1.1 Introduction to the Practice of Statistics

Main ideas and lessons

Purpose of statistics

• Statistics is something people encounter in everyday life (e.g., news).
• It helps you make the best educated guess about whether claims are correct, using data.
• Its central goal is to:
  • collect data from a small part (a sample) of a larger group (a population)
  • and use that information to learn about the population.
• A key added feature is that statistics also aims to provide a measure of confidence in conclusions (often covered later in the course).

Formal definitions

• Statistics (course definition): the science of collecting, organizing, summarizing, and analyzing information to draw conclusions or answer questions.
• Data: observations recorded as numeric or non-numeric.
• Population: the entire group being studied.
• Sample: a subset of the population.
• Statistic: a numerical summary of a sample.
• Parameter: a numerical summary of a population.

Process overview (what statisticians do)

1. Collect data by taking a sample from a population.
2. Organize the data using charts and graphs.
3. Analyze the data.
4. Use the results to make an inference about the population.

Descriptive vs. inferential statistics

• Descriptive statistics:
  • Organize and summarize data.
  • Use numerical summaries, tables, and graphs to describe the data.
• Inferential statistics:
  • Use methods that extend results from a sample to the population.
  • Assess the reliability of the result.

Types of variables

1) Qualitative (categorical) variables

• Classify individuals by an attribute/characteristic.
• Examples: hair color, blood type, ethnic group, car type, street someone lives on.

2) Quantitative variables

• Give numerical measures.
• Examples: amount of money, pulse rate, weight, number of people in a city, age.

3) Discrete vs. continuous (subtypes of quantitative variables)

• Discrete variables

  • Quantitative variables with a finite or countable set of possible values.
  • Think “results of counting.”
  • Cannot take every value in an interval.
  • Examples: number of eggs a hen lays, number of phone calls per day, number of books in a backpack.

• Continuous variables

  • Quantitative variables with an infinite number of possible values that are not countable.
  • Think “results of measuring.”
  • Can take every value between two values (measurements can be refined).
  • Examples: angles in radians, weight of a backpack, area of lawns.
  • Values can land “between” others (e.g., 150.5, 150.52).

Worked examples: statistic vs. parameter

• A: In a poll of 1,000 adults in the U.S., 55% said they use local TV daily.

  • 1,000 adults = sample
  • 55% = statistic

• B: After inspecting all 55,000 kg of meat stored at a company, 45,000 kg was spoiled.

  • all 55,000 kg = population
  • 45,000 kg spoiled = parameter

Quick practice activity (classifying variable types)

The video prompts you to classify each item as qualitative vs quantitative, and if quantitative, discrete vs continuous:

• Number of pairs of shoes you own → quantitative, discrete
• Type of car you drive → qualitative
• Where you go on vacation → qualitative
• Distance from home to nearest grocery store → quantitative, continuous
• Number of classes you take per school year → quantitative, discrete
• Type of calculator you use (brand/function) → qualitative
• Weight of sumo wrestlers → quantitative, continuous
• Number of correct answers on a quiz → quantitative, discrete
• Time to run a mile → quantitative, continuous

Speakers / sources featured

• No specific named speakers or external sources are identified in the provided subtitles.