STATISTICS : INTRODUCTION AND ITS USE IN MANAGERIAL DECISION

MAKING(CHAPTER – 1)

- GAURAV GOYAL(LECTURER)

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CONTENTS INTRODUCTION BROAD CLASSIFICATION WHAT IS STATISTICS? CHARACTERISTICS OF STATISTICAL

DATA STATISTICAL METHODS:CLASSIFICATION OPERATION RESEARCH MODELS SOME STATISTICAL TECHNIQUES ADVANTAGES OF QT TO

MANAGEMENT QT IN BUSINESS AND MANAGEMENT

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INTRODUCTIONBEFORE INDUSTRIAL

REVOLUTIONDecision based on past

experience and intuition

AFTER INDUSTRIAL REVOLUTION

Decision making got complicated and quantitative

techniques were used.

REASONS1. Marketing not a problem since customers were known to the owner.2. Test marketing not needed since choice and requirement of customer was known.3. Personal data not required since manager used to work with the workers at the shop floor level.4. Production records not required since progress was recorded daily at the work centre.5. Most of the facts required by the owner for decision making were known to him.

REASONS1. Complexity of today’s managerial activities2. Availability of different type of tools for quantitative analysis of complex managerial problems.3. Availability of high speed computers to apply the quantitative techniques to real life problems.

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BROAD CLASSIFICATION

QUANTITATIVE TECHNIQUES

STATISTICAL TECHNIQUES

OPERATION RESEARCH (OR PROGRAMMING)

TECHNIQUES

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WHAT IS STATISTICS?

DEFINITIONA science dealing with collection, analysis, interpretation and presentation of numerical data.

APPLICATIONProvides tools for prediction and forecasting using data and statistical models.

BASISMost of the science of statistics is based on mathematical thought and derivation.

MISCONCEPTIONPeople sometimes refer it as a group of data but actually it’s the measured facts & figures.

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CHARACTERISTICS OF STATISTICAL DATA

Must be aggregate of facts Should be affected to a marked

extent by multiplicity of causes Must be enumerated / estimated to a

certain standard of accuracy. Must have been collected in a

systematic manner for a pre-determined purpose.

Must be placed in relation to each other

Must be numerically expressed.04/08/2023 6

STATISTICAL METHODS:CLASSIFICATION

STATISTICAL METHODS

INDUCTIVE STATISTICS

DESCRIPTIVE STATISTICS

STATISTICAL DECISION THEORY

1. Data collection

2. Presentation

1. Statistical Inference

2. Estimation

1. Analysis of Business Decision

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CONTINUED……DESCRIPTIVE STATISTICS

Can be used to summarize or describe a collection of data.

E.g. : an instructor produces statistics to summarize a class’s examination effort and uses those to reach conclusions about that classINDUCTIVE STATISTICS

the pattern in data is modeled in a way to account for randomness and uncertainty and then used to draw inferences about the population being studied.

Also sometimes called inferential statistics.

APPLIED STATISTICS

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DESCRIPTIVE STATISTICS(EXAMPLE)

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INFERENTIAL STATISTICS (EXAMPLE)

Population consists of all bulbs

manufactured with the

new filament. Average

lifetime is unknown.

A sample of 200 bulbs is manufactured with

the new filament.

The sample data provide a sample

average lifetime of 76 hours per bulb.

The sample average is used to estimate

the population average.

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STATISTICAL DECISION THOERY Deals with analyzing complex

business problems with alternative courses of action and possible consequences.

Relies on:- a) nature of problem b) decision environmentSTATE OF

DECISIONCONSEQUENCES

CertaintyRiskUncertaintyConflict

DeterministicProbabilisticUnknownInfluenced by opponent

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OPERATION RESEARCH MODELS MODELS BASED ON PURPOSE

DESCRIPTIVE MODEL

1. Used to describe the behavior of a system based on certain information.

2. Displays the problem situation more vividly including the alternative choices.

e.g. model to describe the behavior of demand for a inventory item for a stated period by keeping record of demand levels and the frequencies.

EXPLANATORY MODEL

1. Used to explain behavior of system by establishing relationship between its components.

e.g. model to explain variations in productivity by establishing relation among the factors such as wages, promotion policy, education levels etc. 04/08/2023 12

OPERATION RESEARCH MODELS MODELS BASED ON PURPOSE

PREDICTIVE MODEL

1. Used to predict status of a system in the near future based on data.

e.g. model to predict stock prices for any given level of earning per share (EPS).

