Data Collection

Introduction to Data

Data are collections of observations, such as measurements (numbers), categories (like gender), or survey responses. Data are essential for drawing conclusions and making decisions in statistics. They can be numerical (e.g., height) or nonnumerical (e.g., hair color), but in all cases, data describe characteristics of individuals. A key aspect of data is that they vary among individuals.

Types of Variables

Variables are characteristics of individuals that are measured, recorded, and analyzed. Variables can be classified as either qualitative or quantitative:

• Qualitative (Categorical) Variables: Allow for classification based on attributes or characteristics. Examples include nationality, model of car, or zip code.

• Quantitative Variables: Provide numerical measures of individuals. Arithmetic operations such as addition and subtraction are meaningful. Examples include number of children, household income, or daily intake of whole grains.

Subtypes of Quantitative Variables

• Discrete Variables: Quantitative variables with a finite or countable number of possible values (e.g., number of children, points scored in a game).

• Continuous Variables: Quantitative variables with an infinite number of possible values within an interval (e.g., time, income, daily intake measured in grams).

If you count to get the value, it is discrete; if you measure, it is continuous.

Statistics: The Science of Data

Statistics is the science of planning studies and experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data.

Distinguishing Between Variables and Data

Individuals, Variables, and Data

In a dataset, the individuals are the entities being studied (e.g., cars, countries, people). Variables are the characteristics measured for each individual, and data are the observed values for these variables.

Example: Country Data Table

In this table, the individuals are the countries, the variables are government type, life expectancy, and population, and the data are the specific values listed for each country.

Example: Parking Meter Data Table

Here, the individuals are the cars, the variables include payment method, amount paid, duration, side of street, and parking space number, and the data are the observed values for each car.

Populations, Samples, and Individuals

Definitions

• Population: The entire group of individuals to be studied (e.g., all students at a college, all US households).

• Sample: A subset of the population that is actually studied.

• Individual: A single member of the population or sample.

For example, if you survey 40 students out of all students at a college, the 40 students are the sample, and each student is an individual.

Descriptive and Inferential Statistics

Descriptive Statistics

Descriptive statistics involve organizing and summarizing data using numerical summaries, tables, and graphs. They describe the sample or population without making generalizations beyond the data at hand.

Inferential Statistics

Inferential statistics use methods that take results from a sample, extend them to the population, and measure the reliability of the result. For example, using a sample proportion to estimate a population proportion with a confidence interval.

Parameters and Statistics

Definitions

• Parameter: A numerical summary of a population (e.g., the percentage of all students who own a car).

• Statistic: A numerical summary of a sample (e.g., the percentage of surveyed students who own a car).

Parameters describe populations; statistics describe samples.

Examples

• If 48.2% of all students own a car, 48.2% is a parameter.

• If 46% of a sample of 100 students have a job, 46% is a statistic.

Matching Key Terms and Definitions

Practice: Parameters vs. Statistics

• 18% of governors are female: Parameter (describes a population).

• 72% average score for a class: Parameter (describes a population).

• 32% of surveyed high school students bullied: Statistic (describes a sample).

• 13.3% of surveyed 12th graders used drugs: Statistic (describes a sample).

Summary Table: Types of Variables

Key Formulas:

• Sample Mean:

• Population Mean:

• Sample Proportion:

• Population Proportion: