CHAPTER-16
CLASSIFCATION OF DATA FREQUENCY DISTRIBUTION
INTRODUCTION
Classification of data
refers to the process of organizing and categorizing data into meaningful
groups or classes. One common way to classify data is through frequency
distribution. A frequency distribution is a tabular representation of data that
shows the number of times each value or range of values occurs in a dataset.
The process of
creating a frequency distribution involves the following steps:
Determine
the range of values: Identify
the range of values present in the dataset. This can be done by finding the
minimum and maximum values.
Decide
on the number of classes: Determine
the number of classes or categories that will be used to group the data. The
number of classes should be appropriate for the dataset size and provide enough
detail to understand the distribution.
Determine
the class intervals: Divide
the range of values into equal or unequal intervals to form the classes. The
class intervals should be mutually exclusive and exhaustive, meaning that each
value falls into one and only one class.
Count
the frequencies: Count
the number of observations that fall into each class. This can be done by
examining each data point and determining its class membership.
Create
the frequency distribution table: Construct a table that displays the classes, their
corresponding class intervals, and the frequencies. Optionally, additional
columns can be included to calculate relative frequencies, cumulative
frequencies, or other statistical measures.
The frequency distribution
provides a summary of the distribution of values in the dataset, allowing for
easier interpretation and analysis. It helps identify patterns, outliers, and
the concentration of values within specific ranges. It also serves as a basis
for further statistical analysis and graphing.
Overall, frequency
distribution is a useful tool in organizing and presenting data in a meaningful
and understandable manner.
EDITING OF DATA
Editing of data refers to
the process of reviewing and modifying data to ensure its accuracy,
consistency, and completeness. It involves checking the data for errors,
inconsistencies, missing values, outliers, and other issues that may affect the
quality and reliability of the data.
The purpose of data editing
is to clean and refine the data before further analysis or reporting. By
identifying and addressing data errors or anomalies, editing helps improve the
overall quality and integrity of the dataset.
The editing process
typically involves the following steps:
Initial
review: Perform an initial
review of the data to identify any obvious errors or inconsistencies. This may
include checking for missing values, data entry errors, incorrect formatting,
or outliers.
Validation
checks: Apply validation
checks or rules to detect errors or inconsistencies in the data. This may
involve logical checks, range checks, consistency checks, or checks against
predefined criteria or business rules.
Identification
of errors: Identify specific
errors or issues within the dataset. This may require comparing the data
against external sources, conducting data profiling, or using statistical
methods to identify outliers or anomalies.
Data
correction: Correct the
identified errors or inconsistencies in the data. This may involve correcting
data entry mistakes, imputing missing values, removing outliers, or resolving
inconsistencies based on established guidelines or expert judgment.
Documentation: Keep a record of the editing process, including the
errors identified, actions taken, and any decisions made during the correction
process. This documentation helps maintain an audit trail and provides transparency
in data quality assurance.
Quality
control: Perform quality
control checks to ensure that the edited data meets the desired quality
standards. This may involve rechecking a sample of the data or conducting
statistical analyses to validate the accuracy and reliability of the edited
dataset.
By conducting a thorough
editing process, data integrity and accuracy can be enhanced, leading to more
reliable and meaningful analyses and interpretations. It is an essential step
in the data management process to ensure that the data used for decision-making
and research is of high quality.
CLASSIFICATION OF DATA
Data classification refers
to the process of organizing and categorizing data based on specific criteria
or characteristics. It involves grouping similar data together and assigning
them into distinct categories or classes. Data classification is important as
it enables efficient data management, retrieval, and analysis. There are
various ways to classify data, including:
Categorical
Classification: Data
can be classified into different categories based on qualitative attributes or
characteristics. For example, data can be classified into categories such as
gender (male, female), occupation (doctor, engineer, teacher), or product types
(electronics, clothing, furniture).
Numerical
Classification: Data
can be classified into numerical ranges or intervals based on quantitative
attributes. For example, data on income can be classified into income brackets
(e.g., <$30,000, $30,000-$50,000, >$50,000), or data on age can be
classified into age groups (e.g., 0-18, 19-35, 36-50, 51+).
Temporal
Classification: Data
can be classified based on time-related attributes. This can include organizing
data into specific time periods, such as days, months, or years, or grouping
data based on specific time intervals or events.
