CHSE Odisha Class 12 Education Solutions Chapter 18 Statistics: Meaning, Nature, and Uses

Odisha State Board CHSE Odisha Class 12 Education Solutions Chapter 18 Statistics: Meaning, Nature, and Uses Questions and Answers.

CHSE Odisha 12th Class Education Chapter 18 Question Answer Statistics: Meaning, Nature, and Uses

Group – A

Short type Questions with Answers
1. Answer with in Two/Three sentence :

Question 1.
What distinguishes statistics from isolated facts or figures?
Answer:
Statistics involve aggregates of facts, where data is collected and compared from multiple related figures within the same framework, providing a basis for analysis and interpretation.

Question 2.
Why are statistics considered numerically expressed?
Answer:
Statistics are presented in numerical figures to ensure quantitative information, allowing for accurate interpretation and comparison; qualitative statements are not classified as statistics.

Question 3.
What is the primary purpose of collecting data in statistics?
Answer:
Data in statistics is collected for a predetermined purpose, with clearly defined objectives, facilitating the collection of relevant information for analysis and decision-making.

Question 4.
According to Croxton and Cowden, what is the most comprehensive definition of statistics?
Answer:
Croxton and Cowden define statistics as the collection, presentation, analysis, and interpretation of numerical data, covering all aspects and fields of statistical inquiry.

Question 5.
Why is classification important in statistics?
Answer:
Classification in statistics organizes collected data, making it easier to draw conclusions and facilitate further analysis; tabulation and presentation in tables enhance data intelligibility.

CHSE Odisha Class 12 Education Solutions Chapter 18 Statistics: Meaning, Nature, and Uses

Question 6.
How does statistics contribute to policy planning in organizations?
Answer:
Statistics aids policy planning by providing data from previous or expected environments, enabling organizations to develop effective strategies based on analyzed information.

Question 7.
In what way is statistics useful in behavioral and social sciences?
Answer:
In social sciences, statistics helps researchers comprehensively alter both quantitative and qualitative information to explain and predict behavioral patterns, contributing to a deeper understanding.

Question 8.
What is the role of statistics in problem-solving?
Answer:
Statistics assists in problem-solving by enabling individuals to identify useful differences between variables, helping analyze response patterns and minimizing error in decision-making.

Question 9.
How does statistics contribute to predicting future trends?
Answer:
Statistical methods analyze past data to predict future trends, allowing for informed decision-making; for example, predicting product sales for the next year based on historical data and market trends.

Question 10.
What is a limitation of statistics in dealing with individual values?
Answer:
Statistics does not deal with individual values; it focuses on aggregate values and requires comparison with standards or other data points for meaningful interpretation.

II. Answer with in Five/Six sentence:

Question 1.
What distinguishes statistics from single or isolated facts?
Answer:
Statistics are aggregates of facts, meaning they involve the collection and comparison of related figures within the same framework. Unlike single or isolated facts, statistics provide a broader perspective by considering multiple data points, allowing for analysis and meaningful interpretation. For example, stating one’s individual income is not statistics, but providing the average salary of a group of individuals constitutes statistical information.

Question 2.
Why are statistics numerically expressed, and why is this important?
Answer:
Statistics are numerically expressed to ensure quantitative information. This numerical format allows for accurate interpretation, comparison, and analysis. Unlike qualitative statements, numerical figures provide a measurable basis for understanding trends, making informed decisions, and drawing meaningful conclusions. For instance, comparing per capita income between countries or expressing a person’s height in numbers involves statistical considerations.

Question 3.
What is the significance of predetermined purpose in statistics?
Answer:
Statistics are collected for a predetermined purpose, meaning the objective of gathering data must be defined before collection. This clarity ensures the relevance and appropriateness of the data collecte(iv) For instance, if collecting data on hospital in-patients waiting for X-rays, the predetermined purpose may be to establish the average waiting time. This focus ensures that data collection aligns with the specific goals, enabling meaningful analysis and interpretation.

