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Business Statistics

Chapter 1

Introductionto Statistics

By Ken Black

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Learning Objectives

• Define statistics• Become aware of a wide range of

applications of statistics in business• Differentiate between descriptive and

inferential statistics• Classify numbers by level of data and

understand why doing so is important

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Statistics in Business

• Best Way to Market• Stress on the Job• Financial Decisions• How is the Economy Doing• The Impact of Technology at Work

Examples of data in functional areas• accounting - cost of goods, salary expense, depreciation, utility costs, taxes, equipment

inventory, etc.

• finance - World bank bond rates, number of failed savings and loans, measured risk of common stocks, stock dividends, foreign exchange rate, liquidity rates for a single-family, etc.

• human resources - salaries, size of engineering staff, years experience, age of employees, years of education, etc.

• marketing - number of units sold, dollar sales volume, forecast sales, size of sales force, market share, measurement of consumer motivation, measurement of consumer frustration, measurement of brand preference, attitude measurement, measurement of consumer risk, etc.

• information systems - c.p.u. time, size of memory, number of work stations, storage capacity, percent of professionals who are connected to a computer network, dollar assets of company computing, number of “hits” on the Internet, time spent on the Internet per day, percentage of people who use the Internet, retail dollars spent in e-commerce, etc.

• production - number of production runs per day, weight of a product; assembly time, number of defects per run, temperature in the plant, amount of inventory, turnaround time, etc.

• management - measurement of union participation, measurement of employer support, measurement of tendency to control, number of subordinates reporting to a manager, measurement of leadership style, etc.

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Examples of data in business industries• manufacturing - size of punched hole, number of rejects, amount of inventory, amount of

production, number of production workers, etc.

• insurance - number of claims per month, average amount of life insurance per family head, life expectancy, cost of repairs for major auto collision, average medical costs incurred for a single female over 45 years of age, etc.

• travel - cost of airfare, number of miles traveled for ground transported vacations, number of nights away from home, size of traveling party, amount spent per day on nonlodging, etc.

• retailing - inventory turnover ratio, sales volume, size of sales force, number of competitors within 2 miles of retail outlet, area of store, number of sales people, etc.

• communications - cost per minute, number of phones per office, miles of cable per customer headquarters, minutes per day of long distance usage, number of operators, time between calls, etc.

• computing - age of company hardware, cost of software, number of CAD/CAM stations, age of computer operators, measure to evaluate competing software packages, size of data base, etc.

• agriculture - number of farms per county, farm income, number of acres of corn per farm, wholesale price of a gallon of milk, number of livestock, grain storage capacity, etc.

• banking - size of deposit, number of failed banks, amount loaned to foreign banks, number of tellers per drive-in facility, average amount of withdrawal from automatic teller machine, federal reserve discount rate, etc.

• healthcare - number of patients per physician per day, average cost of hospital stay, average daily census of hospital, time spent waiting to see a physician, patient satisfaction, number of blood tests done per week. SP

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What is Statistics?

• Science of gathering, analyzing, interpreting, and presenting data

• Branch of mathematics• Course of study• Facts and figures• A death• Measurement taken on a sample• Type of distribution being used to analyze

data

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Population Versus Sample

• Population — the whole– a collection of persons, objects, or items under

study• Census — gathering data from the entire

population• Sample — a portion of the whole

– a subset of the population

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Population

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Population and Census Data

Identifier Color MPG

RD1 Red 12

RD2 Red 10RD3 Red 13

RD4 Red 10RD5 Red 13BL1 Blue 27BL2 Blue 24

GR1 Green 35GR2 Green 35GY1 Gray 15GY2 Gray 18GY3 Gray 17

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Sample and Sample Data

Identifier Color MPG

RD2 Red 10

RD5 Red 13

GR1 Green 35

GY2 Gray 18

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Descriptive vs. Inferential Statistics• Descriptive Statistics — using data gathered

on a group to describe or reach conclusions about that same group only eg. Average score

Graphs, tables and charts that display data so that they are easier to understand are examples of descriptive statistics.

• Inferential Statistics (inductive statistics)— using sample data to reach conclusions about the population from which the sample was taken eg. Pharmaceutical research

The process of estimation of any parameter is referred as statistical inference.

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Parameter vs. Statistic

• Parameter — descriptive measure of the population– Usually represented by Greek letters

• Statistic — descriptive measure of a sample– Usually represented by Roman letters

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Symbols for Population Parameters

mean population denotes 2 denotes population variance

denotes population standard deviation

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Symbols for Sample Statistics

x denotes sample mean2S denotes sample variance

S denotes sample standard deviation

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Process of Inferential Statistics

Population

(parameter)

Sample

x

(statistic)

Calculate x

to estimate

Select a

random sample

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Levels of Data Measurement

• Nominal — Lowest level of measurement• Ordinal• Interval• Ratio — Highest level of measurement

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Nominal Level Data• Numbers are used to classify or categorize

Example: Employment Classification– 1 for Educator– 2 for Construction Worker– 3 for Manufacturing Worker

Example: Ethnicity– 1 for African-American– 2 for Anglo-American– 3 for Hispanic-American

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Ordinal Level Data

• Numbers are used to indicate rank or order– Relative magnitude of numbers is meaningful– Differences between numbers are not comparable

Example: Ranking productivity of employeesExample: Taste test ranking of three brands of soft drinkExample: Position within an organization

– 1 for President– 2 for Vice President– 3 for Plant Manager– 4 for Department Supervisor– 5 for Employee

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Ordinal Data

Faculty and staff should receive preferential treatment for parking space.

1 2 3 4 5

StronglyAgree

Agree StronglyDisagree

DisagreeNeutral

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Interval Level Data

• Distances between consecutive integers are equal– Relative magnitude of numbers is meaningful– Differences between numbers are comparable– Location of origin, zero, is arbitrary– Vertical intercept of unit of measure transform

function is not zeroExample: Fahrenheit TemperatureExample: Calendar Time

Interval Level Data

• Like the others, you can remember the key points of an “interval scale” pretty easily.  ”Interval” itself means “space in between,” which is the important thing to remember–interval scales not only tell us about order, but also about the value between each item.

• Here’s the problem with interval scales: they don’t have a “true zero.”  For example, there is no such thing as “no temperature.”  Without a true zero, it is impossible to compute ratios.  With interval data, we can add and subtract, but cannot multiply or divide. Ok, consider this: 10 degrees + 10 degrees = 20 degrees.  No problem there.  20 degrees is not twice as hot as 10 degrees, however, because there is no such thing as “no temperature” when it comes to the Celsius scale.  I hope that makes sense.  Bottom line, interval scales are great, but we cannot calculate ratios, which brings us to our last measurement scale…

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Ratio Level Data

• Highest level of data measurement– Relative magnitude of numbers is meaningful– Differences between numbers are comparable– Location of origin, zero, is absolute (natural)– Vertical intercept of unit of measure transform

function is zero.These variables can be meaningfully added,

subtracted, multiplied, divided (ratios)Examples: Height, Weight, and VolumeExample: Monetary Variables, such as Profit and

Loss, Revenues, and ExpensesExample: Financial ratios, such as P/E Ratio,

Inventory Turnover, and Quick Ratio.

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Usage Potential of VariousLevels of Data

Nominal

Ordinal

Interval

Ratio

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Data Level, Operations, and Statistical Methods

Data Level

Nominal

Ordinal

Interval

Ratio

Meaningful Operations

Classifying and Counting

All of the above plus Ranking

All of the above plus Addition, Subtraction, Multiplication, and Division

All of the above

StatisticalMethods

Nonparametric

Nonparametric

Parametric

Parametric

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