Data Science Training Courses - Part 7

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STATISTICAL DATA SCIENCE
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Variables
• A variable is a characteristic or condition that can change or take on different
values.
• Most research begins with a general question about the relationship between
two variables for a specific group of individuals.
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Discrete variables (such as class size) consist of indivisible categories, and continuous
variables (such as time or weight) are infinitely divisible into whatever units a researcher
may choose. For example, time can be measured to the nearest minute, second,
half-second, etc.
Y = f(X)
Where,
Y is Dependent variable
X is Independent variable

Measuring Variables
• To establish relationships between variables, researchers must observe the variables and
record their observations. This requires that the variables be measured.
• The process of measuring a variable requires a set of categories called a scale of
measurement and a process that classifies each individual into one category.
Real Limits
To define the units for a continuous variable, a researcher must use real limits which
are boundaries located exactly half-way between adjacent categories.

Measuring variable Example
Example: A supplier fills cans of soda marked 12 ounces. How much soda does each can
really contain?
• It is very unlikely any one can contains exactly 12 ounces of soda.
• There is variability in any process.
• Some cans contain a little more than 12 ounces, and some cans contain a little less.
• On the average, there are 12 ounces in each can.
• The supplier hopes there is little variability in the process, that most cans contain close
to 12 ounces of soda.

Qualitative and quantitative variables may be further subdivided:
Nominal
Qualitative
Ordinal
Variable
Discrete
Quantitative
Continuous
Divisions in variables

Numerical scale of measurement
• Nominal – consist of categories in each of which the number of respective observations is
recorded. The categories are in no logical order and have no particular relationship. The
categories are said to be mutually exclusive since an individual, object, or measurement can
be included in only one of them.
• Ordinal – contain more information. Consists of distinct categories in which order is implied.
Values in one category are larger or smaller than values in other categories (e.g. rating-
excelent, good, fair, poor)
• Interval – is a set of numerical measurements in which the distance between numbers is of a
known, sonstant size.
• Ratio – consists of numerical measurements where the distance between numbers is of a
known, constant size, in addition, there is a nonarbitrary zero point.

Examples of variables
Example: Identify each of the following as examples of qualitative or numerical
variables:
1. The temperature in Barrow, Alaska at 12:00 pm on any
given day.
2. The make of automobile driven by each faculty member.
3. Whether or not a 6 volt lantern battery is defective.
4. The weight of a lead pencil.
5. The length of time billed for a long distance telephone call.
6. The brand of cereal children eat for breakfast.
7. The type of book taken out of the library by an adult.

Examples of variables…
Example: Identify each of the following as examples of
(1) nominal, (2) ordinal, (3) discrete, or (4) continuous variables:
• The length of time until a pain reliever begins to work.
• The number of chocolate chips in a cookie.
• The number of colors used in a statistics textbook.
• The brand of refrigerator in a home.
• The overall satisfaction rating of a new car.
• The number of files on a computer’s hard disk.
• The pH level of the water in a swimming pool.
• The number of staples in a stapler.
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Data Science Training Courses - Part 7

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