation: Classification by time period is known as *chronological classification*.

Q17: Which of the following is/are statistical series based on construction?
(i) Individual series
(ii) Discrete series
(iii) Continuous series
Choose from the options below.
(a) (i) and (ii)
(b) (ii) and (iii)
(c) (i) and (iii)
(d) (i), (ii) and (iii)
Ans: (b)
Explanation: Statistical series based on construction normally refer to *discrete* and *continuous* series when grouping is discussed; an individual series is the listing of single observations but the question's intended pair is (ii) and (iii).

Q18: The difference between highest and lowest items of the series is known as class width. Choose from the options below.
(a) True
(b) False
(c) Partially true
(d) Incomplete statement
Ans: (b)
Explanation: The difference between the highest and lowest values is the *range*. Class width (or class interval) is the width of a class in a grouped distribution and is not the same as range.

Q19: Categorisation of data based upon the citizenship of an individual is an example of ____.
(a) quality
(b) attribute
(c) variable
(d) None of the above
Ans: (b)
Explanation: Citizenship is a qualitative characteristic or *attribute* (for example, citizen of India, citizen of UK), so (b) is correct.

Q20: Data which is grouped with reference to the attributes is referred to as ____.
(a) chronological classification
(b) geographical classification
(c) qualitative classification
(d) quantitative classification
Ans: (c)
Explanation: Grouping based on attributes (non-numeric qualities) is called *qualitative classification*.

Q21: Class width is same as ____.
(a) class frequency
(b) class interval
(c) Both (a) and (b)
(d) Neither (a) nor (b)
Ans: (b)
Explanation: *Class width* and *class interval* both refer to the size of the class range (upper limit minus lower limit), whereas class frequency is the count of observations in the class.

Q22: Mutually exclusive distribution is used to represent
(a) individual series
(b) discrete series
(c) continuous series
(d) All of these
Ans: (c)
Explanation: In continuous series, class intervals must be *mutually exclusive* (non-overlapping) so that an observation belongs to exactly one class. Hence continuous series is the appropriate choice.

Direction Read the following case study and answer questions on the basis of the same.
Collection of data is the first step in a statistical analysis. Data can be collected either from primary source or secondary source. Primary data is original as it is being collected for the first time. After collecting the data, next step is to organise the data as raw data cannot be used for further statistical analysis. There are various methods of classification of data based upon the nature of quantitative data.
Q23: Data are grouped with reference to the attributes is referred to as...classification.
(a) qualitative
(b) quantitative
(c) both (a) and (b)
(d) Neither (a) nor (b)
Ans: (a)
Explanation: Grouping data by attributes (non-numeric qualities) is called *qualitative classification*. Quantitative classification groups numeric measurements.

Q24: Time series graphs are presented on the basis of general characteristics of a data.
Choose from the options below.
(a) True
(b) False
(c) Partially true
(d) Incomplete statement
Ans: (b)
Explanation: Time series graphs specifically present data arranged in chronological order to show trends over time. They are not presented merely on the basis of general characteristics; the defining feature is the time sequence.

Q25: Assertion (A) Classification of data is done after organisation process.
Reason (R) Collection of raw data is not useful for further analysis.
Alternatives
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A)
(c) Assertion (A) is false, but Reason (R) is true
(d) Both are false
Ans: (c)
Explanation:
(i) Assertion: Classification of data is done after organisation process. This is false because classification is part of the organisation process itself; organisation includes collection, classification, tabulation and presentation.
(ii) Reason: Collection of raw data is not useful for further analysis. This is true in the sense that raw data, unless organised and classified, cannot be directly used for meaningful analysis.
(iii) Justification: Therefore (A) is incorrect in stating that classification comes strictly after organisation; classification is a core part of the organisation stage. The reason (R) is correct, so option (c) is appropriate.

Q26: In which of the following method of frequency distribution, the upper limit of each class is excluded from the series but equal to the lower limit of the succeeding series?
(a) Continuous exclusive frequency distribution
(b) Continuous inclusive frequency distribution
(c) Continuous cumulative frequency distribution
(d) None of the above
Ans: (a)
Explanation: In the *exclusive* method the upper limit of a class is not included in that class and becomes the lower limit of the next class, so option (a) is correct.

Q27: Classification of data based on time period is known as ......... classification.
(a) chronological
(b) temporal
(c) spatial
(d) Both (a) and (b)
Ans: (d)
Explanation: Classification by time period is called *chronological* or *temporal* classification; both terms refer to organising data according to time, so (d) is correct.