Hierarchical
Classification: Data
can be classified into a hierarchical structure, where categories are organized
in a hierarchical order or levels. This allows for a more detailed
classification system, with broader categories at higher levels and more
specific subcategories at lower levels. For example, classifying organisms into
kingdoms, phyla, classes, orders, families, genera, and species.
Geographic
Classification: Data can be
classified based on geographic location or spatial attributes. This can involve
categorizing data by regions, countries, cities, or other geographical
boundaries. Geographic classification is commonly used in demographic studies,
market research, and spatial analysis.
Subjective
Classification: Data
can also be classified based on subjective criteria, such as personal opinions,
preferences, or ratings. This is often used in surveys or rating systems, where
respondents provide subjective feedback or evaluations on certain topics or
products.
The choice of data
classification method depends on the nature of the data and the specific
objectives of the analysis. By classifying data, it becomes easier to organize,
analyze, and interpret information, leading to better decision-making and
insights.
OBJECTIVES OF CLASSIFICATION
The objectives of data
classification are as follows:
Organization: Classification helps in organizing large volumes of data
into meaningful categories or classes. It provides a systematic structure that
facilitates easy data management and retrieval.
Simplification: Classification simplifies complex data by grouping
similar items together. It reduces the complexity of data analysis and makes it
more manageable.
Data
Exploration: Classification allows
for a deeper understanding of data by identifying patterns, relationships, and
trends within different classes or categories. It helps in exploring the
characteristics and properties of data.
Comparison
and Comparison: Classification
enables comparison and comparison of data within and across different
categories. It helps in analyzing differences, similarities, and relationships
between various groups.
Decision-Making: Classification provides a foundation for informed
decision-making. By organizing data into meaningful classes, it helps in
identifying relevant information and drawing conclusions based on the characteristics
of each class.
Data
Aggregation: Classification
facilitates data aggregation by combining individual data points into groups or
categories. Aggregated data provides a broader perspective and allows for
analysis at a higher level.
Communication: Classification enhances the communication of data by
providing a clear and concise structure. It enables effective presentation and
sharing of information with others, making it easier to convey findings and
insights.
Overall, the objective of
data classification is to bring order, structure, and meaning to data, allowing
for efficient analysis, interpretation, and utilization of information for
various purposes.
FEATURES OR CHARACTERISTICS OR
ESSENTALS OF CLASSIFICATION
The features or
characteristics of classification are as follows:
Categorical
Division: Classification
involves dividing data into distinct categories or classes based on specific
criteria or characteristics. Each category represents a separate group that
shares similar attributes or properties.
Mutually
Exclusive Classes: The
classes or categories in a classification system should be mutually exclusive,
meaning that each data item should belong to only one category. This ensures
that there is no overlap or ambiguity in the classification process.
Exhaustive
Coverage: The classification
should cover all possible data items or observations. Every data item should
fit into one of the predefined categories without any exceptions. This ensures
that all data is accounted for and there are no gaps in the classification.
Systematic
Organization: Classification
organizes data in a systematic manner, typically following a hierarchical or
sequential structure. It provides a logical arrangement of categories that
allows for easy navigation and retrieval of information.
Clear
and Consistent Criteria: Classification
is based on specific criteria or attributes that define the categories. These
criteria should be well-defined, clear, and consistent throughout the
classification process to ensure accuracy and reliability.
Scalability: Classification should be scalable, allowing for the
inclusion of new data items or the modification of existing categories as
needed. It should be adaptable to accommodate changes or updates in the data
without disrupting the overall classification framework.
Subjective
or Objective Nature: Classification
can be subjective or objective depending on the nature of the criteria used for
classification. Subjective classification involves human judgment or
interpretation, while objective classification relies on measurable and
quantifiable criteria.
Hierarchical
Structure: Classification often
follows a hierarchical structure, where categories are organized in a
hierarchical order from broader groups to more specific subgroups. This
hierarchy allows for a detailed and organized representation of data.
Relevance
to Purpose: The classification
should be relevant to the purpose or objective for which it is being used. The
categories should align with the specific needs of the analysis or application
to ensure that the classification serves its intended purpose.
