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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Mode

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 In statistics, mode refers to the value or values in a dataset that appears most frequently. It is a measure of central tendency, along with the mean and median.

Here are examples of modes for ungrouped and grouped data:

  • Ungrouped data: Consider the following set of numbers: 3, 4, 2, 1, 4, 5, 4, 6, 2. The mode is the value that appears most frequently, which in this case is 4. Therefore, the mode for this dataset is 4.


  • Grouped data: Suppose we have a dataset that represents the number of hours spent watching TV per week for a group of people, and the data is grouped into the following frequency distribution:

Hours per week

Number of people

0-4

10

5-9

15

10-14

5

15-19

3

To find the mode for this dataset, we need to determine which group has the highest frequency. In this case, the group with the highest frequency is 5-9.

Note that in some cases, there may be more than one mode in a dataset, which means that there are multiple values that appear with the same highest frequency. For example, in the ungrouped dataset mentioned earlier, both 2 and 4 appear three times, so the dataset has two modes: 2 and 4.

The formula used to find the mode of grouped data is

Mode = L + ((fm – f1)/[(fm – f1)+(fm – f2)] x h

where:

  • L is the lower class boundary of the class interval with the highest frequency.
  • Fm is the frequency of the class interval with the highest frequency.
  • F1 is the frequency of the class interval immediately preceding the interval with the highest frequency.
  • F2 is the frequency of the class interval immediately following the interval with the highest frequency.
  • h is the class interval height.
  • The mode for the above data will be,
  • Modes= 5+15-10/[(15-10)+(15-5)] *5
  • =5+1.25
  • =6.25

 

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