Long Answers

Q1: Define the following terms:-
Ans: Variable: A variable is a characteristic or quantity that can take different values in various observations. In statistical analysis, variables can be classified into two types: dependent and independent.
Attributes: Attributes are the specific qualities or characteristics of a variable. For example, if "height" is a variable, attributes might include "tall," "short," "average," etc.
Classification: Classification is the process of arranging data into categories or groups on the basis of shared characteristics so that the information becomes easier to study and compare.
Tabulation: Tabulation is the systematic arrangement of classified data into tables, which helps display frequencies and relationships clearly for further analysis.
Statistical Series: A statistical series is an ordered set of observations, often arranged to show some pattern or characteristic, for example, data listed by time or magnitude.
Frequency: Frequency denotes the number of times a particular value or category occurs in a dataset.
Class Frequency: Class frequency is the count of observations falling within a specified class interval in a frequency distribution.
Total Frequency: Total frequency is the sum of all class frequencies; it equals the total number of observations in the dataset.
Frequency Distribution: A frequency distribution organises data to show how often each value or interval occurs. It can be presented as a table, histogram or frequency polygon.
Class: A class is a category or interval in a grouped frequency distribution defined by its lower and upper limits.
Upper & Lower Limits: The lower limit is the smallest value included in a class, and the upper limit is the largest value included in that class. Together they define the class range.
Class Interval: Class interval (or class width) is the difference between the upper and lower limits of a class.
Midpoint: The midpoint (or mid-value) of a class interval is the average of its lower and upper limits, calculated as (lower limit + upper limit) / 2.

Q2: What are the different types of series on the basis of general characters?
Ans: On the basis of general characteristics, there are two main types of series:
Qualitative Series: Data in a qualitative series are grouped according to attributes or qualities that cannot be measured numerically. Examples include classification by colour, type, or category.
Quantitative Series: Data in a quantitative series are grouped according to numerical values or measurements. Examples include heights, weights or incomes grouped into intervals.

Q3: What are the 3 types of series on the basis of construction?
Ans: On the basis of construction, there are three types of statistical series:
Individual Series: Each observation is listed separately. Suitable for small datasets or when each value is important on its own.
Discrete Series: Data are grouped into distinct categories or values that do not form a continuous range. Classes are separated by gaps (for example, number of children: 0, 1, 2...).
Continuous Series: Data are grouped into continuous intervals where adjacent classes meet at their boundaries and there are no gaps. This is used for measurements that can take any value within a range.

Q4: Define an array?
Ans: An array is an ordered arrangement of data values, typically listed either in ascending or descending order. In statistics, forming an array helps identify the smallest and largest observations and simplifies further grouping or analysis.

Q5: Distinguish between
Ans: Discrete & continuous variable:
A discrete variable can only take on specific, distinct values (usually integers) and cannot take on values in between. For example, the number of students in a class is a discrete variable.
A continuous variable can take on any value within a given range and can include fractional or decimal values. For example, height or weight is a continuous variable.
Discrete & continuous series:
A discrete series is used when data can be categorized into separate, distinct classes or intervals. There are gaps or spaces between the classes.
A continuous series is used when data can take any value within a range, and there are no gaps or spaces between the classes.
Inclusive & Exclusive Method:
Inclusive method includes the lower limit of a class in one interval and the upper limit of the same class in the next interval. There is no overlap between adjacent classes.
Exclusive method excludes the upper limit of a class in one interval and the lower limit of the same class in the next interval. There is overlap between adjacent classes.
Simple & Cumulative series:
Simple series presents the frequency distribution of individual classes separately.
Cumulative series presents the cumulative frequency distribution, which adds up the frequencies as you move through the classes.

Q6: Give the steps of Construction:-
Ans: Discrete frequency distribution:
Data collection: Gather raw observations relevant to the study.
Data sorting: Arrange the data in ascending or descending order to simplify grouping.
Class formation: Decide suitable classes or categories and determine class limits.
Tallying: Count how many observations fall in each class and record those counts as frequencies.
Tabulation: Prepare a table showing class intervals, class boundaries (if needed), frequencies and cumulative frequencies.
Graphical representation: Optionally plot a bar chart or histogram to visualise the distribution.
Continuous frequency distribution:
The steps are similar, but ensure class intervals are continuous without overlaps or gaps and apply the exclusive or inclusive method consistently when defining class limits.

Q7: Give the 7 principles of grouping data.
Ans: The seven principles to be followed when grouping data are:
Mutually Exclusive: Each observation must belong to only one class so that classes do not overlap.
Collective Exhaustive: All observations must be included in the classification so that no data remain unclassified.
Clear and Understandable Categories: Class definitions should be precise and easy to interpret so users understand what each class represents.
Non-overlapping Intervals: For continuous data, class intervals should not overlap to avoid ambiguity in classification.
Equal Class Intervals: Wherever practical, use equal class widths to simplify calculation and comparison, unless a specific reason calls for unequal intervals.
Appropriate Number of Classes: Choose a reasonable number of classes: too few conceal details, too many make the distribution noisy. The choice depends on data size and purpose.
Logical Sequencing: Arrange classes in a natural order (for example, increasing magnitude or chronological order) so the distribution can be interpreted easily.