Question 4.
How does statistics contribute to policy planning in organizations?
Answer:
Statistics play a crucial role in policy planning by providing data from previous or expected environments. Organizations analyze data, such as sales figures, to formulate effective strategies and policies for future endeavors. For instance, understanding previous sales data allows organizations to develop strategies that maximize product sales and overall benefit.

CHSE Odisha Class 12 Education Solutions Chapter 18 Statistics: Meaning, Nature, and Uses

Question 5.
What functions does statistics perform in condensing and summarizing data?
Answer:
Statistics condenses and summarizes voluminous data into few presentable, understandable, and precise figures. This process transforms raw and complex data into manageable forms, making it easier to draw conclusions. For example, deriving the average salary from a mass of survey data provides a concjse and informative representation of income for a particular group.

Question 6.
How does statistics contribute to predicting future trends?
Answer:
Statistical methods are instrumental in analyzing past data to predict future trends. For example, by examining sales data for a product over previous years and considering current market trends, organizations can predict future sales patterns. This predictive capability aids in making informed decisions and planning for the future.

Question 7.
What are the limitations of statistics?
Answer:
Statistics has limitations, including its.inability to deal with individual values, qualitative characteristics, and the fact that statistical conclusions are.not universally true. It also requires a high degree of skill for accurate interpretation. For instance, statistics cannot capture individual values effectively and may not be applicable to qualitative traits such as honesty or beauty. Additionally, statistical conclusions are only approximations, and the interpretation demands expertise to avoid fallacious conclusions.

Group – B

Long Type Questions With Answers

Question 1.
What are the various functions of statistics?
Answer:
Statistics is no longer confined to the domain of mathematics. It has spread to most of the branches of knowledge including social sciences and behavioural sciences. One of the reasons for its phenomenal growth is the variety of different functions attributed to it. Some of the most important functions of statistics are described as follows:

• It condenses and summarizes voluminous data into a few presentable, understandable and precise figures: The raw data, as is usually available, is voluminous and haphazard. It is generally not possible to draw any conclusions from the raw data as collected. Hence, it is necessary and desirable to express this data in few numerical values. For example, the average salary of a policeman is derived from a mass of data from surveys. But just one summarized figure gives us a pretty good idea about the income of police officers. Similarly, stock market prices of individual stocks and their trends are highly complex to comprehend, but a graph of price trends gives us the overall picture at a glance.

• It facilitates classification and comparison of data: Arrangement of data with respect to different characteristics, facilitates comparison and interpretation. For example, data on age, height, sex and family income of college students gives us a much better picture of students when the data is categorized relative to these characteristics. Additionally, simply the statements about these figures don’t convey any significant meaning. It is their comparison that helps us draw conclusions.

• It helps in determining functional relationships between two or more phenomenon: Statistical techniques such as correlational analysis assist in establishing the degree of association between two or more independent variables. For example, the coefficient of correlation between literacy and employment gives us the degree of association between extent of training and industrial productivity. Similarly, correlation between average rainfall and agricultural productivity can be obtained by using such statistical tools. Some statistical methods can also be used in formulating and testing hypothesis about a certain phenomenon. For example, it can be tested whether a credit squeeze is effective in controlling prices of consumer goods or whether tenured professors are more motivated to improve their teaching than untenured professors.

• It helps in predicting future trends: Statistical methods are highly useful tools in analysing the past data and predicting some future trends. For example, the sales for a particular product for the next year can be computed by knowing the sales for the same product over the previous years, the current market trends and the possible changes in the variables that affect the demand of the product.

Discuss the limitations of statistics in detail: The field of statistics, though widely used in all areas of human knowledge and widely applied in a variety of disciplines such as business, economics and research, has its own limitations. Some of these limitations are:

• It does not deal with individual values: As discussed earlier, statistics only deals with aggregate values. For example, the marks obtained by one student in a class does not carry any meaning in itself, unless it can be compared with a set standard or with other students in the same class or with his own marks obtained earlier.

• It cannot deal with qualitative characteristics: Statistics is not applicable to qualitative characteristics such as honesty, integrity, goodness, colour, poverty, beauty and so on, since these cannot be expressed in quantitative terms. These characteristics, however, can be statistically dealt with if some quantitative values can be assigned to these with logical criterion. For example,
intelligence may be compared to some degree by comparing IQs or some other scores in certain intelligence tests.

