3 Introduction, Significance, Scope and Limitations of Statistics
Dr Deependra Sharma
Introduction, Significance, Scope and Limitations of Statistics
Learning Objectives
- After careful study of the following, the students will be able to:
- Recall and memorize the important terms mentioned in the chapter. Understand the significance of statistics in various walks of life.
- Assess what kind of problems can be solved using statistics.
- Differentiate between data, information, knowledge and wisdom. Recall the limitations of Statistics.
Introduction to Statistics
Consider the following examples mentioned below:
To travel from Delhi to Gurgaon, the average one-way travel time is 55.3 minutes. Twitterati (Users on twitter) have risen by 176 million in the last year.
2 million new whatsapp users are added every day. This comes to 6 each second.
In 2016, XYZ corp. predicts that 37.5 million people in the India. (19% of Smartphone users) will perform transactions with their phones at sale terminals, which is an approximate 61% increase from the last year.
According to a survey, 9% of all U.S. retail sales in 2016 will be through online medium and, the spending capacity per person is expected to rise from $1,207 to $1,738 from 2015 to 2016.
In all the points mentioned above, there are some numerical figures or facts like 55.3 minutes, 176 million, 6 users per second, 37.5 million, 9%, and $1738. These numerical facts are called Statistics and these numbers, percent, figures allows us to understand business and economic situations.
From the above examples, it becomes clear that numbers, figures are the heart of statistics without which this discipline cannot survive but, it is also imperative that statistics is just not limited to numbers and graphical representation of data. It is about extracting valuable information and conclusions from such data.
The following points become the area of focus in Statistics:
Type and volume of data.
Data organization and summarization. Data analysis and interpretation.
Results representation and judgment on their certainty
Thus, with Statistics, we can design the systems, create a description for them and deduce inferences from them.
Definitions
Merriam-Webster dictionary defines statistics as “classified facts representing the conditions of a people in a state – especially the facts that can be stated in numbers or any other tabular or classified arrangement”.
Renowned Statistician Arthur Lyon Bowley defines statistics as “Numerical statements of facts in any department of inquiry placed in relation to each other”.
He also defined statistics as, “Statistics may be called the science of counting”. At another place he defines, “Statistics may be called the science of averages”.
According to Horace Secrist “By statistics we mean aggregates of facts affected to a marked extent by a multiplicity of causes numerically expressed, enumerated or estimated according to reasonable standards of accuracy collected in a systematic manner for a pre-determined purpose and placed in relation to each other”.
Thus, based on the definitions above, we can say that Statistics possess the following features:
Aggregation of facts.
Affected by several causes. Expressed numerically.
Has an accuracy level to some extent. Represented in some form.
Generally in business and economics, the management and policy makers have a better understanding of the business situations and economic scenario by collecting, analyzing, presenting, and interpreting data. It empowers them to be more informed and help them to take better decisions.
Types of Statistics
Broadly the methods in statistics fall in two types: Descriptive and Inferential
Descriptive Statistics
A discipline that describes the important characteristics of the dataset in a quantitative manner is referred as Descriptive Statistics. To describe the properties of various items in the data set, it uses measures of central tendency, i.e. mean, median, mode and the measures of dispersion i.e. range, standard deviation, quartile deviation and variance, etc.
It also makes use of charts, graphs and tables like bar charts, pie charts, line graphs etc to summarize and present the data in a manner which appears more useful and accurate to the reader.
Example of Descriptive Statistics
1. Out of 150 people who were randomly selected in the town of Tilak nagar, Delhi, 65 people had the last name Singh. An example of descriptive statistics is the following statement :
“43.33 % of these people have the last name Singh.”
2. On the last 3 Sundays, Mr X sold 2, 1, and 0 new mobile phones respectively. An example of descriptive statistics is the following statement :
“X averaged 1 new mobile phone sold for the last 3 Sundays.” These are both descriptive statements because they can actually be verified from the information provided.
Inferential Statistics
As the name suggests, it is about finding inferences or conclusions. In this method, we proceed by taking a sample from the entire population because it is not easy to include each and every data item in the population.
Thereafter, the results of analysis of the sample can be deduced to the larger population, from which the sample is taken. It is a convenient way to draw conclusions about the population when it is not possible to query each and every member of the universe. However, the sample chosen is of great importance because if the chosen sample is a representative of the entire population; therefore, it should contain important features of the population.
