1-1 what is meant by statistics? statistics is the science of collecting, organizing, presenting,...

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What is Meant by Statistics?

Statistics is the science of collecting, organizing, presenting, analyzing, and interpreting numerical data to assist in making more effective decisions.

COPAID

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Types of Statistics

Descriptive Statistics Inferential Statistics

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Descriptive Statistics Descriptive Statistics deals with methods of

Organizing,

Summarizing, &

Presenting data* in an informative way.

Typically, descriptive statistics include Mean, Mode, Median, Variance, Deviation, Skewness,Charts – histogram, bar, pie

(we will see these in later chapters)

* past/current data but not estimated future data

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Excel Example Output of Descriptive Statistics

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PopulationPopulation – all possible individuals, objects.

SampleSample – part of the population of interest

Inferential StatisticsInferential Statistics: : methods used tomethods used to determine something about a population on the basis determine something about a population on the basis

ofof a sample.

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Why sample?

•Time & cost are prohibitive

•Physical impossibility of checking all items in population(eg. Checking quality of product if they are made in the millions)

•Destructive nature of some tests

•Sample results are adequate for decision-making

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Types of Variables

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Types of Variables

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For a Qualitative Qualitative or Attribute VariableAttribute Variable the characteristic being studied is non-numeric. It can only be labeled. (sometimes also called Categorical variable)

T ype of car

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Types of Variables

Number of children in a family

In a Quantitative VariableQuantitative Variable information is reported numerically.

Balance in your checking account

Minutes remaining in class

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Discrete Variables:Discrete Variables: can only assume certain values

-there are usually “gaps” between values

- usually “counted”

Example: the number of bedrooms in a house, or the number of hammers sold at the local Home Depot (1,2,3,…,etc).

Quantitative variables can be classified as either

DiscreteDiscrete or ContinuousContinuous.

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The height or weight of students The height or weight of students in a class.in a class.

A Continuous VariableContinuous Variable can assume any value within a specified range (“no gaps”).

The pressure in a tireThe pressure in a tire

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Chart to remember

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Nominal Nominal OrdinalOrdinalIntervalInterval

RatioRatio

The level of measurement dictates the kind of calculations you can do on the data.

Eg. If one student’s major is Accounting and another’s IS, we cannot calculate the average major.On the other hand, we can average their heights, weights, etc.

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Nominal levelNominal level

Data that is classified into categories.

Can be arranged in any order.

Measurement consists only of counts.

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Other examples: religion, major, gender, ethnicity, …

In this example, Country or Region is Nominal Level data

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Mutually exclusiveMutually exclusive

An individual, object, or measurement is included in only one category.

Nominal level data must be:

Exhaustive Exhaustive Each individual, object, or measurement must appear in one of the categories.

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During a taste test of 4 soft drinks, Coca Cola was ranked number 1, Dr. Pepper number 2, Pepsi number 3, and Root Beer number 4.

Ordinal levelOrdinal level - involves data arranged in some order

- magnitude of differences between data values cannot be determined.

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Also, see the example table in page 12 (Homeland Security Advisory System)

Example of an Ordinal level variable

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Eg.•Temperature on the Fahrenheit scale.•Difference between 10°F - 15°F is same as between 50°F& - 55°F •0° does not represent absence of temperature

Interval levelInterval level - similar to the ordinal level- amounts of differences between data values is of equal size- there is no natural zero point.

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M onthly incomeof surgeons

M iles trav eled by salesrepresentativ e in a month

Ratio level Ratio level (“highest” level of measurement)(“highest” level of measurement)

-- zero value means “absence”- differences and ratios are meaningful for this level of measurement(A person with $2Million is twice as rich as another with $1Million)

Traveled ‘0’ miles means did not travel at all

Monthly income ‘0’ means did not make any money

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N-O-I-R ( Nerd Of India Rocks! )

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Ethical Considerations

Statistics can be used to mislead decision makers Don’t do it!

•Keep taking different samples until you get the result you want

•Quote ‘average’ to hide wide range of data values

•Misleading graphical outputs

•Make unwarranted conclusions on variable relationships

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Ethical Considerations

The cost/year doubled in 5 years. But the graph appears to depict more than that.

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Ethical Considerations

By changing the x-y scale, the rate of change in unemployment appears different.

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Also, a statistical association between two variables does not automatically imply ‘causation’. More in Chapter 13.

Eg.

•Consumption of peanuts is correlated with aspirin consumption (eating peanuts gives headaches)

Ethical Considerations