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DEFINE STATISTICS? STATISTICS IN BUSINESS: ➢ DESCRIPTIVE STATISTICS. ➢ ESTIMATION. ➢ HYPOTHESIS TESTING. FREQUENCY DISTRIBUTION. MANAGEMENT SCIENCES. RELATIONSHIP BETWEEN STATISTICS MANAGEMENT SCIENCES.

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➢ PRESENTATION. ➢ ANALYSIS. ➢ INTERPRETATION. AREAS OF KEEN INTEREST.

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➢ OMISSION OF IMPORTANT FACTORS. ➢ CARELESSNESS. ➢ NON SEQUITUR. ➢ CONCEALED ➢ RESEARCH METHODS. TOOLS OF QUALITY. ➢ HISTOGRAM & ITS IMPORTANCE. ➢ JOINT FREQUENCY DISTRIBUTION IMPORTANCE. ➢ BAR CHARTS & ITS IMPORTANCE. ➢ PARETO CHARTS & ITS IMPORTANCE. ➢ PIE CHARTS & ITS IMPORTANCE. ➢ LINE CHARTS & ITS IMPORTANCE. ➢ FORECASTS. ➢ TIME SERIES ANALYSIS. ➢ TIME SERIES PLOT. ➢ SCATTER DIAGRAM.

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STATISTICS: The term statistics is used in either of two senses. In common parlance it is generally employed synonymously with the word data. Thus someone may say that he has seen “statistics of industrial accidents in the united states.” It would be conducive to greater precision of meaning if we were not to use statistics in this sense, but rather to say “data of industrial accidents in the united states.” “Statistics” also refers to the statistical principles and methods which have been developed for handling numerical data and which form the subject matter of this text. Statistical methods or statistics range from the most elementary descriptive devices which may be understood by anyone to those extremely complicated mathematical procedures which are comprehended by only the most expert’s theoreticians. It is the purpose of this volume not to enter into the highly mathematical and theoretical aspects of the subject but rather to treat of its more elementary and more frequently used phases. Statistics may be defined as the collection, presentation, analysis and interpretation of the numerical data. The facts which are dealt with must be capable of numerical expressions. We can make little use statistically of the information that dwellings are built of bricks, stone, wood and other materials, however if we are able to determine how many or what proportion o dwellings are constructed of each type material we have numerical data suitable for statistical analysis.

STATISTICS IN BUSINESS/BUSINESS STATISTICS: A collection of tools and techniques that are used to convert data into meaningful information in a business environment.

DESCRIPTIVE STATISTICS: The tools and techniques that compromise business statistics include those specially designed to describe data such as charts, graphs and numerical measures. Also included are inferential tools that help decision makers draw inferences from a set of data. Inferential tools include estimation and hypothesis testing.

The inferential tools includes two things the estimation and hypothesis testing. 2

ESTIMATION: In situations where one would like to know about all the data in large data sets but it is impractical to work with all the data, decision makers can use techniques to estimate what the larger data set looks like. The estimates are formed by looking closely at a subset of the larger data set.

HYPOTHESIS DEVELOPMENT: Once the decision maker identified the important variables in a situation and established the relationship among them through logical reasoning in the theoretical framework the decision maker is in a better position to test whether the relationship that have been theorized do in fact hold true. By testing these relationships scientifically through appropriate statistical analysis or through negative case analysis in qualitative research we are able to obtain reliable information on what kind of relationships exist among the variables operating in the problem situation. The results of these tests offer the decision maker some clues as to what could be changed in the situation to solve the problem. Formulating such testable statements is called hypothesis development.

FREQUENCY DISTRIBUTION: Frequency distribution is a summary of a set of data that displays the number of observations in each of the distribution’s categories and classes.

MANAGEMENT SCIENCE:

RELATIONSHIP OF STATISTICS AND MANAGEMENT SCIENCES: 3

The statistics plays a very crucial role in the field of management science. It is practically in practice in the organizations. The management’s main responsibility is to make logically sound decisions and the base of the decisions is the data that depends on the work and the statistical tools. So the statistical is inevitable for the business.