Inferential Statistics is used to determine the probability of properties of the population on the basis of the properties of the sample, by employing probability theory. The major inferential statistics are based on the statistical models such as Analysis of Variance, chi-square test, student’s t distribution, regression analysis, etc. Methods of inferential statistics:
Estimation of parameters Testing of hypothesis
Example of Inferential Statistics
1. In a survey of 250 randomly selected people in Tilak Nagar, Delhi, it was found that 150 people had the last name Singh. An example of inferential statistics is the following statement:
“60% of the total population in Delhi has Singh as their last name.”
In this example, we have information of about 250 people living in Delhi but the meaning from statistical says that the whole population of Delhi is covered in this.
The easiest way to tell that this statement is not descriptive is by trying to If we want to verify it, then the best possible way is to strictly consider the numerical data in the information provided and careful inspection of the statement.
2. Mr X sold 2, 1, and 0 mobile phones respectively on last three Sundays. An example of inferential statistics is the following statements:
“Mr X never sells more than 2 mobile phones on a Sunday.”
Comparison between Descriptive and Inferential Statistics
| Basis | Descriptive | Inferential |
| Meaning | Descriptive Statistics is that branch of statistics which is concerned with describing the population under study. | Inferential Statistics is a type of statistics that focuses on drawing conclusions about some population, on the basis of sample analysis and observation. |
| What it does? | Organize, analyze and present data in a meaningful way. | Compares, test and predicts data. |
| Form of final Result | Charts, Graphs and Tables | Probability |
| Usage | To describe a situation. | To explain the chances of occurrence of an event. |
| Function | It explains the data, which is already known, to summarize sample. | It attempts to reach the conclusion to learn about the population that extends beyond the data available. |
Significance/Scope of Statistics
Statistics have a significant role to play in every business organization as a lot of data is generated from various business functional areas which is supposed to be analyzed by the managers which will further help them in their decision making and framing policies for the organization. Thus Statistics provides those tools for data analysis, it helps in presenting data in figures and facts and it helps managers in analyzing the business situations easily.
Managers feel confident when they have statistical tools by their side as these tools enable them to take business decisions in a quick manner despite the huge data that they have.
The statistics can help CEO’s to have an unbiased look of the market conditions and thus, they can make business strategies that are based on real data and not assumed one.
Statistics can also help managers in understanding the relationships of different variables in business situations For example, by a careful review of data, links between two variables can be revealed, such as discounted sales offers and revenue generation
Statistics also ensure quality into business processes. By using Statistics, the organizations can measure and control production processes to measure differences that will help organizations to know the quantity of raw material required, time required finishing the production, to minimize the waste and so on.
The section below provides insights into the significance hold by Statistics in business and economics:
Accounting
Accounting departments in every organization use statistical sampling procedures on a sample amount of data to ascertain whether their calculations/ formula applied by them is giving a fair response for every value. For instance, in case of issuing tax certificates to all the employees of the organization, the accounts department wants to determine whether the calculations that they had done are fair or not, the common practice in such situations followed by the accounts department is to select a small subset from all the employees which is known as sample and review the accurate value of that sample. After this review, they can easily come to a conclusion as to whether the conditions and formulas used by them were fair or not.
Finance
The financial analysts are able to guide their clients about stocks investments and give their recommendations by using a variety of statistical information and tools. A lot of financial data is reviewed by analysts like price/earnings ratio and dividend yields. Analysts make comparisons between an individual stock and the average of stock market and then come to analyze if a stock is over/underpriced and should be bought or not.
Marketing
Statistics have a lot of scope in marketing research applications. There are organizations like KPMG, NIELSEN etc which specialize in providing national-international level surveys based on marketing. These collect data from various point of sale of super markets like Big Bazaar, Spencers, EasyDay, Vishal Mega Mart etc and analyze the data contained in the invoices generated by terminals using various statistical tools. This type of data is generally not available freely thus such organizations have to spend huge amount to get this data. Similarly, special pricing days, offers, cash backs etc data from all other type of promotional activities is studied and analyzed using statistical tools to come to conclusions to be presented in Survey reports. A careful study of these reports may prove to be quite helpful in formulating marketing strategies for the future.
Economics
How the economy will grow? Whether it will grow or it will fall back? These are some of the forecasts the economists need to make. With statistics, making such forecasting is possible by analyzing the economical factors using Statistics as a lot of statistical information is used by economists in making such forecasts. For instance, while doing trading and buying/selling a particular commodity, the person likes to see how a particular commodity is doing over a past period of time and only then they will be able to decide whether to sell it or retain it. Statistics help in making such decisions. Moreover, statistics is also used to find the relationship between supply and demand, the inflation rate, imports and exports, the per capita income etc.
