Prof. Rajkumar TeotiaInstitute of Advanced Management and Research (IAMR)

Address: 9th Km Stone, NH-58, Delhi-Meerut Road, Duhai,Ghaziabad (U.P) - 201206

Ph:0120-2675904/905 Mob:9999052997 Fax: 0120-2679145e mail: rajkumarteotia@iamrindia.com

What is statistics?

Collection of methods for planning experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions

  Statistics refers to the body of techniques used for collecting,

organizing, analyzing, and interpreting data. The data may be quantitative, with values expressed numerically, or they may be qualitative, with characteristics such as consumer preferences being tabulated. Statistics is used in business to help make better decisions by understanding the sources of variation and by uncovering patterns and relationships in business data.

What is statistics?

Statistics are the aggregates of facts Statistics are affected by a number of factors Statistics must be reasonably accurate Statistics must be collected in a systematic manner Collected in a systematic manner for a pre-determined purpose Lastly, Statistics should be placed in relation to each other

characteristics of statistics

Statistics are the aggregates of facts:- It means a single figure is not statistics. For example, national income

of a country for a single year is not statistics but the same for two or more years is statistics.

  Statistics are affected by a number of factors:- For example, sale of a product depends on a number of factors such as

its price, quality, competition, the income of the consumers, and so on.

Statistics must be reasonably accurate:- Wrong figures, if analyzed, will lead to erroneous conclusions. Hence,

it is necessary that conclusions must be based on accurate figures.

Statistics must be collected in a systematic manner:- If data are collected in a haphazard manner, they will not be reliable and

will lead to misleading conclusions. 

Collected in a systematic manner for a pre-determined purpose

  Statistics should be placed in relation to each other:- If one collects data unrelated to each other, then such data

will be confusing and will not lead to any logical conclusions. Data should be comparable over time and over space.

There are two main branches of statistics Descriptive Statistics Inferential Statistics

Descriptive statistics include the techniques that are used to summarize and describe numerical data for the

Purpose of easier interpretation  EXAMPLE- The monthly sales volume for a product during the past year can be

described and made meaningful by Preparing a bar chart or a line graph. The relative sales by month can

be highlighted by calculating an index number for each month such that the deviation from 100 for any given month indicates the percentage deviation of sales in that month as compared with average monthly sales during the entire year.

 

Descriptive Statistics

Inferential statistics include those techniques by which decisions about a statistical population or process are made based only on a sample having been observed. Because such decisions are made under conditions of uncertainty, the use of probability concepts is required

  EXAMPLE- In order to estimate the voltage required to cause an electrical

device to fail, a sample of such devices can Be subjected to increasingly higher voltages until each device fails. Based on these sample results, the probability of failure at various voltage levels for the other devices in the sampled population can be estimated.

Inferential Statistics

Statistics starts with a question, not with data/information

Every time we use statistic to find the solution for a question. Statistics are what decision makers can use to reduce ambiguity by

qualifying it. 

All Statistics are based on data

Data are what we hear, see, smell, taste, touch, etc. Data requires measuring Statistics are designed to transform data into information Make decisions using that information. Statistics are about and used to measure/assess risk of the decision.

How Statistics Work?

Business and Industry Health and Medicine Learning Research Social Statistics Natural Resources

Importance of Statistics

Statistics to start a Business Statistics to manufacturing  Statistics to marketing Statistics to Engineering

1-Business and Industry

Whether you are writing a business plan, feasibility study, advertising and marketing campaign, or even still deciding on what kind of business to start, start by looking at what is already happening in the field or industry you are interested in.

Statistics are not magic formulas for success, but they can give you important clues about how others are or failing.

Statistics to start a Business

In this process we use statistic to understand the number of products we have to produce and what are the new strategies we have to apply in future. It also gives an overview of the market.

 

Statistics to manufacturing

In marketing we use statistic in many ways banking the money you have in your business bank account can often provoke actions that are regretted at a later time. For example, if you have a healthy balance, you may decide to splash out on a purchase or investment that will in time, leave your account dangerously low: when money comes in, it is not unusual for all common sense to go out of the window…a bit extreme you may think!

Statistics to marketing

Engineers apply physical and chemical laws and mathematics to design, develop, test, and supervise various products and services. Engineers perform tests to learn how things behave under stress, and at what point they might Fail. As engineers perform experiments, they collect data that can be used to explain relationships better and to reveal information about the quality of products and services they provide.