PRESENTATION: Either for one’s own use or for the use of others the data is presented in some suitable form. Usually the figures are arranged in tables or represented by graphic devices as discussed below: ➢ ➢ ➢ ➢

Text presentation . Tabular presentation . Semi tabular presentation. Graphic presentation.

TEXT PRESENTATION: Combining figures and text is not a particularly effective device, since it is necessary to read, or at least scan, all of the paragraphs before one can grasp the meaning of the entire set of figures. Most person cannot easily comprehend the data when set forth in this manner, and it is especially difficult for the reader to single out individuals. There is an advantage, however that the writer can direct attention to, and thus emphasize, certain figures and can also attention to comparisons of importance.

TABULAR PRESENTATION: This method of setting forth statistical data is usually superior to the use of text. A table of its title should be fully self explanatory although it may frequently be accompanied by a paragraph of interpretation or a paragraph directing attention to important figures. It is readily seen that the table is much briefer than the text statement since the row and column headings eliminate the necessity of repeating explanatory matter. As no text appears with the figures, the presentation is more concise. The logical arrangement of items in the stub and the box head makes a table clear and easy to read. The use of columns and rows for the figures facilitates comparisons.

SEMITABULAR PRESENTATION: This method is not often used, but it is survivable in that the figures are made to stand out from the text as they would not do if worked into one or two sentences. Incidentally the figures can be more readily compared than if they were in the text. 4

GRAPHIC PRESENTATION: Graphic devices are extremely useful and effective for quickly presenting a limited amount of information.

ANALYSIS: In the process of analysis, data is classified into useful and logical categories. The possible categories must be considered when plans are made for collecting the data, the data is classified as they are tabulated and before they can be shown graphically. Thus the process of analysis is partially concurrent with collection and presentation. There are four important bases of classification of statistical data: ➢ ➢ ➢ ➢

Qualitative Quantitative Chronological Geographical

QUALITATIVE: When for example employees are classified as union or non union we have a qualitative differentiation. The distinction is one of kind rather than of amount. Individuals may be classified concerning material status, as single, married, widowed, divorced and separated.

QUANTITATIVE: When items are varying in respect to some measureable characteristics, a quantitative classification is appropriate. Families may be classified according to the number of children. Manufacturing concerns may be classified according to the number of workers employed, and also according to the value of goods produced. Individuals may be classified according to the amount of income tax paid. Most quantitative distributions are frequency distributions.

CHRONOLOGICAL: Chronological data or time series show figures concerning a particular phenomenon at various specified times. In a certain sense time series are somewhat akin to quantitative distributions in that each succeeding year or a month of a series is one year or month further removed from from earlier point of reference. Occasionally a time series may be converted into a frequency distribution.

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GEOGRAPHICAL: The geographical distribution is essentially a type of qualitative distribution, but is generally considered as a distinct classification. Sometimes a geographical distribution may be put into the form of a frequency distribution. INTERPRETATION: The results is interpreted in the light of the limitations of the original material. Too exact conclusions must not be drawn from data which themselves are but approximations. It is essential however, that the investigator discovers and clarify all the useful and applicable meaning which is present in its data.

AREAS OF KEEN INTEREST: ➢ ➢ ➢ ➢ ➢

Omission of important factors. Carelessness. Non sequitur. Concealed classification. Research methods.

EXPLANATION: OMISSION OF IMPORTANT FACTOR: This can be easily be understood by the example that one year certain manufacturing company felt called upon to prove that all metal tops did not result in hotter car interiors. They suggested that a test involving three steps: 1) Take a piece of top fabric about 8 inches square. Place a piece of lining material of similar size beneath the fabric and a thermometer beneath the lining material. 2) Take a piece of highly finished steel about 8 inches square. Placed similar sized pieces of ¼ inch felt and lining material beneath the metal and a thermometer beneath the lining material. 6

3) Place each of the above assemblies on a board at room temperature. Carry the entire apparatus out into hot sunshine, leave it exposed for about 10 minutes and then read the Temperature of the thermometer. CARELESSNESS: Human beings cannot go through life without making mistakes, but should be reduced to a minimum.