Computer Science
In computer science, statistics is used for a number of things, including data mining, data compression and speech recognition. Other areas where statistics are use in computer science include vision and image analysis, artificial intelligence and network and traffic modeling. Data mining is performed with the help of statistics by using functions to find irregularities or inconsistencies within data. Data compression uses statistical algorithms to compress data. Statistics are also used in network traffic modeling, whereby available bandwidth is exploited to be usable while the use of statistical programs avoids network congestion. Artificial intelligence tries to simulate human thought using algorithms that are similar to voice recognition or translation software. Other statistical uses in computer science include quality management, software engineering, storage and retrieval processes and software and hardware engineering and manufacturing. Algorithms have become necessary in many facets of computer programming and data mining.
Education
Education is a field where evaluation of students, teachers and other entities is a continuous activity. The collection, organization, analysis, interpretation and presentation of data are the activities that need to be conducted and this data is always huge and thus requires the use of statistical tools. For instance, calculating the average marks of a class can be represented using bar graph and histograms, cumulative frequency distribution curve, pie charts etc. Similarly, the report prepared after the processing of results is supposed to present the data statistically in graphical format. There also, statistical methods come very handy.
In Daily Life
Statistics is used in every walk of life like weather forecasting, detecting an illness, medical research, making policies for business sales, deciding on offers and discounts, in political campaigns, to keep track of sales, and promotion of insurance policies, analyzing the stock market and what not. Thus, statistics find its utility in every industry we can think of and its methods are a great help in analyzing different business situations and data analysis.
Limitations of Statistics
The statistic is restricted by certain limitations:
1. Useful for numerical studies only:
Statistics can work upon only numeric data. By numeric data, we mean data that is available in numbers that can be measured quantitatively and expressed numerically. It cannot be applied to all types of data.
2. Doesn’t consider individual but population:
The results presented by statistical analysis are based on a specific group as it is not feasible to take into account everything, thus that specific group which is called population is considered on behalf for the whole group but the results produced by the statistical methods are said to be applied on the whole group i.e they are not restricted to the population only. For example, in the statement 03 in every 10 Indian adults are obese, it shows the results which are found by considering all individuals.
3. Dependent on estimates and rough calculations:
The results produced by statistical methods are based on a specific population and not for every member of the universe and thus in certain situations are not reliable.
4. May promote false conclusions by deliberate manipulation of figures and unscientific handling:
Results generated from statistical methods are numerical in nature and depicted in figures that can be modified. The data can be represented graphically which is out of the context.
5. More than one method for a single problem:
In statistics, there are several methods available that an analyst may use to solve a single problem and results found through each of the methods may have different results. For example, Variation can be found by quartile deviation, mean deviation or standard deviations and results vary in each case.
6. Provide a basis of judgement but not the whole judgement:
As stated earlier, statistical methods work only on numerical data therefore it may happen that certain factors which are very important but cannot be measured/converted in numerical terms remain ignored and away from the analysis.
7. Misleading results:
Statistics may give misleading results if proper attention is not paid while data collection, analysis and interpretation.
8. Expert knowledge required:
To handle statistics, one must have the required expertise and command on the subject and must be able to apply their wisdom while selecting statistical methods.
Summary
Statistics mean aggregation of facts affected to a marked extent by a multiplicity of causes numerically expressed, enumerated or estimated according to reasonable standards of accuracy collected in a systematic manner for a pre-determined purpose and placed in relation to each other. It can be classified into two types: Descriptive and Inferential. Descriptive statistics refers to a discipline that describes the important characteristics of the dataset in a quantitative manner is referred as Descriptive Statistics. it uses measures of central tendency, i.e. mean, median, mode and the measures of dispersion i.e. range, standard deviation, quartile deviation and variance, etc. It also makes use of charts, graphs and tables like bar charts, pie charts, line graphs etc to summarize and present the data in a manner which appears more useful and accurate to the reader. Inferential Statistics is used to determine the probability of properties of the population on the basis of the properties of the sample, by employing probability theory. The major inferential statistics are based on the statistical models such as Analysis of Variance, chi-square test, student’s t distribution, regression analysis, etc. Statistics has significance in a number of fields like various areas of business like accounting, finance, marketing, production & economics, computer science, education etc. However, there are a few limitations of statistics like, it is useful only for numerical studies, and it doesn’t consider individuals but population, its dependence on estimates and unreliability of results.
Learn More:
- Das, N K, (2008) Statistical Methods, New Delhi, Tata McGraw Hill
- Anderson, David R; Sweeney, Dennis J and Williams, Thomas A (2011) Statistics for Business and Economics, 11/e, Mason, USA Cengage Learning
- Buhlmann, P and van de Geer, Sara (2011) Statistics for High Dimensional Data, Methods Theory and Applications, Springer