Statistical Concepts and Probability Fundamentals

Statistical Characteristics and Variables

A statistical character is a property that enables the classification of individuals in a population. These can be:

• Quantitative: When they are measurable.
• Qualitative: If they are not measurable.

Statistical variables represent the different values a quantitative variable can take. They are classified as:

• Discrete: When they take specific, isolated values.
• Continuous: When they can take any value within a range.

Data Frequency Analysis

Frequency data provides essential information:

• Absolute frequency: The number of times a value repeats.
• Relative frequency: The ratio between the frequency of a value and the total number of data points.
• Cumulative absolute frequency: The sum of the absolute frequency of a value and all preceding values.

The midpoints of each class are called class marks.

Statistical Visualization

• Pie Chart: A circle divided into sectors with areas proportional to the absolute frequency of the data.
• Bar Chart: A graph where the height of each bar corresponds to the absolute frequency of the data.
• Histogram: To construct one, mark the class intervals on the abscissa (x-axis) and draw rectangles with heights proportional to the absolute frequencies.

Measures of Central Tendency

• Arithmetic Mean: The sum of all data divided by the total number of values. To calculate: multiply each data point by its absolute frequency, sum them, and divide by the total count.
• Mode: The value that occurs with the highest frequency. For grouped data, the modal class is the most frequent class, represented by its class mark.
• Median: The middle value in an ordered set. If the number of data points is odd, it is the central value. If even, it is the mean of the two central values.

Probability Fundamentals

A random experiment is one where the outcome cannot be predicted. The set of all possible outcomes is the sample space, and any subset of this space is an event.

• Impossible event: Never occurs.
• Sure event: Always occurs.
• Incompatible events: Cannot occur at the same time.
• Contrary events: Cannot occur simultaneously.