Introduction to Statistics Quiz

Introduction to Statistics

• Statistics is the science of collecting, organizing, analyzing, interpreting, and presenting data.
• It is used to understand patterns, trends, and relationships in data.

Basic Statistical Terms

• Data: Observations or measurements collected about a particular topic.
• Variable: A characteristic or attribute that can take on different values.
• Qualitative variable: A categorical variable, like gender or color.
• Quantitative variable: A numerical variable, like height or weight.
• Discrete variable: A quantitative variable with specific, separate values (e.g., number of cars).
• Continuous variable: A quantitative variable with any value within a range (e.g., temperature, height).
• Population: The entire group of individuals or items of interest.
• Sample: A subset of the population selected for study.
• Parameter: A numerical value describing a population characteristic (e.g., population mean).
• Statistic: A numerical value describing a sample characteristic (e.g., sample mean).

Random Variable

• A random variable is a variable whose value is a numerical outcome of a random phenomenon, taking on different values based on chance.
• Two main categories: discrete and continuous.

Discrete Random Variable

• A discrete random variable can only take on specific, countable values.
• Examples include:
  • Number of heads in 3 coin flips
  • Number of defective items in a batch
  • Number of students in a classroom
• Key features:
  • Possible values are separate (e.g., no 2.5 heads).
  • Probabilities are calculable for each outcome.

Continuous Random Variable

• A continuous random variable can take on any value within a given range.
• Examples include:
  • Height
  • Weight
  • Temperature
  • Time
• Key features:
  • Infinitely many possible values.
  • Probabilities are associated with intervals (e.g., probability between 160 and 170 cm tall). Probability for a single exact value is zero.