 

Statistics to Engineering

Medical statistics deals with applications of including

epidemiology, public health find data on indicators of the nation's health, such smoking drinking and drug use, and abortion statistics. This is of particular importance when attempting to determine whether the pharmacological effect of one drug is superior to another which clearly has implications for drug development Therefore, it is essential for pharmacologists to have an understanding of the uses of the statistics.

2 - Health and Medicine

The techniques of statistics can prove to be valuable tools for teachers of to interpret statistics is advantageous to analyze lab results, book and journal articles, and as an aid in approaching problem-solving scientifically. Statistics will allow you to critically evaluate your students, your teaching, and the results of educational research.

 

3 - Learning

The word researches are depending in statistics, when we

found any data from research we analyze and make decisions using statics. These are the examples for government researches.

Research and Development: DOE Could Enhance the Project Selection Process for Government Oil and Natural Gas Research.

Bureau of Government Research wants 'realistic' development strategy

4 – Research

Social statistics is the use of statistical measurement systems to study human behavior in a social environment. This can be accomplished through polling a particular group of people, evaluating a particular subset of data obtained about a group of people, or by observation and statistical analysis of a set of data that relates to people and their behaviors. Often, social scientists are employed in the evaluation of the quality of services of a particular group or organization, in analyzing behaviors of groups of people in their environment and special situations, or even in determining the wants or needs of people through statistical sampling.  

 

5 - Social Statistics

Child-bearing, Child and elderly populations Housing and Human settlements Education and Literacy Income , economic activity and Unemployment

Social Statistics

Health, nutrition and educational level in country. To identify the strength of working people. To planning the future

Child-bearing, Child and elderly populations

Identify problems in housing planning. to settle the problems in slums.

Housing and Human settlements

Study about the current education system in country. Develop the subject planning Future employment planning.

Education and Literacy

To understand about savings and investment. introduce future investing systems

Income , economic activity and Unemployment

Statistics are used in the scientific study of agriculture as a tool to determine if the differences in variables are real or due to chance. This translates to the farmer to let him know with confidence which varieties are better than other varieties or which fertilizer treatments will give better yields than others. In many countries in agriculture they use so many statistical researches to do their agriculture successfully. These are some of projects that some countries are managed.

6 - Natural Resources

There are certain phenomena or concepts where statistics cannot be used. This is because these phenomena or concepts are not amenable to measurement. For example, beauty, intelligence, courage cannot be quantified. Statistics has no place in all such cases where quantification is not possible.

Statistics reveal the average behavior, the normal or the general trend. An application of the 'average' concept if applied to an individual or a particular situation may lead to a wrong conclusion and sometimes may be disastrous.

For example, one may be misguided when told that the average depth of a river from one bank to the other is four feet, when there may be some points in between where its depth is far more than four feet. On this understanding, one may enter those points having greater depth, which may be hazardous.

LIMITATIONS OF STATISTICS

Since statistics are collected for a particular purpose, such data may not be relevant or useful in other situations or cases. For example, secondary data (i.e., data originally collected by someone else) may not be useful for the other Person.

Statistics are not 100 per cent precise as is Mathematics or Accountancy. Those who use statistics should be aware of this limitation.

In statistical surveys, sampling is generally used as it is not physically possible to cover all the units or elements comprising the universe

At times, association or relationship between two or more variables is studied in statistics, but such a relationship does not indicate cause and effect' relationship. It simply shows the similarity or dissimilarity in the movement of the two variables

In statistics, data are classified into two broad categories:

Quantitative data. Qualitative data.

TYPES OF DATA AND DATA SOURCES

Quantitative data are those that can be quantified in definite units of measurement. These refer to characteristics whose successive measurements yield quantifiable observations. Depending on the nature of the variable observed for measurement.

Quantitative data can be further categorized as Continuous Data Discrete Data.

1 - Quantitative data

Continuous data represent the numerical values of a continuous variable. A continuous variable is the one that can assume any value between any two points on a line segment, thus representing an interval of values. The values are quite precise and close to each other, yet distinguishably different. All characteristics such as weight, length, height, thickness, velocity, temperature, tensile strength, etc., represent continuous variables. Thus, the data recorded on these and similar other characteristics are called continuous data

Continuous Data

Discrete data are the values assumed by a discrete variable. A discrete variable is the one whose outcomes are measured in fixed numbers. Such data are essentially count data. These are derived from a process of counting, such as the number of items possessing or not possessing a certain characteristic. The number of customers visiting a departmental store every day, the incoming flights at an airport, and the defective items in a consignment received for sale, are all examples of discrete data.

Discrete Data

Qualitative data refer to qualitative characteristics of a subject or an object. A characteristic is qualitative in nature when its observations are defined and noted in terms of the presence or absence of a certain attribute in discrete numbers.

