Section 1.1 – Introduction to the Practice of Statistics

What is Statistics?

Statistics is the science of collecting, organizing, summarizing, and analyzing information to draw conclusions or answer questions. It also involves providing a measure of confidence in any conclusions drawn from data.

• Example: A community college surveys 128 randomly selected students to determine how many hours per week they work. The average number of hours worked is 25.

Key Terms in Statistics

• Data: Information collected for analysis. It can be facts or propositions used to draw conclusions or make decisions, and it describes characteristics of individuals. Data can vary.

• Population: The entire group of individuals to be studied.

• Individual: A single member or object from the population being studied.

• Sample: A subset of the population selected for study.

• Statistic: A numerical summary calculated from a sample.

• Parameter: A numerical summary describing a population.

• Descriptive Statistic: Methods for organizing and summarizing data, often using numerical summaries, tables, and graphs.

• Inferential Statistic: Methods that use sample data to make generalizations about a population and measure the reliability of the results.

Examples: Parameter vs. Statistic

• Parameter: The average score for a class of 30 students (entire population) is 75%.

• Statistic: 13.5% of Americans age 12 and over (sample) used drugs in the last month.

Variables and Types of Data

Variables

Variables are characteristics or attributes of individuals within a population that can change or vary.

Qualitative vs. Quantitative Variables

• Qualitative Variables (Categorical): Classify individuals based on attributes or characteristics (e.g., educational level, gender, marital status, name, ID number).

• Quantitative Variables: Provide numerical measures of individuals. These values can be added or subtracted to yield meaningful results (e.g., GPA, bank account balance, salaries, number of followers).

Examples: Qualitative vs. Quantitative

• Gender: Qualitative

• Temperature: Quantitative

• Number of days a student studied: Quantitative

• Zip code: Qualitative

Discrete vs. Continuous Variables

• Discrete Variables: Quantitative variables with a finite or countable number of possible values. If you count to obtain the value, it is discrete.

• Continuous Variables: Quantitative variables with an infinite number of possible values. If you measure to obtain the value, it is continuous.

Examples: Discrete vs. Continuous

• Number of tails in four coin flips: Discrete

• Number of cars at a drive-through between 9 PM and 10 PM: Discrete

• Distance a car can travel on a full tank: Continuous

Levels of Measurement of a Variable

Variables can be classified by their level of measurement, which determines the type of statistical analysis that is appropriate.

• Nominal Level: Values name, label, or categorize. No inherent order. Examples: Blood type, eye color.

• Ordinal Level: Values can be ranked or ordered, but differences between values are not meaningful. Examples: Socio-economic status, satisfaction ratings.

• Interval Level: Values can be ordered, and meaningful differences exist, but zero does not indicate absence of quantity. Examples: Temperature, credit scores.

• Ratio Level: Values can be ordered, meaningful differences and ratios exist, and zero indicates absence of quantity. Examples: Money, weight.

Examples: Levels of Measurement

• Gender: Nominal

• SAT score: Interval

• Number of days a student worked out last week: Ratio

• Letter grade: Ordinal

Additional info: The diagram visually summarizes how qualitative variables are associated with nominal and ordinal levels, while quantitative variables are associated with interval and ratio levels.