Overall, the characteristics
of classification ensure that data is organized, categorized, and presented in
a meaningful and systematic manner, allowing for efficient analysis,
interpretation, and decision-making.
METHODS OF CLASSIFICATION
There are several methods of
classification, depending on the nature of the data and the purpose of
classification. Here are some commonly used methods:
Binary
Classification: This
method divides data into two exclusive categories based on a single criterion.
For example, classifying individuals as "male" or "female"
based on their gender.
Hierarchical
Classification: In
this method, data is classified into multiple levels or tiers, with each level
representing a different level of detail or specificity. It follows a hierarchical
structure, starting from broader categories and gradually moving to more
specific subcategories.
Numeric
or Interval Classification: This
method involves classifying data into numerical intervals or ranges. It is
commonly used when dealing with continuous or interval data, such as age groups
or income brackets.
Qualitative
or Categorical Classification: This method involves grouping data based on qualitative
or categorical attributes. It is used when the data does not have a numerical
or quantitative value. For example, classifying animals into categories such as
"mammals," "reptiles," or "birds" based on their
characteristics.
Time-based
Classification: This
method involves classifying data based on time periods or intervals. It is
commonly used in analyzing temporal data, such as dividing data into days,
months, quarters, or years.
Cluster
Analysis: This method involves
grouping data based on similarities or patterns. It uses statistical techniques
to identify clusters or groups within the data that share similar
characteristics or behaviors.
Decision
Tree Classification: This
method uses a hierarchical structure of decision nodes and branches to classify
data based on a series of if-then rules. It is commonly used in machine learning
and data mining applications.
Neural
Network Classification: This
method uses artificial neural networks to classify data based on patterns and
relationships. It is commonly used in complex classification problems with
large datasets.
These are just a few
examples of the methods of classification. The choice of method depends on the
nature of the data, the purpose of classification, and the specific
requirements of the analysis or application.
STATISTICAL SERIES
Statistical series refers to
the systematic arrangement of data in the form of a table, chart, or graph to
represent the distribution or variation of a particular variable or set of
variables. It is an essential component of statistical analysis and provides a
concise and organized way of presenting data for further examination and
interpretation.
A statistical series
typically includes the following components:
Variable: The characteristic or attribute being studied, which can
be quantitative or qualitative in nature. Examples include age, income,
population, sales, etc.
Observation: Each individual value or data point collected for the
variable.
Frequency: The number of times each observation or value occurs in
the dataset.
Cumulative
Frequency: The running total of
frequencies as you move through the dataset. It helps in analyzing the
cumulative distribution of the variable.
Relative
Frequency: The proportion or
percentage of observations corresponding to each value or category, calculated
by dividing the frequency by the total number of observations.
Cumulative
Relative Frequency: The
running total of relative frequencies as you move through the dataset. It helps
in analyzing the cumulative distribution of the variable in terms of
proportions or percentages.
Statistical series can
be presented in various forms, such as:
Frequency
Distribution Table: A
tabular representation that lists the values of the variable along with their
corresponding frequencies, cumulative frequencies, relative frequencies, and cumulative
relative frequencies.
Histogram:
A graphical representation that uses
rectangular bars to represent the frequency or relative frequency of each value
or category. The bars are typically plotted along the x-axis, with the height
of each bar corresponding to the frequency or relative frequency.
Bar
Chart: Similar to a
histogram, but with space between the bars. It is commonly used for
representing categorical variables.
Line
Chart: A graph that connects
data points with straight lines, typically used to show the trend or change in
a variable over time.
Statistical series provide a
clear visual representation of data, making it easier to understand patterns,
trends, and relationships. They facilitate data analysis and help in drawing
meaningful conclusions and making informed decisions.
Basic concepts concerning or grouped
frequency Distribution
Grouped frequency
distribution is a method of organizing data into intervals or classes to
simplify data analysis and interpretation. It involves grouping individual data
values into predefined ranges and determining the frequency or count of data
values falling within each range. This approach is useful when dealing with a
large dataset or continuous variables where it is impractical to list every
individual value.
The following are some
basic concepts associated with grouped frequency distribution:
Class
Intervals: These are the
predefined ranges or intervals into which the data values are grouped. Each
interval should be mutually exclusive and exhaustive, meaning that every data
value should fit into one and only one interval.
