Introduction to Statistics: Key Concepts and Foundations

Chapter 1: Introduction to Statistics

Chapter Outline

• An Overview of Statistics

• Data Classification

• Data Collection and Experimental Design

An Overview of Statistics

Section 1.1 Objectives

• Define statistics and data

• Distinguish between a population and a sample

• Differentiate between a parameter and a statistic

• Distinguish between descriptive statistics and inferential statistics

What is Data?

Data consist of information collected from observations, counts, measurements, or responses. Data are the raw material for statistical analysis and can be quantitative (numerical) or qualitative (categorical).

• Example: "7 in 10 Americans believe the arts unify their communities." (Source: Americans for the Arts)

• Example: "21% of 8–11 year-olds have a social media profile." (Source: Smart Insights, Ltd)

What is Statistics?

Statistics is the science of collecting, organizing, analyzing, and interpreting data to make decisions. It provides methods for drawing conclusions from data and for quantifying uncertainty.

• Key Steps in Statistics:

  1. Collecting data

  2. Organizing data

  3. Analyzing data

  4. Interpreting results

Data Sets: Populations and Samples

Understanding the difference between a population and a sample is fundamental in statistics.

• Population: The collection of all outcomes, responses, measurements, or counts that are of interest.

• Sample: A subset, or part, of the population.

Example: Identifying Data Sets

In a recent survey, 834 employees in the United States were asked if they thought their jobs were highly stressful. Of the 834 respondents, 517 said yes.

• Population: All employees in the United States.

• Sample: The 834 employees who responded to the survey.

• Data set: The responses (517 yes, 317 no) from the sample.

Parameters and Statistics

It is important to distinguish between a parameter and a statistic:

• Parameter: A numerical description of a population characteristic.

• Statistic: A numerical description of a sample characteristic.

Examples: Distinguishing Parameter and Statistic

• Example 1: A survey of about 9,400 individuals aged 15 and over found that such individuals spent an average of 5.19 hours per day engaged in leisure and sports activities. This is a sample statistic because it is based on a subset of the population.

• Example 2: The freshman class at a university has an average SAT math score of 514. This is a population parameter because it is based on the entire freshman class.

• Example 3: In a random check of several hundred retail stores, the Food and Drug Administration found that 34% of the stores were not storing fish at the proper temperature. This is a sample statistic because it is based on a subset of all stores.

Branches of Statistics

Statistics is divided into two main branches:

Descriptive Statistics	Inferential Statistics
Involves the organization, summarization, and display of data. Examples include tables, charts, and numerical summaries.	Involves using sample data to draw conclusions or make inferences about a population.

Example: Descriptive and Inferential Statistics

• Study: A study of 1,502 U.S. adults found that 18% of adults from households earning less than $30,000 annually do not use the Internet.

• Population: All U.S. adults.

• Sample: The 1,502 U.S. adults in the study.

• Descriptive statistics: The statement "18% of adults from households earning less than $30,000 annually do not use the Internet."

• Inferential statistics: A possible inference is that the Internet has been made inaccessible to lower-income households.

• Study: A study of 1,000 U.S. 401(k) retirement plan participants found that 32% do not know how many years their retirement savings might last.

• Population: All U.S. 401(k) retirement plan participants.

• Sample: The 1,000 participants in the study.

• Descriptive statistics: The statement "32% do not know how many years their retirement savings might last."

• Inferential statistics: A possible inference is that the amount of money a person needs for retirement is difficult to determine.

Summary Table: Key Terms

Term	Definition	Example
Population	All individuals or items of interest	All employees in the U.S.
Sample	Subset of the population	834 employees surveyed
Parameter	Numerical summary of a population	Average SAT score of all freshmen
Statistic	Numerical summary of a sample	Average hours of leisure from a survey

Additional info: Later sections (not included here) will cover data classification and experimental design in more detail.