Data Science Fundamentals

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Questions and Answers

What defines a symmetric binary variable?

  • Both choices have equal importance. (correct)
  • Options can vary in probability.
  • One choice is always more important than the other.
  • It consists of three or more choices.

Which of the following is true regarding ordinal data?

  • Relational operators can't be applied to ordinal data.
  • Ordinal data can reflect a ranking of items. (correct)
  • It always has numerical values.
  • Ordinal data cannot be ranked.

What is an example of an asymmetric binary variable?

  • Age categories
  • Color choices
  • Medical test results (correct)
  • Gender

Which operation is typically NOT permitted on ordinal data?

<p>Performing addition (B)</p> Signup and view all the answers

Which statement is accurate regarding the transformation of variables between numeric and ordinal?

<p>Transforming from numeric to ordinal results in a loss of information. (B)</p> Signup and view all the answers

What type of measurement includes categories without any inherent order?

<p>Nominal scale (B)</p> Signup and view all the answers

Which scale of measurement allows for both order and a measurable difference between values?

<p>Interval scale (D)</p> Signup and view all the answers

Which of the following is an example of document data?

<p>Term-frequency vector (B)</p> Signup and view all the answers

In the NOIR classification, which scale indicates variables that have a true zero point?

<p>Ratio scale (A)</p> Signup and view all the answers

What characterizes binary data in the context of the NOIR classification?

<p>It consists of two distinct categories (C)</p> Signup and view all the answers

Which of the following statements is true about quantitative data?

<p>It can be ordered and have measurable differences (B)</p> Signup and view all the answers

What best describes the properties of categorical data?

<p>They have distinct categories that can be counted (D)</p> Signup and view all the answers

Which type of data is exemplified by a numerical matrix in research?

<p>Record data (A)</p> Signup and view all the answers

What is a characteristic of a nominal variable?

<p>It is used to categorize data without a logical sequence. (D)</p> Signup and view all the answers

Which of the following is an example of a binary variable?

<p>Gender represented as Male and Female (A), Rhesus factor +/- (D)</p> Signup and view all the answers

What does the nominal scale primarily do?

<p>Labels categories without an order. (C)</p> Signup and view all the answers

Which of the following statements is true about nominal data?

<p>Labels can be identical or dissimilar. (A)</p> Signup and view all the answers

Why can mathematical operations not be performed on nominal data?

<p>Nominal data represents categorical variables without inherent values. (D)</p> Signup and view all the answers

In the context of variable types, what distinguishes a binary variable?

<p>It represents exactly two mutually exclusive categories. (A)</p> Signup and view all the answers

Which of the following is a potential misuse of nominal data?

<p>Trying to rank categories. (D)</p> Signup and view all the answers

What is the defining feature of nominal data types?

<p>They can be expressed in numeric form. (D)</p> Signup and view all the answers

What is a characteristic of interval data?

<p>It has equal intervals between values. (A)</p> Signup and view all the answers

Which of the following types of data does not possess a true zero?

<p>Interval data (B)</p> Signup and view all the answers

What type of operation can be performed on interval data?

<p>Addition and negation (D)</p> Signup and view all the answers

Which statement best describes discrete data?

<p>It can only take specific individual values. (C)</p> Signup and view all the answers

Which of the following best exemplifies ratio data?

<p>Age of a person (B)</p> Signup and view all the answers

What is the main difference between continuous and discrete data?

<p>Continuous data can take any value, while discrete data is countable. (C)</p> Signup and view all the answers

Which category does 'temperature in Fahrenheit' fall under?

<p>Interval data (C)</p> Signup and view all the answers

Which of the following is NOT true about operations on interval data?

<p>Only linear transformations can be applied. (C)</p> Signup and view all the answers

Flashcards

Dataset types

Datasets can be categorized into record data (e.g., relational tables, matrices, transaction data, document data) and graph/network data.

Data in Data Science

In data science, data represents measurements of attributes of entities (things).

Data Categorization

Data can be categorized using different scales (NOIR): Nominal, Ordinal, Interval, and Ratio.

Nominal Scale

Nominal data are categorical, without inherent order. Examples: color, gender, country.

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Nominal Scale: Binary

Binary is a type of nominal data with only two categories (e.g., true/false, yes/no).

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Nominal Scale: Binary - Symmetric

Symmetric binary data has equal meaning for both categories.

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Nominal Scale: Binary - Asymmetric

Asymmetric binary data has unequal meaning for categories.

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Ordinal Scale

Ordinal data has inherent order, but distances between values aren't meaningful. Examples: rankings, satisfaction ratings.

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Interval Scale

Interval data has a meaningful order and consistent intervals between values. Temperature is an example.

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Ratio Scale

Ratio data has a meaningful order, consistent intervals, and a true zero point. Examples: height, weight, income.

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Nominal Variable

A variable that assigns mutually exclusive codes with no inherent order to categories. The codes can be letters, numbers, or symbols.

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Nominal Scale Example

Example categories include gender (M/F), blood groups (A, B, AB, O), and rhesus factors (+/-).

