Section1.2

Chapter 1: Introduction to Statistics

Introduction to the Course

• Copyright © 2022, 2018, 2014 Pearson Education, Inc.

• Text: Elementary Statistics, Fourteenth Edition

Overview of Topics

• 1-1 Statistical and Critical Thinking

• 1-2 Types of Data

• 1-3 Collecting Sample Data

Key Concepts

• Understand the terms:

  • Statistics: Numerical measurement describing characteristics of a sample.

  • Parameter: Numerical measurement describing characteristics of a population.

• Data types influence the statistical methods applied in analysis.

Parameters and Statistics

Parameter

• Definition: A numerical measurement that describes a characteristic of a population.

Statistic

• Definition: A numerical measurement that describes a characteristic of a sample.

Types of Data

Quantitative Data

• Definition: Comprises numbers representing counts or measurements.

  • Examples:

    • Weights of supermodels

    • Ages of respondents

Categorical Data

• Definition: Comprises names or labels (not numerical values).

  • Examples:

    • Gender (male/female) of professional athletes

    • Shirt numbers on professional athletes' uniforms (substitutes for names)

Working with Quantitative Data

• Quantitative data is further categorized into:

  • Discrete Data:

    • Values are finite and countable.

    • Example: Number of coin tosses before getting tails.

  • Continuous Data:

    • Values are not countable; can take on an infinite number of values.

    • Example: Lengths from 0 cm to 12 cm.

Levels of Measurement

• Four levels categorize data:

  • Nominal

    • Characteristics: Names, labels, or categories only.

    • Example: Survey responses (yes, no, undecided).

  • Ordinal

    • Characteristics: Can be arranged in order, but differences are not meaningful.

    • Example: Course grades (A, B, C, D, F).

  • Interval

    • Characteristics: Can be arranged in order with meaningful differences, but no true zero.

    • Example: Years (1000, 2000, etc.).

  • Ratio

    • Characteristics: Can be arranged in order, meaningful differences, and a natural zero exists.

    • Example: Class times (50 minutes, 100 minutes).

Summary of Levels of Measurement

• Nominal: Categories only

• Ordinal: Categories with order

• Interval: Differences but no natural zero point

• Ratio: Differences and a natural zero point

Big Data

• Definition: Refers to data sets that are too large and complex for traditional software to analyze.

• Data Science: Application of statistics, computer science, software engineering, and other relevant fields.

Missing Data

• Missing Completely at Random: Missing values do not depend on their value or other values in the set.

• Missing Not at Random: Missing values are related to the reason they are absent.

Correcting for Missing Data

Methods

1. Delete Cases: Remove all subjects with missing values.

2. Impute Missing Values: Substitute missing values with estimated ones.