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The purpose of this article is to provide more information about the importance, scope, and limitations of statistics. As the government relied on statistics solely for administration in ancient times, statistics were limited in scope. This subject became increasingly popular and its application became more extensive as time went on. Almost no field of human activity is exempt from the use of statistics today. It is now used primarily by economists, businessmen, scientists, and administrative professionals.

## What is Statistics?

Data analysis and interpretation are the essences of the science of statistics. Statistics conducts experiments, analyses, interprets, and presents data. There is a significant amount of overlap between statistics and virtually every scientific field, and statistical methods and theories are constantly being developed in response to new research questions in each field.

The mathematical and computational tools statisticians employ in developing methods and in studying the theory behind the methods are varied. It is important to understand that uncertainty and variation are fundamental concepts in the field of statistics.

There are many situations in science (or more generally in our lives) where we have no idea what will happen. Sometimes, the uncertainty is a result of the outcome not yet having been established (e.g., whether it will rain tomorrow) and, in other cases, the uncertainty is a result of not knowing whether we passed a particular exam.

Mathematics is a method for discussing uncertain events, and probability plays a significant role in statistics. The reliability of data collection and measurement efforts can be affected by a number of factors. A repeat of the same measurement will likely change the answer, according to this concept. It is the goal of statisticians to understand and reduce variations (whenever possible) in any situation.

## Limitations of Statistics

- Statistics is unable to explain individual items
- Statistics are unable to study qualitative characters
- Statistical results are not accurately correct
- Statistics deal with average
- Statistics is only one of the methods of studying a given problem
- Statistics is liable to be misused
- Qualitative Aspect Ignored
- Many methods to study problems
- Results are true only on average
- Statistical laws are not exact

## Types of Statistics

There are two major categories of statistics:

- Descriptive statistics
- Inferential statistics

### Descriptive Statistics

The data is summed up using the given observations in this type of statistical. Summarisation refers to a summation of data from a sample of people using parameters such as the arithmetic mean or the standard deviation. A descriptive statistic is the use of tables, graphs, and summary measures to organize, represent, and summarize data. People who have access to the Internet or who use Television in a large gathering. These four categories are also detailed in descriptive statistics:

- Measure of frequency
- Measure of dispersion
- Measure of central tendency
- Measure of position

Using the frequency measurement, you can see how many times a particular piece of data occurs. The range, variance, and standard deviation of data describe how dispersed the data is. Essentially, it determines the way data is spread out. The central tendency may be defined as the average, median, and mode. Moreover, the measure of the position may be expressed as the percentile or quartile rank.

### Inferential Statistics

Interpreting descriptive statistics is done using this type of statistic. When the collected data has been analyzed, analyzed, and summed up, the data can be described using these statistics. A random variate allows us to draw conclusions about data that is dependent on variable stochasticities, such as observation errors, sampling variations, etc.

It is a method of using a sample of data to make inferences about the entire population using the information set obtained from the sample. As a consequence, we are given the right to make claims that are beyond the scope of data and information. A hypothetical study may be used to derive estimates.

### Statistics Example

An individual’s marks obtained after participating in a class are described as data. We can now calculate the average of 50 students’ marks by taking the mean of the data. We can draw a conclusion or make a judgment on the basis of the average mark that 50 students obtained.

## What is the Importance of Statistics?

- Statistics and planning: Taking advantage of statistics has never been more important than it is in this age when planning is king. Almost everywhere in the world, governments use statistics for planning. The use of statistics is re-emerging in economic development planning.
- Statistics and economics: It has become increasingly important to utilize statistical data and statistical analysis in order to involve economic problems. This can be done by analyzing wages, prices, time series, and demand patterns.
- Statistics and business: Controlling production with statistics is an irresponsible practice. For analyzing the wants and needs of their valued clients, business executives are increasingly using statistical tools.
- Statistics and industry: Quality control involves a great deal of statistical analysis in the industry. Checking whether a production component is conforming to the specification is part of production engineering. The data from the inspection plan, control chart, etc., are statistical tools for improving product quality.
- Statistics and mathematics: The development of recent statistical techniques is strongly related to the development of mathematics.
- Statistics and modern science: Statistical tools are of great importance in medical science for collecting, presenting, and analyzing observed facts regarding disease causes and incidence, as well as the application of different drugs and medications.
- Statistics, psychology, and education: The science of statistics is important to education and physiology. For example, it is often used to determine what tests are valid and reliable as well as to analyze factors.
- Statistics and war: Military and personal planning to effectively destroy the enemy with minimum effort can greatly benefit from the theory of decision function in war.

## What is the Scope of Statistics?

Using statistics in research can be very valuable when the researcher understands its importance and scope:

### 1. Statistics help in economic planning

These very countries are useful in solving economic problems thanks to statistical data and various techniques of statistical analysis. Statistic data is the foundation for all economic plans of a country. Statistics also indicate whether a plan has been successful. There are many economic aspects that can be expressed numerically, including production, consumption, wages, price profits, unemployment, and poverty.

We can calculate the balance between supply and demand by studying production statistics. By analyzing the consumption patterns of the various classes of people of society, we can come to some understanding of their purchasing capacity and living standards. With the proper use of statistics, the supply can be matched to the demand.

