McGraw-Hill/Irwin

Copyright © 2009 by The McGraw-Hill Companies, Inc. All Rights Reserved.

Chapter 1

An Introduction to Business Statistics

1-2

Why a Manager Needs to Know about Statistics

• To know how to properly present information

• To know how to draw conclusions about populations based on sample information

• To know how to improve processes

• To know how to obtain reliable forecasts

1-3

Origin

• The word ‘statistics’ has either been derived from the Latin word ‘status’ or Italian word ‘statista’ or the German word ‘statistik’ each of which means a ‘political state’. In the older days, it was considered as ‘the science of statecraft’. The government in those days used to keep records of population, births, and deaths etc. for administrative purposes.

1-4

The Growth and Development of Modern Statistics

Needs of government to collect data on its citizens

The development of the mathematics of probability theory

The advent of the computer

1-5

Definitions of statistics

In the singular Noun

• Statistics is a branch of science which deals with scientific methods of collection, organization, presentation, analysis and interpretation of data obtained by conducting a survey or an experimental study.

• Collection: collection of facts & figures related with the problem. It may be primary and as well as secondary.

• Organization: Editing, classification and tabulation are the three steps in the organization of data.

• Presentation: Organized data are presented with the help of charts, graphs and diagrams.

• Analysis: statistical analysis can be two types descriptive & inferential.

• Interpretation: drawing valid conclusions.

1-6

In the plural noun

• “Statistics are aggregate of facts affected to a marked extent by multiplicity of causes, numerically expressed, enumerated or estimated according to reasonable standard of accuracy, collected in a systematic manner for a predetermined purpose and placed in relation to each other.”

• This definitation highlights a few major CHARACTERISTICS of statistics.– Statistics are aggregate of facts.

– Statistics are affected to a marked extent by multiplicity of causes.

– Statistics must be numerically expressed.

– Statistics must be enumerated or estimated according to reasonable standard of accuracy.

– Statistics should be collected in a systematic manner for a predetermined purpose.

– Statistics should be placed in relation to each other.

1-7

Functions of statistics:

– Simplifies complexities.

– Preciseness and definiteness.

– Enables comparison of phenomenon.

– Study relationship between different facts.

– Helps prediction and formulation of policies.

– Helps in forecasting.

1-8

Basic concepts

Population A set of existing units (usually people, objects or events)

Variable A measurable characteristic of the population

Census An examination of the entire population of measurements

Sample A selected subset of the units of a population

1-9

Sample from Population

Population

Sample

1-10

P

•

opulation and Sample

Population Sample

Use parameters to summarize features

Use statistics to summarize features

Inference on the population from the sample

1-11

Population Size

• Finite

• Infinite

1-12

Finite population

• Finite if it is of fixed and limited size

• Finite if it can be counted

– Even if very large

– For example, all the Chrysler Sebring cars actually made during just this model year is a finite population

• Because a specific number of cars was made between the start and end of the model year

1-13

Infinite population

• Infinite if it is unlimited

• Infinite if listing or counting every element is impossible

– For example, all the Chrysler Sebring cars that could have possibly been made this model year is an infinite population

1-14

Terminology

• Measurement

• Value

• Quantitative

• Qualitative

• Population of Measurement

• Census

• Sample

• Descriptive Statistics

• Statistical Inference

1-15

Measurement

The process of determining the extent, quantity, amount, etc, of the variable of interest for some a particular item of the population.

• Produces data

• For example, collecting annual starting salaries of graduates from last year’s MBA program

1-16

Value

The result of measurement.

• The specific measurement for a particular unit in the population

• For example, the starting salaries of graduates from last year’s MBA Program

1-17

Quantitative

Measurements that represent quantities. (For example, “how much” or “how many.”)

• Annual starting salary is quantitative

• Age and number of children are also quantitative

1-18

Qualitative

A descriptive category to which a population unit belongs: a descriptive attribute of a population unit.

• A person’s gender is qualitative

• A person’s hair color is also qualitative

1-19

Population of Measurements

Measurement of the variable of interest for each and every population unit.

• Sometimes referred to as an observation

• For example, annual starting salaries of all graduates from last year’s MBA program

1-20

Census

The process of collecting the population of all measurements is a census.

• Census usually too expensive, too time consuming, and too much effort for a large population

1-21

Sample

A subset of population units.

• For example, a university graduated 8,742 students

• This is too large for a census

• So, we select a sample of these graduates and learn their annual starting salaries

1-22

Sample of Measurements

• Measured values of the variable of interest for the sample units

• For example, the actual annual starting salaries of the sampled graduates

1-23

Descriptive Statistics

The science of describing the important aspects of a set of measurements.

• For example, for a set of annual starting salaries, want to know:

– How much to expect

– What is a high versus low salary

• If the population is small, could take a census and make statistical inferences

• But if the population is too large, then …

1-24

Statistical Inference

The science of using a sample of measurements to make generalizations about the important aspects of a population of measurements.

• For example, use a sample of starting salaries to estimate the important aspects of the population of starting salaries

1-25

Descriptive Statistics

• Collect data

– e.g. Survey

• Present data

– e.g. Tables and graphs

• Characterize data

– e.g. Sample mean = iX

n

1-26

Inferential Statistics

• Estimation

– e.g.: Estimate the population mean weight using the sample mean weight

• Hypothesis testing

– e.g.: Test the claim that the population mean weight is 120 poundsDrawing conclusions and/or making decisions

concerning a population based on sample results.

1-27

Limitations of statistics

• Deal with quantitative characteristics only

• Deal with averages

• Do not study individuals

• Results are approximately correct

• Results not always beyond the doubt

• Misuse possible

• Should be used only by experts

1-28

Statistics in Business Management:

• Statistics is a method of decision making in the face of uncertainty on the basis of numerical data and calculated risks in business.

• Marketing:• Analysis of data for new product development.• To establishing sales territories.• To establishing advertising strategies.• Production:• In quality control• Decision about the quantity of self manufacturing.• Finance:• In profit & dividend analysis.• In assets & liabilities analysis.• In income & expenditure.• Investment decision under uncertainty.• Personnel:• Analysis of wage rates.• Analysis of labor turnover rates.• Analysis of training & development programmes.

1-29

Summation Notation

• Summation is represented by the Greek letter ∑ (called sigma).• If x1, x2, …….. xn are n values assumed by a variable X, then the sum of the observations

will be (x1+ x2+ ….+ xn) is represented by ∑ xi .• ∑ cxi = c∑ xi, where c is constant.• ∑ c = nc• ∑ (axi + b) = a∑ xi + nb, Here a & b are constants.• ∑ (xi + yi) = ∑ xi + ∑ yi, Here X & Y are constants.• ∑( xi – a) = ∑ xi – na• ∑( xi – a)2 = ∑ xi2 – 2a∑ xi – na2• E.g.: A variable X assumes the values x1 = 8, x2 =3, x3 = 5, x4 = 12 and • x5= 10.• Calculate • (i) ∑ xi • (ii) ∑ xi2 • (iii) ∑ (xi + 5) • (iv) ∑( xi – 2)2• (v) ∑ (2xi + 3)