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Nominal Data Numerical Interpretation

Numerical values in nominal data are just labels; calculations like addition or order have no meaning.

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Binary Variable

A special type of nominal variable with exactly two mutually exclusive categories. No logical order.

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Binary Variable Examples

Examples include switch status (ON/OFF), attendance (present/absent), and entry status (yes/no).

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Categorical Data

Data consisting of categories;Qualitative data classified into groups without numerical meaning.

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Numerical Data

Data expressed as numbers, suitable for mathematical analysis. Quantitative data.

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Interval Data

Numerical data with equal intervals between values, but no true zero.

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Ratio Data

Numerical data with equal intervals and a true zero point.

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Discrete Data

Data that can only take on specific, separate values.

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Continuous Data

Data that can take on any value within a certain range.

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NOIR Classification

A system for categorizing data based on the type of scale (Nominal, Ordinal, Interval, Ratio).

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Nominal Data

Categorical data with no inherent order.

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Ordinal Data

Categorical data with inherent order, but intervals aren't meaningful.

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Symmetric Binary

Binary variable where both categories have equal importance.

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Asymmetric Binary

Binary variable where one category is more important than the other.

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NOIR Classification

Categorization system for variables (Nominal, Ordinal, Interval, Ratio).

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Nominal Data

Categorical data without inherent order, like colors or countries.

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Ordinal Data

Categorical data with inherent order but no meaningful distances between values.

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Ordinal Variable

Variable that generates ordinal data (ordered categories).

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Ordinal Scale Operations

Relational operators ( <, ≤, >, ≥) and summary measures (mode, median) are applicable.

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Ordinal Data Ranking

Ordinal data can be ranked numerically or alphabetically.

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Converting between numerical and ordinal data

Possible to transform but results in data loss

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Binary data type

A type of nominal data with two categories

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Study Notes

Attendance

  • Mark attendance within a minute.

Data in Data Science

  • Entity: A particular thing.
  • Attribute: Measurable/observable property of an entity.
  • Data: A measurement of an attribute.
  • Computers can manage various data types (audio, video, text, etc.).

Data Categorization

  • NOIR: Nominal, Ordinal, Interval, Ratio
  • Classification scheme for data types.

Types of Datasets (1): Record Data

  • Relational records: Database tables with highly structured data.
    • Example tables: "Person" (Pers_ID, Surname, First_Name, City) and "Car" (Car_ID, Model, Year, Value, Pers_ID).
  • Data matrix: Numerical matrix, crosstabs. Example includes a table of sales data organized by region/product.
  • Transaction data: Example includes a table detailing orders with items and unique order IDs.
  • Document data: Term-frequency vector/matrix describing text documents. Example includes a table listing documents with counts/frequencies of words like "team" or "coach".

Types of Datasets (2): Graphs and Networks

  • Transportation networks: Maps of transportation routes.
  • World Wide Web: Network of interconnected webpages.
  • Molecular structures: Network of atoms.
  • Social or information networks: Relationships between entities.

Nominal Scale

  • Definition: A variable with values from a set of mutually exclusive codes with no logical order.
  • Example Codes: Gender (M, F); Blood groups (A, B, AB, O); Country code (048, 040).
  • Note: The variable can be numbers, letters, strings in label format. The number of categories should be finite and mutually exclusive.
  • Note: Numerical values don't have mathematical meaning.
  • Important: Values can't be ordered. (A != B, but A=A).

Binary Scale

  • Definition: A special case of nominal scale with two mutually exclusive categories (e.g., ON/OFF, True/False).
  • Example: Switch status, attendance (Yes/No).
  • Note: A binary variable is only two values.

Symmetric and Asymmetric Binary Scales

  • Symmetric: Binary choices have equal importance, e.g., Gender.
  • Asymmetric: Binary choices have unequal importance, e.g., medical test outcome (covid positive/negative).

Ordinal Scale

  • Definition: Ordered nominal data; the variable generates ordered data.
  • Example: Shirt size (S, M, L, XL, XXL).
  • Note: Values can be ordered; use relational operators ( <, >, =).

Interval Scale

  • Definition: Data measured on a numerical scale with equal intervals between adjacent values.
  • Example: Temperature (Celsius, Fahrenheit), IQ scores.
  • Note: An interval scale does not have a true zero.

Ratio Scale

  • Definition: Data measured on a numerical scale with equal intervals and a true zero.
  • Example: Weight (kg), Income (USD),
  • Note: All arithmetic operations (addition, subtraction, multiplication, division) are permissible.

Operations on Data

  • Distinctiveness: Data values are distinct.
  • Order: Data values are ordered.
  • Addition: Data values can be added.
  • Multiplication: Data values can be multiplied.

Continuous and Discrete Data

  • Discrete: Data can only take on certain individual values, e.g., the number of pages in a book.
  • Continuous: Data can take on any value within a certain range, e.g., the length of a film.

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Data Categorization Lecture Notes PDF

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