• Statistical conclusions are not universally true: Since statistics is not an exact science, as is the case with natural sciences, the statistical conclusions are true only under certain assumptions. Also, the field deals extensively with the laws of probability which at best are educated guesses. For example, if we toss a coin 10 times, where the chances of a head or a tail are 1:1, we cannot say with certainty that there will be 5 heads and 5 tails. Thus the statistical laws are only approximations.

• Statistical interpretation requires a high degree of skill and understanding of the subject: In . order to get meaningful results, it is necessary that the data be properly and professionally collected and critically interpreted. It requires extensive training to read and analyse statistics in its proper context. It may lead to fallacious conclusions in the hands of the inexperienced. Describe the areas in which statistics have been extensively and effectively used :

Statistics has emerged as a versatile tool and has found extensive and effective applications across various domains. The utilization of statistical methods has significantly contributed to decision¬making, analysis, and understanding complex phenomena in the following areas:

• Economics and Business : In economics, statistical techniques are widely employed to analyze economic trends, forecast market behavior, and inform policy decisions. Businesses utilize statistics for market research, demand forecasting, cost-benefit analysis, and financial planning. Stock markets rely on statistical models to analyze stock prices, trends, and risks.

• Healthcare and Medicine : Statistical ihethods are crucial in medical research for clinical trials, drug development, and epidemiological studies. They help analyze the effectiveness of treatments, assess the impact of risk factors on health outcomes, and understand disease patterns. Public health officials use statistics to make informed decisions about healthcare resource allocation and disease prevention strategies.

• Social Sciences : Statistics play a vital role in sociology, psychology, political science, and other social sciences. Researchers use statistical methods to analyze survey data, study human ffehavior, and draw conclusions about social trends. Polls and surveys rely on statistical sampling techniques to ensure representative results.

• Education : In education, statistics are employed to assess student performance, evaluate teaching methods, and make data-driven decisions for curriculum development. Educational researchers use statistical analysis to identify factors influencing academic achievement and to gauge the effectiveness of educational interventions.

• Government and Public Policy: Governments utilize statistics for policy formulation, implementation, and evaluation. Census data, labor statistics, and economic indicators provide crucial information for understanding population dynamics, employment trends, and economic health. Statistical models help assess the impact of policy interventions.

• Environmental Science : Statistical methods are applied in environmental science to analyze climate data, assess the impact of pollution, and model ecological systems. Environmental researchers use statistics to study trends in deforestation, biodiversity loss, and climate change.

• Marketing and Advertising : Businesses use statistics to analyze consumer behavior, conduct market research, and tailor advertising strategies. A/B testing, a statistical method, is commonly employed to assess the effectiveness of marketing campaigns and website designs.

• Quality Control in Manufacturing : Statistical process control (SPC) is extensively used in manufacturing to monitor and improve production processes. It helps identify variations, reduce defects, and ensure consistent product quality.

• Sports Analytics : Statistics have revolutionized sports analysis, helping teams make informed decisions about player performance, strategy, and game outcomes. In sports like baseball, basketball, and soccer, advanced statistical models are employed for player
evaluation and team optimization.

• Finance and Banking: Financial institutions rely on statistical models for risk assessment, portfolio management, and fraud detection. Credit scoring, a statistical method, is used to evaluate the creditworthiness of individuals and businesses.
The widespread and effective use of statistics in these diverse areas underscores its significance in contemporary decision-making and research. As technology advances and data availability increases, the role of statistics is likely to expand even further across various disciplines.

