Introduction to Discrete & Continuous Probability Distributions

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  ✅ 1. What is a Probability Distribution? A probability distribution describes how probabilities are distributed over the values of a random variable . Random Variable : A variable whose values are outcomes of a random phenomenon. ๐Ÿงฎ 2. Types of Probability Distributions Type Description GIS Example Discrete           Takes countable values  Number of landslides per year in a          valley Continuous          Takes infinite values over an                 interval Rainfall (mm), elevation, temperature  ๐Ÿ“Œ Discrete Probability Distributions ๐ŸŽฏ 3. Binomial Distribution ✅ Definition : Used when an experiment is repeated n times , and each trial has two outcomes : success or failure. ✅ Conditions : Fixed number of trials (n) Only two possible outcomes per trial (success/failure) Constant probability of success (p) Trials are in...
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Bar Graph

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 A bar graph, also known as a bar chart, is a visual representation of data using rectangular bars of varying lengths. It is commonly used to compare and display categorical or discrete data, where each category or group is represented by a separate bar.

Creating a Bar Graph: To create a bar graph, follow these steps:

  1. Identify the data: Determine the data you want to represent in the bar graph. This data should be categorical or discrete, such as different categories, groups, or time periods.
  2. Choose the axes: Decide which variable you want to represent on the x-axis (horizontal axis) and which variable you want to represent on the y-axis (vertical axis). The x-axis typically represents the categories or groups, while the y-axis represents the values or frequencies associated with each category.
  3. Determine the scale: Determine the appropriate scale for each axis. The scale should allow for a clear and meaningful representation of the data. Consider the range of values and choose a scale that accommodates the data without compressing or distorting it.
  4. Draw the bars: Draw rectangular bars for each category or group along the x-axis. The height of each bar corresponds to the value or frequency associated with that category.
  5. Label the axes and bars: Label the x-axis and y-axis with appropriate category names or labels and numerical values, respectively. Add a title to the graph that reflects the data being presented. Label each bar if necessary.

Types of Bar Graphs:

  1. Vertical Bar Graph: In a vertical bar graph, the bars are drawn vertically, with the x-axis representing the categories or groups and the y-axis representing the values or frequencies. This is the most common type of bar graph.
  2. Horizontal Bar Graph: In a horizontal bar graph, the bars are drawn horizontally, with the y-axis representing the categories or groups and the x-axis representing the values or frequencies. This format is useful when the category names or labels are lengthy.



  3. Stacked Bar Graph: A stacked bar graph represents multiple variables or subcategories within each category. Each bar is divided into segments or sections, and the length of each segment represents the contribution of the respective variable or subcategory

   4. Grouped Bar Graph: A grouped bar graph displays multiple bars side by side for each category. It is useful for comparing values between different groups or subcategories within each category.



 5. Clustered Bar Graph: A clustered bar graph is similar to a grouped bar graph, but the bars are grouped together for each category instead of being displayed side by side. It allows for easy comparison of values within and between groups.



Bar graphs are versatile and widely used in various fields, such as statistics, market research, and data analysis, as they provide a clear visual representation of categorical data and facilitate easy comparison between different categories or groups

 

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