NON SEQUITUR: This can easily be understood by an example of one of the weekly news magazine the circulation of which had been growing in a healthy fashion, undertook to demonstrate for a particular year that its readers greatly exceeds in circulation. It is possible because of the involvement of statistics which tells the exact figures of the increase in the number of readers and the number of magazines in circulation. CONCEALED CLASSIFICATION: Conclusions drawn from the statistical data may sometimes be invalid because of the presence of the concealed classification which is overlooked. One such concealed classification was found to be present in a study of suicides. The data seemed to show that suicides were more likely to occur among certain religious groups than among others. Upon further consideration it was apparent that the matter of the urban or rural occurrence of the suicides had been overlooked.

RESEARCH METHODS: It is assumed that the statistical method is the only method to be used in research; neither should this method be considered as the best attack for every problem. There are various method followed in the research that includes the case study method, experimental method, deductive method and the inductive method. The complementary nature of these methods of research is also reflected in operations research. This relatively new field is the application o quantitative methods to specific management problems which revolve around the use of men and machines within an organization. The objective is to optimize the solution to the problems. In operation research (sometimes called management science) the principles of such physical science as physics and chemistry are frequently combined. Of particular importance in operation research is the mathematical techniques of linear programming in which the inputs, the outputs and the objectives are completely quantified. 7

TOOLS OF QUALITY: ➢ ➢ ➢ ➢ ➢ ➢ ➢ ➢ ➢ ➢

Histogram. Joint frequency distribution. Bar charts. Pareto charts. Pie charts. Line charts. Forecasts. Time series analysis. Time series plot. Scatter diagram.

HISTOGRAM: A graph called histogram can be used to transform a frequency distribution into a visually appealing format. Histogram is a graph of frequency distribution with the horizontal axis showing classes the vertical axis showing the frequency count and the rectangles having a height equal to frequency in each class. Histogram is very useful for decision making when a data is of sequential nature and result required in comparison form to be shown to the management or directors for choosing among various options given. Such methods of pictogram clearly give the decision maker an idea in a bird’s eye view without going through the whole data.

JOINT FREQUNCY DISTRIBUTION: Frequency distributions are effective tools for describing data. Joint frequency distribution is a summary of a vicariate set of data that displays the number of observations that exhibit the respective joint characteristics of one value taken from each of the variables that define the data set. Distributions or data which is shown or required in such a manner that each variable is connected with the other hand or accumulated previous data so that the analyst can draw the result through escalated values. 8

BAR CHARTS: Bar charts are the graphical presentation of a categorical data set in which a rectangle or bar is drawn over each category or class. The length of each bar represents the frequency or percentage of observations contained in a category. The bars may be vertical or horizontal. The bars may all be the same color or they may be different colors depicting different categories. Additionally multiple variables can be graphed on the same bar chart. When data has different values under same heads like prices of food grains, cost of living indexes etc then bar charts are used to help the decision maker to analyze various and multiple nature values single glance. By multiple or complexbar charts joint data like sales of different items in given month, in a given time period, profits of different cumulative distributions in time period can be analyzed and compared and decision can be arrived quickly otherwise detailed study would have been required. Example diagram:

PARETO CHARTS: Pareto charts is a bar chart that is sorted so that the categories or classes are arranged from highest to the lowest with respect to the magnitude of the displayed variable associated with each category or class. These charts are used for ascending and descending order data i.e. four products are being manufactured in an organization and their respective sales is to be shown for deciding to give away the least selling commodity. Pareto chart is used in ascending order hence the least or the last bar drawn will show the least selling commodity. Yet it is another important tool of decision making.

PIE CHARTS: A pie chart is a graph in the shape of a circle. The circle is divided into slices corresponding to the categories or classes to be displayed. The size of the slices is proportional to the magnitude of the displayed variable associated with each category or class. 9

These charts represents the different sales volume of many things such as sales of car in a given year, sales of costumes etc. when total of a given data is known and it required to show the proportion of various value in the whole or share of individual items in the whole then pie chart is used for determining the larger or smaller share. Pie charts also helps the organization in decision making because the suggestions given by different employees can easily be accumulated by such charts and it also represents the most weighted opinion or the suggestion which helps the organization to be stuck at the best option. Example diagram: Sales 1st Qtr 2nd Qtr 3rd Qtr 4th Qtr

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LINE CHARTS: Line charts are two dimensional charts showing time on the horizontal axis and the variable of interest on the vertical axis. When trends are require to deciding about the future, decision making or determining the future performance of the sales, production, employees turnover etc line charts are used. They represents comparisons between trends of previous year in different phases i.e. months, forth night, quarters, semis etc. with the previous year’s trends with similar backups.