Group – C

Objective type Questions with Answers
I. Multiple Choice Questions with Answers:

Question 1.
Why is a single birth in a hospital not considered statistics?
(i) Lack of numerical expression
(ii) Absence of predetermined purpose
(iii) Inadequate causes
(iv) Inability to compare with other births
Answer:
(iv) Inability to compare with other births

Question 2.
According to L. Bowley, what is one aspect of statistics?
(i) Science of measurement
(ii) Science of average
(iii) Science of counting
(iv) Science of enumeration
Answer:
(ii) Science of average

Question 3.
Which definition of statistics is considered most appropriate among the given options?
(i) “Science of counting”
(ii) “Science of measurement of social organism”
(iii) “Collection, presentation, analysis, and interpretation of numerical data”
(iv) “Science of average”
Answer:
(iii) “Collection, presentation, analysis, and interpretation of numerical data”

Question 4.
What is the first basic step in any statistical inquiry?
(i) Analysis of Data
(ii) Collection of Data
(iii) Interpretation of Data
(iv) Presentation of Data
Answer:
(ii) Collection of Data What is tabulation in the context of statistics?
(i) Collection of Data
(ii) Presentation of Data
(iii) Analysis of Data
(iv) Arrangement of classified data in the form of a table
Answer:
(iv) Arrangement of classified data in the form of a table

Question 5.
Which field uses statistics for predicting future trends based on past data?
(i) Commerce and Accounts
(ii) Industries
(iii) Behavioural and Social Sciences
(iv) Pure Sciences and Mathematics
Answer:
(i) Commerce and Accounts

Question 6.
What is one of the functions of statistics in determining relationships between phenomena?
(i) Condensing data
(ii) Predicting future trends
(iii) Classifying and comparing data
(iv) Establishing functional relationships
Answer:
(iv) Establishing functional relationships

CHSE Odisha Class 12 Education Solutions Chapter 18 Statistics: Meaning, Nature, and Uses

Question 7.
Which area of human knowledge has statistics not widely spread to?
(i) Mathematics
(ii) Social Sciences
(iii) Natural Sciences
(iv) Economics
Answer:
(iii) Natural Sciences

Question 8.
What is a limitation of statistics in dealing with individual values?
(i) Lack of universal truth
(ii) Inapplicability to qualitative characteristics
(iii) Requirement of numerical expression
(iv) Only dealing with aggregate values
Answer:
(iv) Only dealing with aggregate values

Question 9.
Why are statistical conclusions not universally true?
(i) Lack of precision
(ii) Dependence on probability
(iii) Inability to deal with qualitative characteristics
(iv) Requirement of numerical expression
Answer:
(ii) Dependence on probability

Question 10.
What is essential for meaningful statistical interpretation?
(i) Lack of skill
(ii) Inexperienced handling
(iii) Proper collection and professional interpretation
(iv) Numerical expression
Answer:
(iii) Proper collection and professional interpretation

Question 11.
In which field is statistics considered a basic tool for handling daily matters?
(i) Education
(ii) Pure Sciences and Mathematics
(iii) Industries
(iv) Policy planning
Answer:
(iii) Industries

Question 12.
Which function of statistics involves predicting future trends based on past data?
(i) Condensation of data
(ii) Classification and comparison of data
(iii) Determining functional relationships
(iv) Predicting future trends
Answer:
(iv) Predicting future trends

Question 13.
What does the science of statistics primarily deal with?
(i) Individual values
(ii) Quantitative information
(iii) Qualitative characteristics
(iv) Random facts and figures
Answer:
(ii) Quantitative information

II. Fill in the blanks:

Question 1.
Statistics are aggregates of facts: Single or isolated facts cannot be called statistics as they need to be ______ for meaningful comparison and analysis.
Answer:
Aggregated or combined

Question 2.
Statistics are numerically expressed: All statistics are stated in ______ figures, emphasizing the quantitative nature of the information.
Answer:
Numerical

Question 3.
Statistics, generally, are not the outcome of a single cause but are affected by ______ causes working together.
Answer:
Multiple or various

Question 4.
L. Bowley gave several definitions of Statistics: One definition emphasizes enumeration, stating “Statistics may be called the science of ______.”
Answer:
Counting

Question 5.
Statistics are collected for a predetermined purpose: The purpose of collecting pertinent data must be clearly defined ______ data collection.
Answer:
Prior to

Question 6.
Classification and Presentation: The process of presenting classified data in the form of a table is known as ______.
Answer:
Tabulation

CHSE Odisha Class 12 Education Solutions Chapter 18 Statistics: Meaning, Nature, and Uses

