Prompt Title: Statistical Concepts Study Sheet

Statistics in STEM Study Sheet

Module 1 - Descriptive Statistics and Probability

1.1 What is data?

• Definition: Raw facts and figures representing quantities, characters, or symbols.
• Types:
  • Qualitative (descriptive, non-numeric)
  • Quantitative (numeric)

1.2 Data Visualization

• Definition: Graphical representation of information and data to understand trends, outliers, and patterns.
• Tools: Charts, graphs, maps.

1.3 Python for Data Visualization

• Libraries: matplotlib, seaborn, plotly.
• Purpose: Create static, animated, and interactive visualizations.

1.4 Data Frames

• Definition: Two-dimensional, size-mutable, heterogeneous tabular data with labeled axes.
• Use: Essential in data analysis, especially with Python's pandas library.

1.5 Bar Charts

• Represents: Categorical data.
• Features: Rectangular bars with lengths proportional to the values they represent.

1.6 Pie Charts

• Represents: Numerical proportion.
• Features: Circular charts divided into slices or segments; each slice represents a percentage of the whole.

1.7 Scatter Plots

• Represents: Values of two different variables.
• Features: Dots plotted on x and y axes to observe relationships.

1.8 Line Charts

• Represents: Information over intervals or time.
• Features: Data points connected by straight line segments.

1.9 Box Plots (Whisker Plots)

• Represents: Data through quartiles.
• Features: Shows median, interquartile range, and potential outliers.

1.10 Histograms

• Represents: Frequency of data points in specified ranges.
• Features: No gaps between bars, unlike bar charts.

1.11 Survey Sampling

• Definition: Selecting a subset from a population to estimate characteristics of the whole.
• Techniques: Random sampling, stratified sampling, cluster sampling.

1.12 Measures of Center

• Definition: Values describing the center point of a dataset.
• Types:
  • Mean (average)
  • Median (middle value)
  • Mode (most frequent value)

1.13 Measures of Variability

• Definition: Quantify the spread or dispersion of data.
• Key Measures:
  • Range
  • Variance
  • Standard Deviation

1.14 Probability

• Definition: Measures the likelihood of an event occurring.
• Scale: 0 (impossibility) to 1 (certainty).

1.15 Addition Rule and Complements

• Addition Rule: Finds the probability of the union of two events.
• Complement: The event that does not occur, denoted A′.

1.16 Multiplication Rule and Independence

• Multiplication Rule: Computes the probability of both events occurring.
• Independence: Two events are independent if one's occurrence doesn't affect the other's.

1.17 Conditional Probability

• Definition: Probability of an event given another event has occurred.

1.18 Bayes' Theorem

• Purpose: Revise predictions based on new evidence.
• Formula: Relates current to prior probability using a likelihood and a normalizing constant.

1.19 Combinations and Permutations

• Combinations: Arrangement where order doesn't matter.
• Permutations: Arrangement where order matters.

Key Terms & Formulas

• Describe: Summarizing main characteristics of a dataset.
• Mean: $\mu = \frac{\sum x}{n}$
• Median: Middle value in an ordered dataset.
• Variance: $\sigma^2 = \frac{\sum (x - \mu)^2}{n}$
• Standard Deviation: $\sigma = \sqrt{\sigma^2}$
• Distribution: How data points are spread. Types include uniform, normal, skewed.
• Measure of Central Tendency: Mean, median, mode.
• Deviation: $x - \mu$

Examples:

• Mean of [2, 4, 6] = $\frac{2+4+6}{3}$ = 4
• Standard Deviation: If variance is 9, then standard deviation is 3.

Remember to practice with real datasets to solidify these concepts and always refer back to this sheet for quick reference!