ALGEBRA

Descriptive Statistics

Measures of Central Tendency (where the data “sits”)

  • Mean (average) – The balance point of the data; pulled by outliers.

  • Median (middle value) – The central value when ordered; not affected by extremes.

  • Mode (most common value) – The value that appears most often.

2. Measures of Spread / Dispersion (how spread out the data is)

  • Range (max − min) – How wide the data is overall.

  • Variance – How far values spread from the mean, on average (squared units).

  • Standard Deviation – Typical distance from the mean; variance in original units.

  • Interquartile Range (IQR) – Spread of the middle 50% of the data; ignores outliers.

3. Measures of Position (where a value stands)

  • Minimum – The smallest observed value.

  • Maximum – The largest observed value.

  • Quartiles (Q1, Q2, Q3) – Cut the data into four equal parts.

  • Percentiles – Show the percentage of data below a value.

4. Measures of Shape (how the data looks)

  • Skewness – Tells if the data leans left or right.

  • Kurtosis – Tells how heavy the tails are (outlier-prone or not).

5. Counts / Frequency

  • Count (n) – Number of observations.

  • Frequency – How often values occur.

Vectors

List of attributes of an object

We can get the size of a vector by taking the square root of the dot product:

  • Vectors have the associativity property : A+B = B+A

  • Dot product is commutative and distributive over addition and associative over scalar multiplication

    • A*B=B*A

    • r.(S+T)= rS+rT

    • a*rs= r*as

Cosine Rule - (2 sides + angle)

a²= c²+b² -2bcCosA

c.b = |c|. |b|CosA

The Identity matrix is the matrix that does not change a vector when multiplied by it for example 1 0

                  0 1

Inverse of A * A = Identity Matrix