Scope, importance and limitation of statistics - class-XII

In a normal distribution, approximately 68.26% of the data falls within one standard deviation (sigma) of the mean, which is represented as the range between -1 sigma and +1 sigma.

Statistics collates data in a manner that makes it easy to draw meaningful conclusions from, which provided the empirical evidence that allows us to prove or disprove theories. 

The word 'Statistics' is derived from the Italian word 'Statista', which means a statesman or politician.

The word Statistics stems from the word Statistik, from the German language as introduced by Gottfried Achenwall.

No, Statistics isn't a pure science like physics or chemistry as it is not absolute and universal in nature. The observations made in statistics are more susceptible to a change in the situation, which will give a wildly different conclusion. 

Statistics uses quantitative data to draw conclusions and find evidences to prove the formulated hypothesis. 

Statistics is used in two senses: as plural (statistical data) and as singular (statistical methods/science). Therefore, both I and II are correct.

Statistics deals with aggregates of facts rather than single, isolated figures, as individual data points cannot be analyzed statistically.

Statistics is widely used in economics, business management, commerce and industry as it provides empirical evidence for theories constructed in these fields of study. 

Statistics does not analyse qualitative phenomenon, statistical methods deal with those objects which can be measured in quantitative terms. Qualitative phenomenons such as beauty, goodwill etc cant be captured by statistics.

Statistics is defined in two senses: as statistical data (plural) and as statistical methods (singular).

All three statements are related to a major limitation of statistics which is "improper use of statistics". There is a vast scope for error in the data and it may be misused by people with agendas, these people may manipulate the data to gain favour or popularity. 

The word 'Statistics' is derived from the German word 'statistik', which was used to describe the political state.

Inferential statistics involves using data from a sample to make estimates, decisions, or predictions about the larger population from which the sample was drawn.

Descriptive statistics focuses on summarizing data, while inferential statistics uses probability to draw inductive conclusions about a population based on sample data.

Statistics is derived from the french word "Statistique"

Descriptive statistics is the branch concerned with collecting, organizing, summarizing, and presenting data.

Statistics is considered a science because it uses systematic methods, and an art because it requires judgment and skill in the application of those methods.

Statistic must relate to aggregate facts only, it is not concerned with individuals. Statistical methods can be used to study and analyse only aggregate facts.

A key characteristic of statistics is that it deals with aggregates affected by multiple causes, not single isolated factors. Statistical facts are numerically expressed (Option A is wrong), deal with aggregates not single facts (Option C is wrong), so Option D is incorrect.

Statistical data is often estimated or collected through sampling, as it is rarely possible to achieve a perfect degree of accuracy in large-scale data collection.

Statistics is defined as the science of numerical data. Both numerical and quantitative data are synonymous in this context.

Statistics serves multiple functions, including making data precise, simplifying complex information, and enabling comparisons, so all listed options are correct.

The main goal of statistics is to collect, collate and analyse data and present its findings is an accurate and precise manner such that it enables meaningful conclusions to be drawn from the data. 

Statistics is a scientific method used to draw conclusions out of raw data. Statistics uses qualitative data to draw conclusions and find evidences to prove the formulated hypothesis. 

Statistics helps in grasping the meaning of certain laws of behavior in social sciences and lends precision to scientific inquiry. It helps finding out how various factors of production interact and contribute to economic activity. Analysts are able to collect and collate data in a precise manner to provide empirical evidence to a theory. Thus, it helps in condensing the mass of data into a few numerical measures and it enables an economist to present economic facts in a precise and definite form.

Statistics is the study of the collection and analysis of data, which is then collated and presented to provide empirical evidence to a hypothesis. It can be used to prove or disprove theories.

Statistics comprises data to present it in an understandable manner and relate it to a theory, it presents facts in a precise form and it makes the comparison of data possible.

Statistics is a scientific method used to draw conclusions out of raw data. 

Statistics deals with aggregates of data. A single, isolated fact cannot be analyzed statistically, so this statement is true.

Statistical facts can be affected by multiple causes, there is a lot of scope for error to be embedded in the data collected, one reason is that people interviewed may be lying. There may be bias on the part of the interviewer etc. Thus large samples are taken to ensure error is reduced.

Data for the entire population may not be available, or it may be impossible to collect and thus reasonable estimators must be used.  

Statistical regularity is a law in statistics that states that random events will exhibit similar properties when repeated enough times, that it they will follow a regular pattern. All central limit theorems and low of large numbers are laws of statistical regularity.

Descriptive statistics is the branch that deals with the numerical data collected, organized, and summarized to describe the main features of a dataset.

Descriptive statistics includes techniques like collection, tabulation, averages, dispersion, and skewness, which are used to summarize and describe data.

Applied statistics involves the practical application of statistical methods to real-world problems and data. Descriptive and inferential statistics are branches of statistics, but applied statistics specifically focuses on the use of these tools in actual situations.

The law of large numbers theorem states that identically distributed random variables will approach their normal distribution, theoretical mean and the size of the sample increases.

The law of statistical regularity states that a large sample taken at random from a population will likely possess the characteristics of the population. Therefore, both a large sample size and random sampling are necessary conditions.

Statistical regularity is a law in statistics that states that random events will exhibit similar properties when repeated enough times, that it they will follow a regular pattern. All central limit theorems and law of large numbers are laws of statistical regularity.

