Statistical Foundations: Concepts, Variables, and Data Visualization

1. Statistics: Classes and Basic Concepts

Statistics is the science that deals with data collection, organization, and analysis, as well as the predictions that can be made from it.

Descriptive Statistics

Descriptive statistics is concerned with collecting data from a set, organizing it into tables, and calculating numerical summaries that comprehensively describe the studied whole.

Inferential Statistics

Inferential statistics aims to draw conclusions about a population based on the results of a sample and the reliability of these findings.

2. Statistical Variables and Characteristics

Qualitative variables or characteristics are those that cannot be measured and are described in words.

Quantitative variables or characteristics are those that can be measured and expressed with numbers.

Discrete Quantitative Variables

Discrete quantitative variables or characteristics are those that can take only a finite number of numerical values.

Continuous Quantitative Variables

Continuous quantitative variables or characteristics are those that can take any value within a given range.

3. Statistical Tables: Counting Data

Statistical counting is performed as follows:

1. The qualities or values that the statistical variable can take are ordered and placed in the first column of the table.
2. For every occurrence of a data point corresponding to a quality or value, a segment is plotted.
3. In the total column, the total number of segments is recorded.

In the case of continuous or discrete quantitative variables with many values, the data should be grouped into classes or intervals. The average value of each class or interval is called the class mark and is calculated as half the sum of the ends of the interval.

4. Statistical Tables: Frequencies

Absolute Frequency

Absolute frequency, F_i, for a quality or value X_i of the statistical variable, is the number of occurrences of that quality or value. (N)

Relative Frequency or Proportion

Relative frequency or proportion, H_i, for a quality or value X_i, is the quotient obtained by dividing the absolute frequency by the total number, N, of individuals.

Frequency Percentage or Percentage

Frequency percentage or percentage, P_i, for a quality or value X_i, is the percentage that represents the value or quality of the total. It is calculated by multiplying the relative frequency by 100.

Cumulative Frequency

• Cumulative Absolute Frequency

  Cumulative absolute frequency, F_i, for a value x_i, is the sum of all absolute frequencies corresponding to the previous values of x_i and its own.

• Cumulative Relative Frequency

  Cumulative relative frequency, H_i, for a value x_i, is the sum of all relative frequencies for the previous values of x_i and its own.

• Cumulative Percentage Frequency

  Cumulative percentage frequency, P_i, for a value x_i, is the sum of the percentage frequencies that correspond to previous values of X_i and its own.

Stem-and-Leaf Diagram

A stem-and-leaf diagram is a procedure that allows for the semi-graphical representation of information for quantitative variables, especially useful when the number of data points is small.

Common Types of Statistical Charts

• Bar Chart
• Pie Chart
• Pictograms
• Cartograms
• Column Chart
• Frequency Chart
• Histograms