Example: Series 1 Categor y1 Categor y2 Categor y3

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FORECASTS: No organization large or small can function effectively without a demand forecast for the goods or services provides. A retail clothing store must forecast the demand for the shirts it sells by the shirt size. The concessionaire at dodger stadium at Los Angeles must forecast each game attendance to determine how many soft drinks and hot dogs to have on hand. The state elected officials must forecast tax revenues in order to establish a budget each year. There are only a few of the instances in which forecasting is required. For many organizations the success of the forecasting effort will play a major role in determining the general success of the organization. When one graduate and join the organization in the public or the private sector, that person will almost definitely be required to prepare forecast or to us forecast provided by someone else in the organization. One would not have an access to crystal ball on which to rely for an accurate prediction of the future.

TIME SERIES ANALYSIS: Decision makers often confuse in forecasting and planning. Planning is the process of determining how to deal with the future. On the other hand forecasting is the process of predicting what the future will be like. Forecasts are used as inputs for the planning process. Experts agree that good planning is essential for an organization to be effective. Since forecast is an important part of the planning process. You need to be familiar with forecasting methods. There are two broad categories of forecasting techniques: a) Qualitative forecasting technique. b) Quantitative forecasting technique.

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The qualitative forecasting technique are based upon expert opinion and judgment. Qualitative forecasting techniques are based on statistical methods for analyzing quantitative historical data. In general quantitative forecasting techniques are used whenever the following conditions are true: a) Historical data relating to the variable to b forecast exist. b) The historical data can be quantified. c) One can assume that the historical pattern will continue in the future. If these conditions do not exist qualitative forecasting techniques may be employed.

TIME SERIES PLOT: Time series plot is a two dimensional plot of time series. The vertical axis measures the variable of interest and the corresponds to the time period. In plotting the time series the following steps are to be followed: ➢ ➢ ➢ ➢

Model fitting. Model diagnosis. Forecasting period. Forecasting intervals.

MODEL FITTING: Model fitting is the process of determining how well a specified a model fits past data. The idea is that if the future trends look like the past a model must adequately fit the past data to have a reasonable chance of forecasting the future. As a forecaster the decision maker will spend much time selecting the models specification and estimating the models parameters to reach an acceptable fit of the past data.

MODEL DIAGNOSIS: Model diagnosis is the process of determining how well the model fits the past data and how well the models assumptions to be satisfied. The decision maker will need to determine how well the model fits the past data, how well it performs in forecasting trials, and how well the models assumptions appear to be satisfied. If the model is unacceptable in any of these areas the decision maker will be forced to revert to the model specification step and begin 12

again. An important consideration when the decision makers are developing forecasting model is to use the simplest available model that will meet the decision makers forecasting needs. The objective of forecasting is to provide the good forecast. The decision maker does not feel that the sophisticated approach is better if a simpler one will provide acceptable forecast.

FORECASTING PERIOD: Forecasting period is the unit of time for which forecasts are to be made. The forecasting period may be one day, one month, a week, a quarter or a year. Thus the forecasting horizons consist of one or more forecasting periods. If quantitative forecasting is to be employed, historical quantitative data must be available for a similar period. For instance if we want weekly forecast, weekly historical data must be available.

FORECAST INTERVALS: Forecasting intervals are the frequency with which new forecasts are prepared. The forecasting interval is generally the same length as the forecast period. That is, if the forecast period is one week, then we will provide a new forecast each week.

SCATTER DIAGRAM: Scatter diagram is a two dimensional graph of plotted points in which the vertical axis represents values of the other. Each plotted point has coordinates whose values are obtained from the respective variables.

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