Class
Limits: Each class interval
has two limits, namely the lower class limit and the upper class limit. The
lower class limit is the smallest value that can be included in the interval,
while the upper class limit is the largest value that can be included. The
difference between the upper and lower class limits gives the width or size of
the interval.
Class
Boundaries: These are the
midpoints between the upper limit of one interval and the lower limit of the
next interval. Class boundaries help in determining the exact position of data
values within the intervals.
Class
Width: It refers to the
range or width of each class interval. It is calculated by subtracting the
lower class limit of one interval from the lower class limit of the next
interval. The class width should be uniform throughout the distribution.
Frequency: It represents the number of data values falling within
each class interval. The frequency is typically denoted by "f" and is
counted or obtained by tallying the data values within each interval.
Cumulative
Frequency: It is the running
total of frequencies as you move through the intervals from the beginning. It
helps in analyzing the cumulative distribution of the data and identifying the
total number of data values up to a certain interval.
Grouped frequency
distribution simplifies data analysis by condensing large datasets into
meaningful intervals and frequencies. It provides a concise summary of the data
distribution, highlighting the concentration of data values within specific
ranges. Grouped frequency distribution is commonly used in various statistical
techniques and is a fundamental concept in data analysis.
Types of continuos series
Continuous series, also
known as grouped data, refers to a type of data presentation where the values
are grouped into intervals or classes. There are different types of continuous
series based on the width or size of the class intervals. The commonly used
types are:
Exclusive
series: In this type of
continuous series, the lower limit of one class interval is excluded from the
upper limit of the previous interval. For example:
0 - 10, 10 - 20, 20 - 30,
...
Inclusive
series: In contrast to
exclusive series, inclusive series includes both the lower and upper limits of
each class interval. For example:
0 - 9, 10 - 19, 20 - 29, ...
Open-end
series: Open-end series is
used when the lower limit of the first class and/or the upper limit of the last
class is not specified. Instead, it is denoted by an open-ended symbol, such as
(<) for the lower limit or (>) for the upper limit. For example:
<10, 10 - 20, 20 - 30,
..., >90
Continuous
series with unequal class intervals: In some cases, the class intervals in a continuous series
may not have equal widths. This occurs when the data values are unevenly
distributed and require different interval sizes to accurately represent the
data. For example:
0 - 5, 6 - 12, 13 - 22, 23 -
40, ...
These types of continuous
series are used to present and analyze data in a grouped form, making it easier
to interpret and understand large datasets. The choice of the series type
depends on the nature of the data, the purpose of the analysis, and the
preferences of the researcher or analyst.
VERY SHORT QUESTIONS ANSWER
Q.1.What is raw data?
Ans. Observations
Q.2.Why do we prefer classified data
over raw data?
Ans. Summarization.
Q.3. Define classification of data?
Ans. Grouping.
Q.4.What is chronological
classification of data?
Ans. Time-based
Q.5. Define statistical series?
Ans. Data set
Q.6. Define frequency distribution?
Ans. Counting
Q.7.What is central value of a class
interval?
Ans. Midpoint
`SHORT QUESTIONS
ANSWER
Q.1.What is meant by classification of
data?
Ans. Classification of data refers to the process of
organizing and categorizing raw data into meaningful groups or classes based on
specific characteristics or criteria. It involves grouping similar data
together to facilitate analysis and interpretation.
Q.2.What do you mean by organization of
statistical data?
Ans. Organization of statistical data refers to the
arrangement and structuring of data in a systematic and logical manner. It
involves sorting and grouping the data based on relevant categories or
variables, such as time, location, or characteristics of the data points. The
organization of data allows for easier interpretation, analysis, and
presentation of the information.
Q.3. Enlist the objects of
classification of data?
Ans. The objects of classification of data include:
Simplification: Classification helps in simplifying complex and large
data sets by grouping similar data together, making it easier to understand and
analyze.
Organization: Classification allows for the systematic organization of
data, enabling efficient storage, retrieval, and management of information.
Comparison: Classification facilitates the comparison of data across
different categories or groups, highlighting similarities, differences, and
patterns.
Analysis: Classification aids in data analysis by providing a
structured framework for examining relationships, trends, and distributions
within and between different groups.