These data are further classified as Nominal Data Rank data

Qualitative data

Nominal data are the outcome of classification into two or more categories of items or units comprising a sample or a population according to some quality characteristic. Classification of students according to sex (as males and

females), of workers according to skill (as skilled, semi-skilled, and unskilled), and of employees according to the level of education (as matriculates, undergraduates, and post-graduates), all result into nominal data. Given any such basis of classification, it is always possible to assign each item to a particular class and make a summation of items belonging to each class. The count data so obtained are called nominal data.

 

Nominal Data

Rank data, on the other hand, are the result of assigning ranks to specify order in terms of the integers 1,2,3, ..., n. Ranks may be assigned according to the level of performance in a test. a contest, a competition, an interview, or a show. The candidates appearing in an interview, for example, may be assigned ranks in integers ranging from I to n, depending on their performance in the interview. Ranks so assigned can be viewed as the continuous values of a variable involving performance as the quality characteristic.

Rank data

Data sources could be seen as of two types, viz., secondary and primary. The two can be defined as under:

 (i) Secondary data: They already exist in some form: published or

unpublished - in an identifiable secondary source. They are, generally, available from published source(s), though not necessarily in the form actually required.

 (ii) Primary data: Those data which do not already exist in any

form, and thus have to be collected for the first time from the primary source(s). By their very nature, these data require fresh and first-time collection covering the whole population or a sample drawn from it.

DATA SOURCES

FREQUENCY DISTRIBUTIONS:- A frequency distribution is a table in which possible values for a

variable are grouped into classes, and the number of observed values which fall into each class is recorded. Data organized in a frequency distribution are called grouped data. In contrast, for ungrouped data every observed value of the random variable is listed.

 EXAMPLE 1. A frequency distribution of weekly wages is shown

in Table 2.1. Note that the amounts are reported to the nearest dollar. When a remainder that is to be rounded is “exactly 0.5” (exactly $0.50 in this case), the convention is to round to the nearest even number. Thus a weekly wage of $259.50 would have been rounded to $260 as part of the data-grouping process.

Statistical Presentations and Graphical Displays

CLASS INTERVALS:- The class interval identifies the range of values included

within a class and can be determined by subtracting the lower exact class limit from the upper exact class limit for the class. When exact limits are not identified, the class interval can be determined by subtracting the lower stated limit for a class from the lower stated limit of the adjoining next-higher class. Finally, for certain purposes the values in a class often are represented by the class midpoint, which can be determined by adding one-half of the class intervals to the lower exact limit of the class.

 

 

EXAMPLE:- Table 2.2 presents the exact class limits and the class midpoints for the frequency distribution in Table 2.1.

A histogram is a bar graph of a frequency distribution. As indicated in Fig. 2-1, typically the exact class limits are entered along the horizontal axis of the graph while the numbers of observations are listed along the vertical axis. However, class midpoints instead of class limits also are used to identify the classes.

HISTOGRAMS AND FREQUENCY POLYGONS:-

A frequency polygon is a line graph of a frequency distribution. As indicated in Fig. 2-2, the two axes of this graph are similar to those of the histogram except that the midpoint of each class typically is identified along the horizontal axis. The number of observations in each class is represented by a dot above the midpoint of the class, and these dots are joined by a series of line segments to form a polygon, or “many-sided figure.”

 

EXAMPLE- frequency polygon for the distribution of weekly wages in Table 2.2 is shown in Fig. 2-2.

 

FREQUENCY POLYGONS:-

A cumulative frequency distribution identifies the cumulative number of observations included below the upper exact limit of each class in the distribution. The cumulative frequency for a class can be determined by adding the observed frequency for that class to the cumulative frequency for the preceding class

 

CUMULATIVE FREQUENCY DISTRIBUTIONS AND OGIVE CURVE

The graph of a cumulative frequency distribution is called an Ogive. For the less-than type of cumulative distribution, this graph indicates the cumulative frequency below each exact class limit of the frequency distribution. When such a line graph is smoothed, it is called an Ogive curve.

 

A pie chart is a pie-shaped figure in which the pieces of the pie represent divisions of a total amount, such as the distribution of a company’s sales dollar. A percentage pie chart is one in which the values have been converted into percentages in order to make them easier to compare

EXAMPLE:- Figure 2-12 is a pie chart depicting the revenues and the percentage of total revenues for the Xerox Corporation during a recent year according to the categories of core business (called “Heartland” by Xerox), growth markets; developing countries, and niche opportunities

PIE CHARTS