PRESCRIPTIVE MODEL

1. Provides norms for comparison of alternative solutions to select the best alternative out of it.

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OPERATION RESEARCH MODELS MODELS BASED ON DEGREE OF ABSTRACTION

PHYSICAL MODEL

1. A three-dimensional model that looks like the real thing, either reduced in size or scaled up.

2. It is LEAST ABSTRACT

e.g. city planning maps, plant layout charts, airplane model etc.

GRAPHIC MODEL

1. A model showing relationship in a graphical manner.

2. MORE ABSTRACT than the Physical model.

e.g. organisation chart

SCHEMATIC MODEL

1. A model depicting sequence of activities.

2. MORE ABSTRACT than the Graphical model.

e.g. a flow chart, computer program whose main features are depicted by schematic description of steps.04/08/2023 14

OPERATION RESEARCH MODELS MODELS BASED ON DEGREE OF ABSTRACTION

ANALOG MODEL

1. Closely associated with physical models, and are not replica of the problem situations.

2. Small physical model, works like the system it represents.

3. MORE ABSTRACT than schematic.

e.g. children toys, model rail-roads etc.

MATHEMATICAL MODEL

1. Represents the systems by using mathematical symbols and relationships.

2. MOST ABSTRACT

e.g. the input-output model of the national economy.

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OPERATION RESEARCH MODELS MODELS BASED ON DEGREE OF CERTAINTY

DETERMINISTIC MODEL

1. In this model, selection of each course of action results in unique and known pay-off.

e.g. linear programming, transportation and assignment models.

PROBABILISTIC MODEL

1. Situations in which each course of action can result in more than one pay-offs

e.g. simulation model, decision-theory model

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OPERATION RESEARCH MODELS MODELS BASED ON SPECIFIC BEHAVIOR

CHARACTERISTICS

STATIC MODELS

1. Models concerned with a particular set of fixed conditions and do not change in a short-term period.

2. Are independent of time and only one decision required for a period.

e.g. resources for a particular product, Linear programming etc

DYNAMIC MODEL

1. Decision-maker has to make a sequence of optimal decisions at every decision point regardless of what the prior decision has been.

2. Decision changes over a period of time.

e.g. product development, dynamic programming

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http://www.free-training-tutorial.com/format-cells.html 

Link for Excel

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OPERATION RESEARCH MODELS MODELS BASED ON SPECIFIC BEHAVIOR

CHARACTERISTICSLINEAR MODELS

1. Models in which each component exhibits a linear behavior.

e.g. Z = 5 + 3x

NON-LINEAR MODELS

1. If one or more components in a model exhibits a non-linear behavior.

e.g. Z = 5x2 + 3xy + y2

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OPERATION RESEARCH MODELS MODELS BASED ON PROCEDURE OF SOLUTION

ANALYTICAL MODELS

1. Model consisting of a mathematical structure and solved by known mathematical or analytical techniques to yield a general solution.

e.g. PERT/CPM, Linear programming, game theory models, inventory control models etc

SIMULATION MODELS

1. Is the experimentation on a mathematical structure of real life system.

2. Done by inserting specific values of decision variables into the given structure under certain assumptions.e.g. test effect of different number of service counters based on different arrival rate.04/08/2023 21

Measures of Location

If the measures are computed for data from a sample,they are called sample statistics.

If the measures are computed for data from a population,they are called population parameters.

A sample statistic is referred toas the point estimator of thecorresponding population parameter.

Mean Median Mode Percentiles Quartiles

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Mean

The mean of a data set is the average of all the data values.

The sample mean is the point estimator of the population mean m.

x

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Sample Mean x

Number ofobservationsin the sample

Number ofobservationsin the sample

Sum of the valuesof the n observationsSum of the valuesof the n observations

ixx

n

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Population Mean m

Number ofobservations inthe population

Number ofobservations inthe population

Sum of the valuesof the N observationsSum of the valuesof the N observations

ix

N

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Seventy efficiency apartments were randomlysampled in a small college town. The monthly

rentprices for these apartments are listed on the

next slide.

