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Statistics and Its Applications, Example - Coggle Diagram
Statistics and Its Applications
Unit I
Introduction to Statistics and Its Applications
Specific Objective
To manage the key concepts of statistics
Origins of Statistics
Two Meanings
Collection of information (e.g., "elaborating statistics")
Scientific discipline to obtain conclusions and deduce relationships
Etymological Meaning
"Science of the State."
Unit II
Statistical Analysis of One Variable
Specific Objective
To perform estimations and predictions.
Statistical Tables
Definition
A set of data organized in rows and columns
Utility
To present synthesized information
To compare and interpret data
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Statistical Graphs
Definition
A visual way to represent numerical data
Utility
To visualize complex data
To present accurate and clear information
To facilitate understanding for different audiences
Measures of Concentration
Origin: Lorenz Curve (Max Lorenz, 1905)
Purpose: To measure the degree of concentration or distribution (e.g., of income)
Idea: To compare the percentage of individuals with the percentage of income they hold
Unit III
Index Numbers
Specific Objective
To organize frequency distributions
Simple Index Numbers
Definition
Measures the variation of a single variable over time relative to a base period
Calculation
Relative value of the variable in the current period divided by its value in the base period, multiplied by 100
Weighted Index Numbers
Definition
Considers the relative importance (weight) of each element in the calculation.
Types
Laspeyres Index
Weights refer to the base period (w i)
Paasche Index
Weights refer to the current period (w′i), more complex calculation
Fisher Index
Combines Laspeyres and Paasche (generally as a geometric mean
Unit IV
Statistical Analysis of Two or More Variables
Specific Objective
To calculate statistical measures.
Bidimensional Distributions
Definition
Measures of two characteristics (qualitative or quantitative) are collected for each element.
Examples
Grades in two subjects, height and weight
Two-Way Table (Contingency Table)
Structure
xi values in the first row, yi values in the first column
Kendall's Coefficient of Concordance (W)
Purpose: To measure the degree of agreement among different judges or experts
Formula and Components
W: Coefficient of concordance
K: Number of experts
T: Correction factor
Rj: Sum of ranks assigned to each variable.
S: Sum of squared deviations
t: Number of observations in a tied group
Calculation Steps
Order observations by ranks.
Sum ranks by variable
Obtain summation and average of summations
Calculate S (squared differences)
Apply equation for adjustment for ties
Calculate W
Transform W into chi-squared (χ2) and calculate degrees of freedom (gl=N−1).
Decide hypothesis (e.g., reject or accept null hypothesis)
Example
Domain of a Function
To Avoid
Zero in the denominator of fractions
Negative values inside square roots
Possible values of the independent variable (x).
Key Concepts
y= √x+2 -> Domain: x≥−2