Inferential statistics is the branch concerned with drawing conclusions or making inferences about a population based on sample data. It uses sample statistics to estimate population parameters.

Inductive statistics, often used interchangeably with inferential statistics in some contexts, involves drawing general conclusions from specific observations. Business forecasting relies on these inductive processes to predict future trends based on historical data.

Mathematical statistics is the branch that provides the theoretical foundation for statistics. It involves the application of advanced mathematics like calculus and algebra to develop new statistical methods.

Statistics is a versatile tool used extensively in economics for testing hypotheses, analyzing problems, and planning. All the listed areas are standard applications of statistical techniques in economics.

Statistics has several limitations: it deals with aggregates rather than individuals, it can be misused or manipulated, and it primarily focuses on quantitative data rather than qualitative attributes. All these are recognized limitations.

Analytical statistics is specifically concerned with establishing functional relationships between variables. It involves comparing data sets to understand how one variable influences another.

Analytical statistics focuses on relationships between variables. Correlation and regression are the primary tools used to measure and model these relationships.

Statistics are aggregate of facts, a single numerical fact can't be called statistics. Thus they only deal with groups and not individuals. Statistics only deals with quantitative data it does not deal well with qualitative data beauty, honesty, goodwil etc cant be measured. The laws of statistic are not exact and they might be used improperly to misinform. Political parties may create misleading statistics to gain favor with the people.

All three statements are related to a major limitation of statistics which is "improper use of statistics". There is a vast scope for error in the data and it may be misused by people with agendas, these people may manipulate the data to gain favour or popularity. 

A major limitation of statistics which is "improper use of statistics" which is a result of the laws of statistic not being an exact science. There is a vast scope for error in the data and it may be misused by people with agendas, these people may manipulate the data to gain favour or popularity. eg. politicians publishing misleading statistics on employment and inflation to remain in power.

The law of statistical regularity states that, as the sample size is increased, the data collected from this group will reflect the data of the population, i.e., irregularities in the data begin diminishing as the size of the sample increases, as the characteristics of the group is the characteristics of the data.

Option D is correct. Preciseness and definiteness do not feature in process of data collection and analysis, rather it is an innate quality that is likely to be ensured at each stage of the data collection and refinement process. 

Statistics are numerically expressed as it solely deals with quantitative data. They are aggregate of facts as a single numerical fact cannot be termed as statistics, and only then can these facts be compared and conclusion drawn about the aggregate general facts.

The progression in data analysis is data to information, and information to knowledge. Knowledge is what allows for informed decision-making.

Inferential statistics involves using sample statistics to estimate population parameters and test hypotheses. Estimating a statistic is a descriptive process, not an inferential one, as the statistic is already calculated from the sample.

Statistics is broadly defined as the science of collecting, organizing, summarizing, analyzing, and interpreting data to make decisions.

Statistics carries out analysis of past data, which allows a trend line to be constructed, and thus the company has a higher chance of success as data regarding past performance is available. The data that is collated has to be accurate and systematically organized to help in the formation of developing decision policies. 

The data collected should be numerically expressed as statistics deals with quantitative data. should be collected with a purpose in order to for it to be accurate. Data should also be useful and sufficient to make estimations and draw conclusions.

The data collected should be numerically expressed and collated in a way that enables to draw conclusions. Data should be collected with a purpose in order for it to be accurate. It can be estimated to a degree as it may be highly impossible to collect data for the entire population, thus data that has reasonable accuracy is sufficient. Statistics is not concerned with a single observation, and has to be related to aggregate facts to be comparable and carry meaning. 

Statistical averages (measures of central tendency) are used to summarize large data sets, allow for comparisons between different groups, and provide a basis for informed decision-making.

This statement is correct. Descriptive statistics summarize the sample data, while inferential statistics use that sample to make generalizations about the larger population.

The computation of statistics is immensely helpful in the planning of policies as the government can now see how its progressing and implement targeted policies to improve the situation. E.g.: if the unemployment level is higher than average the government can choose to have targeted employment schemes in that area of the country. 

Statistics encompasses the entire lifecycle of data, including collection, organization, analysis, and interpretation.

It is usually either impossible or impractical (eg: it would cost too much money for it to be efficient) to collect data from each unit of the universe, thus samples are assumed to carry the characteristics of the population, which might not exactly be true.

Statistics is derived from the latin word "status".

Analytical statistics is defined by its focus on establishing functional relationships between variables through comparison, whether cross-sectional or longitudinal.

Statistics is widely used in all fields of human activity, these include but are not limited to economics, business studies, natural sciences, political science etc. 

Statistic usually relies on empirical evidence of the past in order to formulate a hypothesis and the possible long run path. Since the hypothesis is based on real data, it makes forecasting easier, it can help verify hypothesis which in turn can then help form targeted policies to aid in economic growth. 

Inductive statistics involves drawing conclusions about a larger population based on random observations or samples. It is the process of moving from the specific to the general.

Mathematical statistics is the branch that applies mathematical theories (like calculus, matrix theory, etc.) to develop the underlying theories and techniques used in other branches of statistics.

Statistics is derived from the italian word "statista ".

Statistics provides the empirical evidence necessary for state authorities to formulate effective fiscal, personnel, and training policies. It is essential for evidence-based governance.