### 2. Statistics in business and management

The use of statistics by businessmen has become increasingly popular. By forecasting trends and formulating policies regarding the business, it assists businessmen. It is crucial that businessmen estimate and make decisions with accuracy and precision regarding the future demand for products, market trends, and so on.

A successful business depends on the ability to make accurate estimations and decisions using statistical methods. Wallis and Roberts state that statistics is a set of practices that can help people make well-informed decisions when facing an uncertain future.

### 3. Statistics in administration

Statistics are essential for assessing whether an administration is efficient. Statisticians have collected information regarding military and fiscal policies since the advent of statistics. Statistics on different aspects of people are collected by the state, which is then used to formulate policies that will improve the welfare of the people.

### 4. Statistics in research

There are many different types of research that use statistical methods. Statistics are useful for different types of research, whether it is in agriculture, health, or social science. A variety of seeds, fertilizers, etc. can affect the yield of a crop in agriculture. Using appropriate statistical tools, one can assess the yield.

As well as insurance companies, industries in physical science, banking, railroads, transportation, astronomy, etc., statistics have a strong impact on all these fields. Considering this, we can conclude that nowadays only a small number of activities do not use statistics.

## What are the Limitations of Statistics?

The use of statistics in all fields is extremely widespread, but there are still some limitations. There are three main limitations of statistics:

### 1. Statistics is unable to explain individual items

Statistics examines a mass of phenomena and reaches conclusions based on the results of the mass of observations instead of a single observation. Statisticians study the income of a single employee of a company but are non-statisticians when studying the incomes of fifty employees. Rather, the average income of 1,000 workers of a company forms statistics, not the incomes of 1,000 workers of a company on an individual basis.

### 2. Statistics are unable to study qualitative characters

Statistical research generally focuses only on the quantitative aspects of a given problem rather than its qualitative attributes. It’s not possible to study directly the problems that cannot be studied quantitatively (as numerical data) such as poverty, leadership, beauty, intelligence, honesty, etc, through statistical calculations.

### 3. Statistical results are not accurately correct

The results of most statistical tests are more or less approximate and only a few are actually correct. To be more precise, statistical laws are average-based, so it is impossible to achieve 100 percent accuracy.

### 4. Statistics deal with average

The study of statistics involves determining averages based on individual observations. Statistical laws can only be applied on average.

### 5. Statistics is only one of the methods of studying a given problem

The statistical method cannot provide the best solution in all circumstances for the given problem. Unless they are supplemented by other evidence, statistics cannot be very useful for examining a given problem, such as a culture, religion, or philosophy.

### 6. Statistics is liable to be misused

Statistical science has one of its greatest limitations: it can be abused. Only someone skilled in statistical methods is capable of handling statistical data scientifically. When inexperienced, incompetent, and unskilled people use statistical methods, they may cause false predictions.

### 7. Qualitative Aspect Ignored

In addition, statistical methods do not take into account phenomena that are unmeasurable. This means that statistics cannot be used for such phenomena. There are several of these, such as health, wealth, and intelligence. To calculate them, qualitative data must be converted to quantitative data.

### 8. Too many methods to study problems

There are so many methods we use in this subject just to find one result. The results of quartile deviations, mean deviations, and standard deviations vary depending on the type of variation. We should not assume that statistics are the only method to use in research. We shouldn’t consider this the best method to use either. Cowden and Croxton.

### 9. Results are true only on average

Using this method, time series, regressions, and probability can be used to interpolate the results. However, these are not necessarily accurate. A student in section A gets the same marks as he or she does in section B simply because the average of the two sections is the same. Both sections often have their own differences. As a result, there are average marks.

### 10. Statistical laws are not exact

The laws of statistics are not as precise as those of natural science. The law of averages applies to statistics. The law will hold up under certain circumstances. Their application cannot be universal.

## Important Questions of Limitations of Statistics

**What are the main limitations of statistics?**

# It is generally true that statistics laws apply. Observations are not statistics, since statistics are composed of aggregates of facts. Statistical methods are limited to groupings and aggregates.

# Quantitative data lends itself better to statistical analysis.

# Analyzing heterogeneous data is not feasible through statistics.

# The outcome of statistical analysis could be misleading if data collection, analysis, and interpretation are not done meticulously.

# Statistics can only be understood by someone who has a thorough understanding of the subject.

# It is possible to make statistical mistakes. Inferential statistics are particularly prone to making mistakes. There is no way to determine whether an error was made.

**What are the two types of statistics?**

Descriptive statistics and inferential statistics differ in their methods.

**What is the use of statistics in real life?**

The statistics field plays a significant role in everyday life, especially for large industries that calculate their data in mass quantities. It assists in collecting, analyzing, and interpreting the data. In addition, statistical graphs, charts, and tables are a great way of presenting the data.

**What is the meaning of the measure of dispersion?**

In statistics, dispersion is defined as the spread of given data, its variation, and its standard deviation. The intervals are fixed, so it illustrates the data spread.

**Is the measure of central tendency also a type of statistics?**

Descriptive statistics are used to describe central tendencies. Average, median, and mode are three examples.

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##### What are the Limitations of Statistics Class 11 2021 | Explain the Importance and Limitations of Statistics PDF in English

What are the Limitations of Statistics Class 11 Scope and importance and limitations of statistics? It is now used primarily by economists, businessmen, etc.

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