Question 7.
Functions of Statistics: It condenses and summarizes voluminous data into a few presentable, understandable, and precise ______ .
Answer:
Figures

Question 8.
It helps in determining functional relationships between two or more phenomena: Statistical techniques such as correlational analysis assist in establishing the degree of association between independent ______.
Answer:
Variables

Question 9.
Scope and Use of Statistics: In social sciences, where both quantitative and qualitative information are used, statistics helps researchers to alter the information in a comprehensive way to explain and predict ______.
Answer:
Patterns of behavior/trends

Question 10.
Limitations of Statistics: Statistical conclusions are not universally true, as they are only ______ under certain assumptions and are approximations.
Answer:
True

III. Answer the following questions in one word:

Question 1.
What is the primary characteristic that distinguishes statistics from isolated facts?
Answer:
Aggregation

Question 2.
Why are single or isolated facts not considered statistics?
Answer:
Lack of comparability or relation to other figures.

Question 3.
What is the key feature of statistics in terms of expression?
Answer:
Numerical representation

Question 4.
According to L. Bowley, what did he emphasize in his definition of statistics?
Answer:
Enumeration aspect

Question 5.
What is the first basic step in any statistical enquiry?
Answer:
Collection of data

Question 6.
Which definition of statistics is considered most appropriate as it covers all aspects?
Answer:
Croxton and Cowden’s definition

CHSE Odisha Class 12 Education Solutions Chapter 18 Statistics: Meaning, Nature, and Uses

Question 7.
In which field does statistics help in determining functional relationships between variables?
Answer:
Social sciences

Question 8.
What is the purpose of condensing and summarizing voluminous data in statistics?
Answer:
To make it presentable, understandable and precise

Question 9.
What is a significant limitation of statistics in terms of dealing with values?
Answer:
It does not deal with individual values.

Question 10.
Why are statistical conclusions not universally true?
Answer:
They are based on assumptions and probabilities.

Meaning of Statistics:

• Statistics are aggregates of facts: Single or isolated facts or figures cannot be called statistics as these cannot be compared or related to other figures within the same framework. Accordingly, there must be an aggregate of these figures. For example, if I say that I earn $30,000 per year, it would not be considered statistics. On the other hand, if I say that the average salary of a professor at our college is $30,000 per year, then this would be considered statistics since the average has been computed from many related figures such as yearly salaries of many professors. Similarly, a single birth in a hospital is not statistics, as it has no significance for analytical purposes. However, when such information about many births in the same hospital or birth information for different hospitals is collected, then this information can be compared and analysed, and thus this data would constitute statistics.

• Statistics, generally are not the outcome of a single cause, but are affected by multiple causes: There are a number of forces working together that affect the facts and figures. For example, when we say that the crime rate in New York city has increased by 15 per cent over the last year, a number of factors might have affected this change. These factors may be: general level of economy such as state of economic recession, unemployment rate, extent of use of drugs, areas affected by crime, extent of legal effectiveness, social structure of the family in the area and so on.

While these factors can be isolated by themselves, the effects of these factors cannot be isolated and measured individually. Similarly, a marked increase in food grain production in India may have been due to combined effect of many factors such as better seeds, more extensive use of fertilizers, mechanisation in cultivation, better institutional framework and governmental and banking support, adequate rainfall and so on. It is generally not possible to segregate and study the effect of each of these forces individually.

• Statistics are numerically expressed: All statistics are stated in numerical figures which means that these are quantitative information only. Qualitative statements are not subject to accurate interpretations and hence cannot be called statistics. For example, qualitative statements such as India is a developing country or Jack is very tall would not be considered statistical statements. On the other hand, comparing per capita income of India with that of America would be considered statistical in nature. Similarly, Jack’s height in numbers compared to average height in America would also be considered statistics.