Sample Mean

Example: Apartment Rents

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Apartment Rent Sample Data

Sample Mean

445 615 430 590 435 600 460 600 440 615440 440 440 525 425 445 575 445 450 450465 450 525 450 450 460 435 460 465 480450 470 490 472 475 475 500 480 570 465600 485 580 470 490 500 549 500 500 480570 515 450 445 525 535 475 550 480 510510 575 490 435 600 435 445 435 430 440

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Sample Mean

445 615 430 590 435 600 460 600 440 615440 440 440 525 425 445 575 445 450 450465 450 525 450 450 460 435 460 465 480450 470 490 472 475 475 500 480 570 465600 485 580 470 490 500 549 500 500 480570 515 450 445 525 535 475 550 480 510510 575 490 435 600 435 445 435 430 440

34,356 490.80

70ixx

n

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Median

Whenever a data set has extreme values, the median is the preferred measure of central location.

A few extremely large incomes or property values can inflate the mean.

The median is the measure of location most often reported for annual income and property value data.

The median of a data set is the value in the middle when the data items are arranged in ascending order.

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Median

12 14 19 26 2718 27

For an odd number of observations:

in ascending order

26 18 27 12 14 27 19 7 observations

the median is the middle value.

Median = 19

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12 14 19 26 2718 27

Median

For an even number of observations:

in ascending order

26 18 27 12 14 27 30 8 observations

the median is the average of the middle two values.

Median = (19 + 26)/2 = 22.5

19

30

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Median

Averaging the 35th and 36th data values:Median = (475 + 475)/2 = 475

Note: Data is in ascending order.

425 430 430 435 435 435 435 435 440 440440 440 440 445 445 445 445 445 450 450450 450 450 450 450 460 460 460 465 465465 470 470 472 475 475 475 480 480 480480 485 490 490 490 500 500 500 500 510510 515 525 525 525 535 549 550 570 570575 575 580 590 600 600 600 600 615 615

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Mode

The mode of a data set is the value that occurs with greatest frequency. The greatest frequency can occur at two or more different values. If the data have exactly two modes, the data are bimodal.

If the data have more than two modes, the data are multimodal.

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SOME STATISTICAL TECHNIQUES MEASURES OF CENTRAL TENDENCY1. MEAN: Computed by dividing sum of

the values of observations by the number of items.

2. MEDIAN: Item which lies exactly midway between the lowest and the highest value when data is arranged in ascending or descending order.

3. MODE: It is the central value that occurs most frequently.

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SOME STATISTICAL TECHNIQUES MEASURES OF DISPERSION The difference between the

maximum and the minimum value of a distribution is called the measure of dispersion.

1. SKEWNESS: the measure of the direction and degree of symmetry are called measures of skewness

2. KURTOSIS: The measure of peakedness in a distribution is called Kurtosis. 04/08/2023 35

SKEWNESS AND KURTOSIS

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SOME STATISTICAL TECHNIQUES CORRELATION It measures the degree to which the

change in the dependent variable is associated with change in the independent variable.

REGRESSION ANALYSIS Used for determining the causal

relationship between 2 variables. TIME SERIES ANALYSIS Consists of a set of data recorded

over successive periods of time. Measures the effect of the following

4 forces:-

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SOME STATISTICAL TECHNIQUES TIME SERIES ANALYSIS Consists of a set of data recorded

over successive periods of time. Analysis is done on the above data

taking the periodic changes, cyclical changes, seasonal variations and random variations into consideration.

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ADVANTAGES OF QT TO MANAGEMENT

Definiteness Condensation Comparison Formulation of policies Formulating and testing hypothesis Prediction

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QT IN BUSINESS AND MANAGEMENT MANAGEMENT

i) Marketing: analysis market research information Statistical records for building and maintaining an extensive market Sales forecastingii) Production Production planning, control and analysis Evaluation of machine performance Quality control requirements Inventory control measures

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QT IN BUSINESS AND MANAGEMENTiii) Finance, Accounting and

Investment: financial forecast, budget preparation financial investment decisions Selection of securities Auditing functioniv) Personnel labour turnover rate employment trends performance appraisal wage rates and incentive plans

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QT IN BUSINESS AND MANAGEMENT ECONOMICS

measure of GNP. determination of business cycle. comparison of market prices etc. analysis of population formulation of appropriate economic policies

RESEARCH AND DEVELOPMENT development of new product lines optimum use of resources evaluation of existing products

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