Introduction to Statistics and Data Analysis

Statistics deals with collecting, presenting, analyzing, and using data to make informed decisions, solve problems, and design products and processes. It's essentially the science of data.

Descriptive Statistics (DS): Focuses on describing characteristics of a group of people, places, or things using easily verifiable facts or meaningful information. It doesn't draw conclusions about larger datasets.
- Examples: Determining the number of students who passed an exam, analyzing the breakdown time of an insulating fluid. The slide provides specific examples of time data.
Inferential Statistics (IS): Uses data from samples to draw conclusions and make predictions about a larger population. Data analysis is done on a smaller sample group to predict larger dataset patterns.
- Examples: Measuring the correlation between study time and grades in an aeronautical engineering course; analyzing engine performance data to improve maintenance scheduling; and preventing unexpected engine failures to enhance flight safety.

Population: The complete set of all possible observations. Variables describing a population are called parameters.
- Example: All students enrolled in a specific course (IE 101). The parameter of 203 represents the total number of students.
Sample: A smaller, representative subset of the population. Variables describing a sample are called statistics.
- Example: 95 female students enrolled in the same course (IE 101). The statistic of 95 represents the sample selection.

Variables are the characteristics being studied in statistics.
- Qualitative Variables (Categorical Data): Describe qualities or characteristics using non-numeric data; examples include preferences, gender, civil status, or location.
- Quantitative Variables (Numerical Data): Represent measurable quantities or countable characteristics; examples include force, weight, height, voltage, current, resistance, tensile strength, and grades.
  - Continuous Data: Measurable quantities with infinite values between intervals; examples include height, weight, or ratios of measured values.
  - Discrete Data: Countable quantities with finite equal intervals; examples include the number of days in a year, or the number of months in a year.

Independent Variable: A naturally occurring phenomenon that can be controlled or adjusted.
- Examples: temperature, light exposure, wingspan, altitude, and Mach number.
Dependent Variable: A variable observed in response to changes in the independent variable.
- Examples: test scores, sales, reaction time, lift, thrust, drag.
Controlled Variable: Variables held constant to isolate the effects of the independent variable on the dependent variable.
- Examples: temperature, light, water, airspeed, and propeller pitch.
Extraneous Variable: A variable that might influence the dependent variable but is not being studied or controlled.
- Examples: personality, motivation, noise level, and gender.

Nominal: Assigning numerical values to categorical data (e.g., assigning 1 for male and 2 for female).
Ordinal: Assigning rank order to data levels (e.g., race results, ranking in a beauty pageant).
Interval: Fixed differences between numerical values, but zero point is arbitrary (e.g., years, temperatures in Celsius or Fahrenheit scales).
Ratio: Numerical data with a true zero point where values can undergo all basic mathematical operations (e.g., length, mass, angles, charge, and energy).