• Statistics are collected for a predetermined purpose: The purpose and objective of collecting pertinent data must be clearly defined, decided upon and determined prior to data collection. This would facilitate the collection of proper and relevant data. For example, data on the heights of students would be irrelevant if considered in connection with the ability to get admission in a college, but may be relevant when considering qualities of leadership. Similarly, collective data on the prices of commodities in itself does not serve any purpose unless we know, for the purpose of comparison, the type of commodities under investigation and whether these relate to producer, distributor, wholesale or retail prices. As another example, if you are collecting data on the number of in-patients in the hospital waiting to be X-rayed, then the pre-determined purpose may be to establish the average time for the patients before X-ray and what can be done to reduce this waiting time.

Definition of Statistics :
L. Bowley gave several definitions of Statistics :

  1. “Statistics may be called the science of counting”. This definition emphasises enumeration aspect only.
  2. In another definition he describes it as “ Statistics may rightly be called the science of average”.
  3. At another place Statistics is defined as, “Statistics is the science of measurement of social organism regarded as a whole in all its manifestations”.

• All three definitions given by Bowely seem to be inadequate because these do not include all aspects of statistics.

• According to Selligman “Statistics is the science which deals with the methods of collecting, classifying, presenting, comparing and interpreting numerical data collected to throw some light on any sphere of enquiry”.

• Croxton and Cowden defined “statistics as the collection , presentation, analysis ,and interpretation of numerical data”. Among all the definitions , the cme given by Croxton and Cowden is considered to be most appropriate as it covers all aspects and field of statistics.

These aspects are given below:
• Collection of Data : Once the nature of study is decided , it becomes essential to collect information in form of data about the issues of the study. Therefore, the collection of data is the first basic step. Data may be collected either from primary source or secondary or from both the sources depending upon the objective/s of the investigation

• Classification and Presentation : Once data are collected , researcher has to arrange them in a format from which they would be able to draw some conclusions. The arrangement of data in groups according to some similarities is known as classification. Tabulation is the process of presenting the classified data in the form of table. A tabular presentation of data becomes’ more intelligible and fit for further statistical analysis. Classified and Tabulated data can be presented in diagrams and graphs to facilitate the understanding of various trends as well as the process of comparison of various situations.

• Analysis of Data: It is the most important step in any statistical enquiry. Statistical analysis is carried out to process the observed data and transform it in such a manner as to make it suitable for decision making.

• Interpretation of Data : After analysing the data, researcher gets information partly or wholly about the population. Explanation of such information is more useful in real life. The quality of interpretation depends more and more on the experience and insight of the researcher.

Scope and use of Statistics :

• Policy planning: To finalise a policy, it requires some data from previous or expected environment that the policy can be effectively utilised with maximum favourable results. For example, in an organisation the previous sales data are analysed to develop future strategies in the field to obtain maximum benefit in terms of product sale.

• Management: Statistics is very useful tool in an organisation to view various aspects of work and well being of the employees as well as keeping an eye on the progress trend of the organisation.

• Behavioural and Social Sciences : In social sciences where both types (quantitative and qualitative) of information are used, statistics helps the researchers to alter the information in a comprehensive way to explain and predict the patterns of behaviour/ tren(iv) Where the characteristics of the population being studied are normally distributed, the best and statistically important decision about variables being investigated is possible by using parametric statistics or nonparametric statistics to explain the pattern of activities.

• Education : If education is intended to be well dispersed and effective in the interest of the population, the characteristics of students, instructor’s contents and infrastructure are very important to understand and again statistics enable these characteristics being analysed in context of needs of the nation. Once the parameters of all components are analysed, areas needing more emphasis become obvious.

• Commerce and Accounts : Where money matters are involved, it is essential to take extra care to manage the funds properly enabling efforts in various sectors. The cost and benefit analysis helps to decide putting money and regulating it for maximum benefit at minimum cost.

• Industries : Statistics is a basic tool to handle daily matters not only in big organisations but also in small industries. It is required, at each level, to keep data with care and look at them in different perspectives to mitigate the expenditure and enable each employee to have his/ her share in the benefit. Psychologists/ personnel officers dealing with selection and training in industries also use statistical tools to differentiate among employees.

• Pure sciences and Mathematics : Statistical tools are also instrumental to have precise measures in pure sciences and to see differences .on different occasions in various conditions. Statistics itself is a branch of mathematics which helps them understand differences among properties of various applications in mathematics.

