BUSINESS STATISTICS

An Applied Approach

Chapter 1

Introduction

• “I hear and I forget.

• I see and I remember.

• I do and I    understand."                       (Confucius)

Why a Manager needs to Know about Statistics

• Why? Because you want to know :– Best use of imperfect information:

• e.g., 50,000 customers, 1,600 workers, 386,000 transactions,

– How to prepare ,present and describe information .

– Good decisions in uncertain conditions:

Why a Manager needs to Know about Statistics

– How to draw conclusions about large populations based on only information obtained from samples

• e.g., new product launch: Fail? OK? Make you rich?

• – Competitive Edge

• e.g., for you in the job market!

– How to obtain reliable forecasts

Why a Manager needs to Know about Statistics

• Simply speaking the subject of statistics is

• The Art and Science of Collecting, Summarizing ,Interpreting and thus Understanding DATA:– DATA = Recorded Information

• e.g., Sales, Productivity, Quality, Costs, Return, Patients,Drugs etc

Descriptive Statistics

• Descriptive statistics – summaries of data presented in tabular, graphical, and numerical forms that are easy for the reader to understand.

• Most of newspapers, magazines, white papers and reports use descriptive statistics.

Example: Diagnostic CentreExample: Diagnostic Centre

• The manager of a Diagnostic Centre The manager of a Diagnostic Centre would like to have a better understanding would like to have a better understanding of the chemicals used in the blood tests of the chemicals used in the blood tests performed in the centre. She examines 25 performed in the centre. She examines 25 customer blood samples for tests. The customer blood samples for tests. The costs of chemical, rounded to the nearest costs of chemical, rounded to the nearest Rupee, are listed on the next slideRupee, are listed on the next slide

95 35 65 40 50

65 75 30 35 40

55 60 25 70 65

35 90 65 45 45

75 65 35 40 55

Chemical cost5- Frequency Freq. percentage

25-40

40-55

55-70

70-85

85-100

Statistical InferenceStatistical Inference

• Population --he set of all elements of Population --he set of all elements of interest in a particular studyinterest in a particular study

• Sample -- a subset of the populationSample -- a subset of the population

• Statistical inference --he process of using Statistical inference --he process of using data obtained from a sample to make data obtained from a sample to make estimates and test hypotheses about the estimates and test hypotheses about the characteristics of a populationcharacteristics of a population

• Census-- collecting data for a populationCensus-- collecting data for a population

Process of Statistical Inference

• 1. Population consists of all chemical 1. Population consists of all chemical costs for all diagnosis. Average cost of costs for all diagnosis. Average cost of chemical is unknownchemical is unknown.

• A sample of 25 chemical costs is A sample of 25 chemical costs is examined.examined.

• The sample data provide a sample The sample data provide a sample average chemical cost of Rs per test .average chemical cost of Rs per test .

• The sample average is used to estimate The sample average is used to estimate the population average.the population average.

• As an example ----a study was conducted l comparing four groups of patients being treated for their stomach ulcers under the following regime:

• Group 1 received placebo (an inert compound)• Group 2 received active drug at dose d, twice

per day• Group 3 received active drug at dose 2d, once

per day• Group 4 received active drug at dose 2d, twice

per day

• So there were interesting comparisons to be made particularly between a dose of 2d once or twice a day and between a total daily dose 2d taken in one or two ‘shots’ per day. 500 patients were to be recruited into the study across

• Table 1. Crude Cure Rates.

• Treatment Cure Rates

• Placebo 98/124 79%

• d twice/day 107/126 85%

• 2d once/day 106/130 82%

• 2d twice/day 115/130 88%

How to approach

• Designing the study:– First step

• Plan for data-gathering• Random sample (control bias and error)

• Exploring the data:• First step (once you have data)• Look at, describe, summarize the data• Are you on the right track?

