Statistics Basics

Study Notes

Types of Data:
- Qualitative (categorical): describes characteristics (e.g., colors, shapes)
- Quantitative (numerical): describes amounts (e.g., length, time)
Measures of Central Tendency:
- Mean: average value
- Median: middle value (when data is in order)
- Mode: most frequent value
Measures of Variability:
- Range: difference between largest and smallest values
- Interquartile Range (IQR): difference between Q3 and Q1 (75th and 25th percentiles)

Variables and Constants:
- Variables: letters or symbols representing unknown values
- Constants: numbers
Equations and Inequalities:
- Equations: statements with an equal sign (=)
- Inequalities: statements with an inequality sign (>, <, ≥, ≤)
Linear Equations:
- Standard form: Ax + By = C (A, B, and C are constants)
- Slope-Intercept form: y = mx + b (m is slope, b is y-intercept)

Properties of Multiplication:
- Commutative: a × b = b × a
- Associative: (a × b) × c = a × (b × c)
- Distributive: a × (b + c) = a × b + a × c
Division:
- Definition: a ÷ b = c if and only if a = c × b
- Rules:
  - Division by zero is undefined
  - Division is the inverse operation of multiplication

Qualitative Data: describes characteristics, such as colors, shapes, and categories
Quantitative Data: describes amounts, including length, time, and numerical values
Mean: the average value of a dataset, calculated by summing values and dividing by the number of values
Median: the middle value in a dataset when arranged in order, providing a middle point
Mode: the most frequent value in a dataset, which may not exist in every dataset
Range: the difference between the largest and smallest values in a dataset, providing a sense of spread
Interquartile Range (IQR): the difference between the 75th percentile (Q3) and 25th percentile (Q1) in a dataset, providing a more robust measure of spread

Variables: letters or symbols used to represent unknown values or quantities, often used to solve equations
Constants: numbers that do not change, often used in equations and formulas
Equations: statements that express the equality of two expressions, often containing variables, constants, and various operations
Inequalities: statements that express a relationship between two expressions, such as "greater than" or "less than", often containing variables, constants, and various operations

Multiplication is a mathematical operation that represents repeated addition.
Multiplication is denoted by the multiplication symbol (×) or an asterisk (*).
The commutative property of multiplication states that the order of numbers being multiplied does not change the result.
The associative property of multiplication states that the order in which numbers are multiplied does not change the result.
The distributive property of multiplication states that multiplication distributes over addition.
There are two types of multiplication: scalar multiplication and matrix multiplication.
Scalar multiplication involves multiplying a number by a scalar value.
Matrix multiplication involves multiplying matrices.

Division is a mathematical operation that represents sharing or grouping.
Division is denoted by the division symbol (÷) or a forward slash (/).
The order of numbers being divided changes the result, making division non-commutative.
The order in which numbers are divided changes the result, making division non-associative.
There are three types of division: whole number division, fractional division, and long division.
Whole number division involves dividing whole numbers.
Fractional division involves dividing fractions or decimals.
Long division is a step-by-step procedure for dividing one number by another.