Presentation: Classification helps in presenting data in a clear and
concise manner, often through tables, charts, or graphs, making it more
accessible and understandable to others.
Interpretation: Classification enhances the interpretability of data by
grouping similar data points together, enabling the identification of
meaningful patterns, associations, and insights.
Decision-making: Classification provides a foundation for making informed
decisions based on the analysis and interpretation of data, allowing for better
planning, forecasting, and problem-solving.
Q.4. Give in briefly the
characteristics of classification of statistical data?
Ans. The characteristics of classification of statistical data
include:
Grouping: Classification involves grouping similar or related data
items together based on common characteristics or attributes.
Order: The data within each group or category are arranged in a
logical and meaningful order, such as ascending or descending values,
alphabetical order, or chronological sequence.
Exhaustiveness: The classification should be comprehensive and cover all
possible variations or categories relevant to the data set, leaving no data
items unclassified.
Mutually
Exclusive: Each data item should
fit into only one category or group, ensuring that there is no overlap or ambiguity
in the classification.
Homogeneity: The data items within each group should be similar or
homogeneous in terms of the attribute or characteristic used for
classification.
Objectivity: The classification criteria should be objective and based
on measurable or observable attributes, avoiding any subjective interpretations
or biases.
Relevance: The classification should be relevant and meaningful in
the context of the data analysis or research objective, allowing for effective
data interpretation and decision-making.
Flexibility: The classification system should be flexible enough to
accommodate changes or additions in the data set, allowing for updates or
modifications as needed.
Standardization: The classification should follow standardized conventions
or guidelines to ensure consistency and comparability across different data
sets or studies.
Documentation: The classification process should be documented and
clearly explained, including the criteria used, categories established, and any
assumptions made, to enhance transparency and reproducibility.
Q.5. Explain briefly the basis of
classification of a statistical data?
Ans. The basis of classification of statistical data refers to
the criteria or factors used to group the data into different categories or
classes. The choice of basis depends on the nature of the data and the specific
objective of the analysis. Here are some common bases of classification:
Numerical
Basis: Data can be classified
based on numerical values, such as age groups, income brackets, or temperature
ranges. This basis allows for quantitative analysis and comparison.
Categorical
Basis: Data can be
classified based on categories or attributes, such as gender, occupation, or
type of product. This basis allows for qualitative analysis and understanding
of characteristics.
Temporal
Basis: Data can be
classified based on time periods, such as years, months, or seasons. This basis
allows for studying trends, seasonal variations, or changes over time.
Geographical
Basis: Data can be
classified based on geographical locations, such as countries, regions, or
cities. This basis allows for analyzing variations across different areas.
Alphabetical
Basis: Data can be
classified based on alphabetical order, such as names of individuals or
organizations. This basis is useful for organizing and referencing data.
Hierarchical
Basis: Data can be
classified based on hierarchical levels or categories, such as a classification
tree with multiple levels of subcategories. This basis allows for a structured
representation of data relationships.
Qualitative
Basis: Data can be
classified based on qualitative characteristics, such as opinions, preferences,
or ratings. This basis is often used in survey-based research or subjective
assessments.
Combination
Basis: Classification can
also be done based on a combination of multiple factors, such as age and
occupation, to create more detailed and specific categories.
The choice of the basis of
classification should align with the research objective, data characteristics,
and the type of analysis or interpretation desired.
Q.6 Explain briefly the inclusive form
of class intervals with the help of an example?
Ans. In the inclusive form of class intervals, the lower limit
and upper limit of each class interval are included in the interval. This means
that the values falling on the exact boundaries of the interval are considered
part of that interval.
For example, let's consider
the data set of students' heights (in centimeters) in a class:
165, 170, 175, 180, 185,
190, 195, 200, 205, 210
To create class intervals
using the inclusive form, we can set a class width of 10. Starting from the
minimum value (165), we can form the following class intervals:
165-174
175-184
185-194
195-204
205-214
In this inclusive form, the
lower limit of the first interval (165) and the upper limit of the last
interval (214) are included in their respective intervals. So, a student with a
height of exactly 165 cm would fall in the first interval, and a student with a
height of exactly 214 cm would fall in the last interval.
The inclusive form of class
intervals is commonly used when we want to include the exact boundary values as
part of the interval for accuracy and precision in data representation and
analysis.