• Problem solving : Knowing the useful difference between two or more variables enable the individual to find out the best applicable solution to a problem situation and it is possible because of statistic?. During problem solving statistics helps the person analyse his/ her pattern of response and the correct solution thereby minimising the error factor.

• Theoretical researches: Theories evolve on the basis of facts obtained from the fiel(iv) Statistical analyses establish the significance of those facts for a particular paradigm or phenomen(i) Researchers are engaged in using the statistical measures to decide on the facts and data whether a particular theory can be maintained or challenge(iv) The significance between the facts and factors help them to explore the connectivity among them.

Functions of Statistics :
Statistics is no longer confined to the domain of mathematics. It has spread to most of the branches of knowledge including social sciences and behavioural sciences. One of the reasons for its phenomenal growth is the variety of different functions attributed to it. Some of the most important functions of statistics are described as follows:

• It condenses and summarizes voluminous data into a few presentable, understandable and precise figures: The raw data, as is usually available, is voluminous and haphazar (iv) It is generally not possible to draw any conclusions from the raw data as collecte (iv) Hence, it is necessary and desirable to express this data in few numerical values. For example, the average salary of a policeman is derived from a mass of data from surveys. But just one summarized figure gives us a pretty good idea about the income of police officers. Similarly, stock market prices of individual stocks and their trends are highly complex to comprehend, but a graph of price trends gives us the overall picture at a glance.

• It facilitates classification and comparison of data: Arrangement of data with respect to different characteristics, facilitates comparison and interpretation. For example, data on age, height, sex and family income of college students gives us a much better picture of students when the data is categorized relative to these characteristics. Additionally, simply the statements about these figures don’t convey any significant meaning. It is their comparison that helps us draw conclusions.

It helps in determining functional relationships between two or more phenomenon:
Statistical techniques such as correlational analysis assist in establishing the degree of association between two or more independent variables. For example, the coefficient of correlation between literacy and employment gives us the degree of association between extent of training and industrial productivity.

Similarly, correlation between average rainfall and agricultural productivity can be obtainedby using such statistical tools. Some statistical methods can also be used in formulating and testing hypothesis about a certain phenomenon. For example, it can be tested whether a credit squeeze is effective in controlling prices of consumer goods or whether tenured professors are more motivated to improve their teaching than untenured professors.

• It helps in predicting future trends: Statistical methods are highly useful tools in analysing the past data and predicting some future trends. For example, the sales for a particular product for the next year can be computed by knowing the sales for the same product over the previous years, the current market trends and the possible changes in the variables that affect the demand of the product.

Limitations of Statistics :
The field of statistics, though widely used in all areas of human knowledge and widely applied in a variety of disciplines such as business, economics and research, has its own limitations. Some of these limitations are:

• It does not deal with individual values: As discussed earlier, statistics only deals with aggregate values. For example, the marks obtained by one student in a class does not carry any meaning in itself, unless it can be compared with a set standard or with other students in the same class or with his own marks obtained earlier.

• It cannot deal with qualitative characteristics: Statistics is not applicable to qualitative characteristics such as honesty, integrity, goodness, colour, poverty, beauty and so on, since these cannot be expressed in quantitative terms. These characteristics, however, can be statistically dealt with if some quantitative values can be assigned to these with logical criterion. For example, intelligence may be compared to some degree by comparing IQs or some other scores in certain intelligence tests.

• Statistical conclusions are not universally true: Since statistics is not an exact science,, as is the case with natural sciences, the statistical conclusions are true only under certain assumptions. Also, the field deals extensively with the laws of probability which at best are educated guesses. For example, if we toss a coin 10 times, where the chances of a head or a tail are 1:1, we cannot say with certainty that there will be 5 heads and 5 tails. Thus the statistical laws are only approximations.

Statistical interpretation requires a high degree of skill and understanding of the subject: In order to get meaningful results, it is necessary that the data be properly and professionally collected and critically interpreted. It requires extensive training to read and analyse statistics in its proper context. It may lead to fallacious conclusions in the hands of the inexperienced.

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