1. Chapter 1
An Introduction to Business
Statistics
McGraw-Hill/Irwin
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
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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.
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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
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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.
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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.
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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.
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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
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10. Population and Sample
•
Population Sample
Use statistics to
summarize features
Use parameters to
summarize features
Inference on the population from the sample
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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
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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
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14. Terminology
• Measurement
• Value
• Quantitative
• Qualitative
• Population of Measurement
• Census
• Sample
• Descriptive Statistics
• Statistical Inference
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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
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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
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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
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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
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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
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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
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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
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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
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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
…
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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
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25. Descriptive Statistics
• Collect data
– e.g. Survey
• Present data
– e.g. Tables and graphs
• Characterize data
– e.g. Sample mean = ∑X i
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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 conclusions and/or making decisions
Drawing 120 pounds
concerning a population based on sample results.
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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
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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.
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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)
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