Q.7.What do you mean by exclusive form
of class intervals?
Ans. In the exclusive form of class intervals, the lower limit
of each interval is included in the interval, but the upper limit is excluded.
This means that values falling on the exact upper boundary of an interval are
not considered part of that interval.
For example, let's consider
a data set of monthly incomes (in thousands of dollars):
10, 15, 20, 25, 30, 35, 40,
45, 50, 55
To create class intervals
using the exclusive form, we can set a class width of 10. Starting from the
minimum value (10), we can form the following class intervals:
10-19
20-29
30-39
40-49
50-59
In this exclusive form, the
lower limit of each interval (e.g., 10, 20, 30) is included, but the upper
limit (e.g., 19, 29, 39) is excluded. This means that if someone has an income
exactly equal to the upper boundary of an interval (e.g., $19,000), they would
not be included in that interval but would be assigned to the next interval.
The exclusive form of class
intervals is commonly used when we want to avoid ambiguity and overlap between
adjacent intervals. It allows for clear differentiation and avoids double
counting of values at the boundary points.
Q.8.What are open ends class intervals?
Iiiustrate giving example?
Ans. Open-end class intervals refer to the class intervals
where one or both of the ends are left open, meaning there is no specified
upper or lower limit. These intervals are used when there are extreme values
that fall outside the range of the data but are still worth considering.
For example, let's
consider a dataset of ages:
12, 15, 18, 21, 24, 27, 30,
33, 36, 60
If we want to create class
intervals for age groups, we can use open-end intervals to accommodate the
extreme values.
One possible way to create
open-end class intervals for this data is as follows:
0-20
21-35
36 and above
In this example, the first
interval is open at the upper end, meaning it includes values up to 20 but does
not specify an upper limit. The second interval is open at both ends, including
values from 21 to 35 but not specifying specific upper or lower limits. The
last interval includes all values 36 and above.
Open-end class intervals are
useful when there are outliers or extreme values in the data that may not fit
well within the regular intervals. They allow for capturing the presence of
these extreme values without specifying specific limits.
Q.9. Explain the Sturgis formula for
determining the number of class intervals?
Ans. The Sturges formula is a commonly used method for
determining the number of class intervals in a frequency distribution. It
provides an estimate based on the sample size of the data. The formula is as
follows:
k = 1 + 3.322 log N
Where:
k = Number of class
intervals
N = Sample size (number of
observations)
The formula calculates the
number of intervals based on the logarithm of the sample size. The constant
value 3.322 is derived from statistical calculations.
The Sturges formula aims to
strike a balance between having too few intervals, which may result in loss of
information and hiding data patterns, and having too many intervals, which may
lead to overcomplication and difficulty in interpreting the distribution.
It's important to note that
the Sturges formula provides an estimate, and the final choice of the number of
class intervals can also depend on the nature of the data, the intended
analysis, and the preferences of the researcher.
Q.10. Write brief note on bivariate
frequency distribution?
Ans. Bivariate frequency distribution is a statistical
technique used to analyze the relationship between two variables
simultaneously. It involves organizing data into a two-dimensional table or
matrix, with one variable represented on the rows and the other variable
represented on the columns.
In a bivariate frequency
distribution, the cells of the table contain the frequency or count of
occurrences for each combination of values between the two variables. This
allows for a comprehensive examination of the joint distribution of the
variables and enables the exploration of patterns, associations, and
dependencies between them.
Bivariate frequency
distributions are commonly presented in the form of a contingency table, where
the rows represent one variable, the columns represent the other variable, and
the values in the cells represent the frequencies or counts. These tables can
be further analyzed using statistical measures and techniques such as
chi-square tests, correlation coefficients, and cross-tabulations to uncover
relationships and associations between the variables.
Bivariate frequency
distributions are useful in various fields such as social sciences, economics,
market research, and data analysis, as they provide valuable insights into the
relationships between two variables and help in making informed decisions based
on the observed patterns.
LONG QUESTIONS ANSWER
Q.1.What do you understand by
classification Explain classification according to attributes and
classification according to class-intervals?
Ans. Classification is the process of organizing and
categorizing data into meaningful groups or classes based on certain
characteristics or criteria. It helps in systematically arranging data to
facilitate analysis, interpretation, and understanding.
