Statistics for Financial Engineering - Part 1
What is Statistics?
Statistics is a branch of mathematics that involves the collection, analysis, interpretation, presentation, and organization of data.
Determining the whether data is sample or population is important, before actually performing analysis.
Sample and Population
A population refers to the entire group that is the subject of a study, while a sample is a subset of that population.
Sampling involves selecting a representative portion of the population to conclude the whole. The goal is to ensure that the sample accurately reflects the characteristics of the larger population, allowing for generalization of findings. Proper sampling techniques are essential for obtaining reliable and valid results in statistical analysis, as studying an entire population may be impractical or impossible.
Types of data
Data can be categorized into two main types:
Categorical: Categorical data represents categories or labels and cannot be measured in numerical terms. Examples: Gender (male, female), colors (red, blue, green), types of fruits, etc.
Numerical: Numerical data consists of measurable quantities and can be expressed in numerical terms. Numerical Data has 2 types
- Discrete: Countable and distinct values. Example: number of students in a class, etc
- Continuous: Values that can take any real number within a range. Example: Height, weight, temperature, etc.
Level of Measurement:
Levels of measurement, also known as scales of measurement, classify data into different categories based on the nature and characteristics of the values. There are four main levels of measurement:
- Nominal Level: Represents categories with no inherent order or ranking. Only qualitative distinctions; no meaningful numerical value. Examples: Colors, gender, and types of fruits.
- Ordinal Level: Represents categories with a meaningful order or ranking. Relative ranking but no consistent intervals between values. Examples: Educational levels (e.g., high school, bachelor’s, master’s), survey ratings.
- Interval Level: Represents values with a meaningful order and consistent intervals between them. No true zero point; ratios are not meaningful. Examples: Temperature measured in Celsius or Fahrenheit, IQ scores.
- Ratio Level: Represents values with a meaningful order, and consistent intervals. Has a true zero point, allowing for meaningful ratios. Examples: Height, weight, income, and number of items.
