Basic Statistics¶

Histogram¶

A histogram is a graphical representation of data that shows how values are distributed across ranges (bins).

It helps to: - Visualize the shape of the data - Identify skewness and spread - Detect outliers or unusual patterns

Histograms are commonly used as a first step in data exploration.

To approximate and understand real-world data, we often assume that data follows a distribution.

Commonly used distributions include: - Normal distribution - Exponential distribution

A distribution is a graphical or mathematical description of how measurements are spread across possible values.

It answers questions such as: - Which values occur most often? - How spread out is the data? - Is the data symmetric or skewed?

The normal distribution (also called the Gaussian distribution) has a: - Bell-shaped curve - Symmetric form around the center

Key properties: - Most values cluster around the mean - Mean, median, and mode are equal - Extreme values are increasingly rare

This distribution is common in natural and measurement-based data.

The exponential distribution is commonly used when estimating: - Time between two events

Characteristics: - Values are always positive - Many small values, fewer large values - Right-skewed shape

Typical use cases: - Time until a system failure - Time between customer arrivals - Waiting times

These are measures of central tendency.