Classification according to
attributes refers to the grouping of data based on qualitative characteristics
or attributes. In this type of classification, the data is classified based on
the presence or absence of specific attributes or qualities. For example,
classifying students based on their gender (male or female), classifying
animals based on their species (dog, cat, bird), or classifying products based
on their colors (red, blue, green).
On the other hand,
classification according to class intervals involves grouping numerical data
into intervals or ranges. This type of classification is commonly used when
dealing with continuous or quantitative data. Class intervals are defined based
on the range of values present in the data, and each interval represents a
specific range or category. For example, classifying heights of individuals
into intervals such as 150-160 cm, 160-170 cm, and so on, or classifying ages
into intervals such as 20-30 years, 30-40 years, and so on.
Classification according to
attributes focuses on qualitative characteristics, while classification
according to class intervals deals with quantitative data. Both types of
classification serve the purpose of organizing data for analysis, but they
differ in terms of the nature of the variables being classified.
Q.2.What are the essentials of a good
classification Give its modes enlist the object of classification of data?
Ans. Essentials of a good classification:
Clear
and well-defined criteria: A
good classification should have clear and well-defined criteria for grouping
the data. The criteria should be objective, relevant, and easily understood.
Exhaustive
and mutually exclusive classes: The classes or categories in a classification should be
exhaustive, meaning that they should cover all possible cases or data points.
Additionally, the classes should be mutually exclusive, ensuring that each data
point belongs to only one class and avoids overlapping or ambiguity.
Consistency
and uniformity: A
good classification should be consistent and uniform across different data sets
or contexts. It should follow the same principles and criteria regardless of
the specific dataset being classified.
Modes of
classification:
Qualitative
classification: This
mode involves grouping data based on qualitative characteristics or attributes,
such as gender, occupation, nationality, etc.
Quantitative
classification: This
mode involves grouping data based on quantitative variables or measurements,
such as age groups, income brackets, height ranges, etc.
Objects of classification of data:
Organization
and arrangement: The
primary object of classification is to organize and arrange data in a
systematic and structured manner. It helps in making the data more manageable
and understandable.
Comparison
and analysis: Classification
facilitates the comparison and analysis of data within and across different
categories or classes. It allows for the identification of patterns, trends,
and relationships among variables.
Presentation
and communication: Classification
provides a clear and concise way to present data, making it easier to
communicate and share information with others. It helps in summarizing and
visualizing complex data sets.
Decision-making
and inference: Classification
supports decision-making processes by providing insights and information based
on the characteristics of different classes. It aids in drawing inferences and
making predictions based on the classified data.
Overall, the essentials of a
good classification involve clarity, comprehensiveness, and consistency, while
the modes and objects of classification depend on the nature and purpose of the
data being classified.
Q.3. Give the characteristics and
explain the basis of classification of a statistical?
Ans. Characteristics of classification of statistical data:
Systematic
organization: Classification
involves the systematic organization of data into categories or classes based
on specific criteria or characteristics.
Order
and hierarchy: The classes in a
classification are typically arranged in a logical order or hierarchy, allowing
for easier understanding and analysis of the data.
Exhaustiveness
and exclusivity: A good classification
should ensure that all data points are assigned to appropriate classes,
ensuring exhaustiveness. Additionally, each data point should belong to only
one class, ensuring exclusivity and avoiding overlap or ambiguity.
Objectivity
and consistency: Classification
should be based on objective criteria and consistent principles, ensuring that
the same classification can be applied consistently to different datasets or
contexts.
Basis of
classification of statistical data:
Classification
according to attributes: This
basis involves grouping data based on qualitative characteristics or
attributes, such as gender, occupation, nationality, etc. It focuses on
classifying data into distinct categories based on non-measurable
characteristics.
Classification
according to class intervals: This basis involves grouping data based on quantitative
variables or measurements, such as age groups, income brackets, height ranges,
etc. It focuses on creating class intervals or ranges that capture the
variation in numerical data.
The choice of basis for
classification depends on the nature of the data and the objectives of the
analysis. Classification according to attributes is suitable for categorical or
qualitative data, while classification according to class intervals is suitable
for numerical or quantitative data.
