Objectives and Introduction to Statistics

Overview of Statistics

Statistics is the science of collecting, organizing, analyzing, and interpreting data to make decisions. It is foundational for understanding data-driven conclusions in many fields.

• Definition of statistics: The study of methods for collecting, analyzing, interpreting, and presenting empirical data.

• Distinguishing between population and sample: A population includes all subjects of interest, while a sample is a subset of the population.

• Distinguishing between parameter and statistic: A parameter describes a characteristic of a population; a statistic describes a characteristic of a sample.

• Descriptive vs. inferential statistics: Descriptive statistics summarize data; inferential statistics use sample data to make generalizations about a population.

Data: Definitions and Examples

What is Data?

Data consists of information coming from observations, counts, measurements, or responses. It forms the basis for statistical analysis.

• Examples:

  • 7 in 10 Americans believe the arts unify their communities.

  • 21% of 8–11 year-olds have a social media profile.

Data Sets: Population and Sample

Definitions

• 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 survey of 834 U.S. employees, 517 said their jobs were highly stressful.

• Population: All employees in the U.S.

• Sample: The 834 employees surveyed.

• Sample data set: The responses of 517 "yes" and 317 "no".

Parameter and Statistic

Definitions

• Parameter: A numerical description of a population characteristic. Example: Average age of all people in the United States.

• Statistic: A numerical description of a sample characteristic. Example: Average age of people from a sample of three states.

Example: Distinguishing Parameter and Statistic

• Survey of 9400 individuals: Average of 5.19 hours per day spent in leisure and sports activities. Solution: Since the average is based on a subset, it is a sample statistic.

• Freshman class average SAT math score: If based on the entire class, it is a population parameter.

• Food and Drug Administration check: 34% of stores not storing fish at proper temperature. Solution: Based on a subset, it is a sample statistic.

Branches of Statistics

Descriptive Statistics

Descriptive statistics involve the organization, summarization, and display of data.

• Examples: Tables, charts, averages.

Inferential Statistics

Inferential statistics use sample data to draw conclusions about a population.

• Example: Using survey results to estimate population characteristics.

Examples: Descriptive and Inferential Statistics

• Study of 1502 U.S. adults: 18% of adults from households earning less than $30,000 do not use the Internet. Population: All U.S. adults. Sample: 1502 adults surveyed. Descriptive: "18% do not use the Internet." Inferential: The Internet may be less accessible to lower-income households.

• Study of 1000 U.S. 401(k) participants: 32% do not know how many years their retirement savings might last. Population: All U.S. 401(k) participants. Sample: 1000 participants surveyed. Descriptive: "32% do not know." Inferential: Retirement planning is challenging for many.

Chapter 1.2: Data Classification

Types of Data

• Qualitative Data: Consists of attributes, labels, or nonnumerical entries. Examples: Major, place of birth, eye color.

• Quantitative Data: Numerical measurements or counts. Examples: Age, weight, temperature.

Example: Classifying Data by Type

The following table shows sports-related head injuries treated in U.S. emergency rooms. Types of sports are qualitative; head injuries treated are quantitative.

Levels of Measurement

Nominal Level

• Qualitative data only

• Data categorized using names, labels, or qualities

• No mathematical computations possible

Ordinal Level

• Qualitative or quantitative data

• Data can be arranged in order, or ranked

• Differences between data entries are not meaningful

Interval Level

• Quantitative data

• Data can be ordered

• Differences between entries are meaningful

• Zero represents a position on a scale, not an inherent zero

Ratio Level

• Similar to interval level

• Zero entry is an inherent zero (implies "none")

• Ratios of data values can be formed

• One data value can be expressed as a multiple of another

Example: Classifying Data by Level

Interval vs. Ratio Example

Summary Table: Four Levels of Measurement

Examples of Data Sets and Calculations

Additional info: These notes provide foundational concepts for introductory statistics, including definitions, examples, and classification tables. All equations and formulas referenced in this section are conceptual; no explicit mathematical formulas are required for these topics.