Session 1.pdf

7/24/2019 Session 1.pdf

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Advanced Business Statistics

Introduction and Descriptive Statistics

Session 1


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Itis better to be roughly right than

precisely wrong.

John Maynard Keynes


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Information resulting from a good statistical analysis isalways concise, often precise, and never useless!


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Statistics teach us how to summarize data, analyze

them, and draw meaningful inferences that then lead to

improved decisions. These better decisions we make

help us improve the running of a department, a company,

or the entire economy.


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Scope of Statistics

HR Problems

Retention rate

Staffing

% of Increment/year/ six months

Factors influencing productivity

Operations Problems

System studyUtilization of staff

Minimizing idle time of machines

Quality/Production Problems

Processing time Volume of

business per day

Meeting clients requirements:

Volume, Precision, TimeError report analysis: QA & QC

Inspection plans


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Why Statistics?


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A quantitative variablecan be described by a number for

which arithmetic operations such as averaging make

sense.


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A qualitative (or categorical) variable simply records a

quality. If a number is used for distinguishing members of

different categories of a qualitative variable, the number

assignment is arbitrary.


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Quantitative or Qualitative?


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Types of Scales

Nominal Ordinal

Interval Ratio


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Nominal Ordinal

Interval Ratio


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Nominal Ordinal

Interval Ratio


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Nominal Ordinal

Interval Ratio


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Nominal Ordinal

Interval Ratio


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In general, the interval between two interval scale

measurements will be in ratio scale.


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19

Binary Orderedcategories

Count

Classifiedinto one of

two categories

Rankingsor ratings

Counteddiscretely

Measuredon a continuous

scale

Votingfor / against

a move

Training feedbackon a 5 point scale

Number oferrors in aninstruction

Time (inhours) to

process aninstruction

Description

Example

Discrete Continuous

Continuumof

Data Types

Flow Chart for Data Types


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The populationconsists of the set of all measurements in

which the investigator is interested. The population is also

called the universe. A sample is a subset of

measurements selected from the population.


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Population vs. Sample?


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A set of measurements obtained on some variable is

called a data set.


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Class Exercise

A survey by an electric company contains questions on the following:

1. Age of household head.

2. Sex of household head.

3. Number of people in household.

4. Use of electric heating (yes or no).

5. Number of large appliances used daily.6. Thermostat setting in winter.

7. Average number of hours heating is on.

8. Average number of heating days.

9. Household income.

10. Average monthly electric bill.

11. Ranking of this electric company as compared with two previouselectricity suppliers.

Describe the variables implicit in these 11 items as quantitative or

qualitative, and describe the scales of measurement.


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25

Population size = N

Population mean =

Standard deviation =Sample size = n

Mean = x

Standard deviation= s

s

Some Symbols


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The Pth percentile of a group of numbers is that value

below which lie P% (P percent) of the numbers in the

group. The position of the Pth percentile is given by:

(n + 1)P/100

, where n is the number of data points.


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First quartile (25thpercentile) >> Lower quartile

Median (50thpercentile) >> Middle quartile

Third quartile (75thpercentile) >> Upper quartile


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We define the interquartile range as the differencebetween the first and third quartiles.


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Class Exercise

The following data are numbers of passengers on flights of Delta

Air Lines between San Francisco and Seattle over 33 days in

April and early May.

128, 121, 134, 136, 136, 118, 123, 109, 120, 116, 125, 128, 121,

129, 130, 131, 127, 119, 114, 134, 110, 136, 134, 125, 128, 123,128, 133, 132, 136, 134, 129, 132

Find the lower, middle, and upper quartiles of this data set.

Also find the 10th, 15th, and 65th percentiles. What is theinterquartile range?


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Measures of Central Tendency

The median

The mode of the data set is the value that occurs

most frequently.

The meanof a set of observations is their average.


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A Symmetrically Distributed Data Set


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Measures of Variability

the interquartile range

The rangeof a set of observations is the difference

between the largest observation and the smallest

observation.


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Measures of Variability

The variance of a set of observations is the

average squared deviation of the data points from

their mean.

The standard deviation of a set of observations isthe (positive) square root of the variance of the set.


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Shortcut Formula for the Sample Variance

In financial analysis, the standard deviation is often

used as a measure of volatility and of the risk

associated with financial variables.


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Skewness and Kurtosis


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Skewness and Kurtosis

Relative kurtosis = Absolute kurtosis - 3


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ChebyshevsTheorem

A mathematical theorem called Chebyshevs theorem

establishes the following rules:

1. At least three-quarters of the observations in a set

will lie within 2 standard deviations of the mean.

2. At least eight-ninths of the observations in a set will

lie within 3 standard deviations of the mean.

In general, the rule states that at least of the

observations will lie within k standard deviations of

the mean.


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Methods of Displaying Data

23%

14%

14%11%

9%

8%

4%

5%

3%

3%

3%3%

0%

0%

0%

Semester 1, 2015/2016

OB, Operation and HRM Innovation and Technology Management

Marketing Consumer and Customer-related Studies

Accounting Supply Chain Management

Service Quality and Customer Satisfaction Tourism

Corporate Governance and Ethics Finance and Economics

Social Responsibility and Sustainabil ity Strategy

Entrepreneurship / Social Entrepreneurship International BusinessLeadership / Ethical Leadership

Pie Chart


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23%

37%

51%

62%

71%

78%83%

88%91% 94%

97% 100%

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0

2

4

6

8

10

12

14

16

Semester 1, 2015/2016

No. Cumulative %

Bar Chart and Ogive

An ogiveis a cumulative-frequency (or cumulative relative-frequency) graph. An ogive starts

at 0 and goes to 1.00 (for a relative-frequency ogive) or to the maximum cumulative

frequency.


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Stem and Leaf Box Plot


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Outlier


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Outlier is an observation point that is distant from

other observations.


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Dont misuse statistics!


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Class Exercise

Heart Rate


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Thank you

Dr. Mehran Nejati

[email protected]

Documents

Session 1.pdf