Definition: Data points significantly different from other observations.

Detection Techniques:

Z-score (for normal distributions).
IQR method: Values outside $[Q1 - 1.5 \times IQR, Q3 + 1.5 \times IQR]$.
Box plots.
Clustering (e.g., DBSCAN).
Isolation Forests.

Filtering: Removal, transformation, or capping/winsorizing.

Data Visualization

Purpose: Aids in understanding data, identifying patterns, communicating insights effectively.
Common Types of Errors: Misleading scales, inappropriate chart types, poor color choices, cluttered designs.
Matplotlib:
- Basic plotting library in Python.
- Subplots: `plt.subplots()` allows creating multiple plots within a single figure.
- Commands for plot customization:
  - Title: `plt.title("Sales Data")`
  - X-axis label: `plt.xlabel("Months")`
  - Y-axis label: `plt.ylabel("Revenue")`
- Scatter Plot: `plt.scatter(x, y)`.
  - Example: `x = [5, 7, 8]`, `y = [12, 19, 21]`.
  - Marker: `plt.scatter(x, y, marker='s', s=100)` (squares, size 100).
- Density Plot (Hexbin/Contour): Useful for visualizing concentration of points in 2D data.
Seaborn:
- High-level data visualization library based on Matplotlib.
- Provides a simpler interface for creating informative and attractive statistical graphics.
- Excellent for visualizing statistical relationships (univariate, bivariate).
- Example: `sns.scatterplot()`, `sns.lineplot()`, `sns.histplot()`.
Histograms vs. Bar Charts:
- Histogram: Displays the distribution of a continuous variable (bars represent frequency within bins). Bars touch.
- Bar Chart: Displays frequency/counts for categorical variables. Bars typically don't touch.
- A histogram is a barchart in appearance but represents continuous data grouped into bins, not distinct categories.
Basemap Toolkit: Used for geographic data visualization, enabling display of world boundaries and custom map projections.
Style Sheets (Matplotlib/Seaborn): Improve visual appeal and consistency (e.g., 'ggplot', 'seaborn').

Variables

Independent Variable: The variable that is changed or controlled in an experiment (input).
Dependent Variable: The variable being tested and measured (output), whose value depends on the independent variable.

Time Series Analysis

Definition: Analyzing data points collected over time.
Smoothing: Used to remove noise and highlight trends or cycles in time series data.
Lorenz Curves: Graphical representation of income or wealth distribution, often used to illustrate inequality.

Data Aggregation & Joins (Pandas)

Aggregation: Combining multiple rows into a single summary row (e.g., `groupby().sum()`, `groupby().mean()`).
Joins: Combining DataFrames based on common columns.
- Inner Join: Returns only rows with matching keys in both DataFrames.
- Left Outer Join: Returns all rows from the left DataFrame and matching rows from the right. If no match, fills with `NaN`.
- Right Ou