How to approach

• Estimating an unknown:– Best “guess” based on data– Wrong - buy by how much?– Confidence interval - “we’re 95% sure that the

unknown is between …”

• 4. Hypothesis testing:– Data decide between two possibilities– Does “it” really work? [or is “it” just randomly better?]– Is financial statement correct? [or is error material?]– Whiter, brighter wash?

Statistical View of the World

• Data are imperfect– We do the best we can -- Statistics helps!

• Events are random– Can’t be right 100% of the time

• Use statistical methods– Along with common sense and good judgment

• Be skeptical!– Statistics can be used to support contradictory

conclusions– Look at who funded the study?

Statistics in Business: Examples

• Advertising– Effective? Which commercial? Which markets?

• Quality control– Defect rate? Cost? Are improvements working?

• Finance– Risk - How high? How to control? At what cost?

Statistics in Business: Examples

• Accounting– Audit to check financial statements. Is error material?

• Marketing • Consumer behaviour study , Test marketing • Other• Economic forecasting, background

information, measuring and controlling productivity (human and machine), …

Data Structures: Classifying the Various Types of Data Sets

• Data Set:– Measurements of items

• e.g., Yearly sales volume for your 23 salespeople• e.g., Cost and number produced, daily, for the past month

• Elementary Units:– The items being measured

• e.g., Salespeople, Days, Companies, Catalogs, …

• A Variable:– The type of measurement being done

• e.g., Sales volume, Cost, Productivity, Number of defects, …

How Many Variables?

• Univariate data set: One variable measured for each elementary unit– e.g., Sales for the top 30 computer companies.– Can do: Typical summary, diversity, special

features• Bivariate data set: Two variables

– e.g., Sales and # Employees for top 30 computer firms

– Can also do: relationship, prediction• Multivariate data set: Three or more variables

– e.g., Sales, # Employees, Inventories, Profits, …– Can also do: predict one from all other variables

Numbers or Categories?

• Quantitative Variable: Meaningful numbers– e.g., Sales, # Employees– Can add, rank, count

• Qualitative Variable: Categories– Ordinal Variable: Categories with meaningful ordering

• e.g., Bond rating (AA, A, B, …), Gold (24,22, …)• Can rank, count

– Nominal Variable: categories without meaningful ordering

• e.g., State, Type of business, Field of study

• Can count

Attributes

• Certain description about any object

• e.g. Defective ,Non-defective

• B.P.High, B.P. Low

Time-Series or Cross-Sectional?

• Time-Series Data: Data values recorded in meaningful sequence– Elementary units might be days or quarters or years– e.g., Daily Dow-Jones stock market average close for

the past 90 days– e.g., Your firm’s quarterly sales over the past 5 years

• Cross-Sectional Data: No meaningful sequence– e.g., Sales of 30 companies– e.g., Productivity of each sales division

– Easier than time series!

Data Presentation

• Histogram• Relative frequency Histogram• Skewness• Kurtosis• Pie chart• Bar Diagram• Ogive• Line Chart

Histogram and Bar Chart

• Histogram is a bar chart of the frequencies of the data– Histogram: bar height represents number of cases

within the range– Ordinary bar chart: bar height represents data value

for just one case

• Histogram shows overall distribution– Histogram: the “big picture” of patterns in the data– Ordinary bar chart: often too much detail (each

individual case)

Frequency Histogram

Histogram Example

Relative Frequency Histogram

Histogram Example

• Normal– Symmetric– Bell-Shaped

• Skewed– Not symmetric– Can cause trouble

Skewed to left

Skewness

Skewness

Symmetric

Skewness

Skewed to right

Kurtosis

Platykurtic - flat distribution

Kurtosis

Mesokurtic - not too flat and not too peaked

Pie Chart

Bar Chart

Average Revenues

Average Expenses

Fig. 1-11 Airline Operating Expenses and Revenues

1 2

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6

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A i r li n e

American Continental Delta Northwest Southwest United USAir

Relative Frequency Polygon Ogive

Frequency Polygon and Ogive

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M o nthly S te e l P ro d uc tio n

(P ro b le m 1 -4 6 )

Time Plot