A probability distribution provides a comprehensive description of how probabilities are allocated among the possible values of a random variable. In statistics and probability theory, a random variable represents a numerical outcome determined by a random phenomenon. The probability distribution, therefore, serves as a mathematical model for expressing the uncertainty associated with such outcomes. Random…
Conditional probability is the probability of an event occurring, given that another event has already happened. It’s written as P(A|B), which is read as “the probability of A given B”. This means we’re considering the probability of A happening, but only within the reduced sample space where B is already known to have occurred. Formula:…
The theory of probability is a branch of mathematics that provides a numerical framework for measuring uncertainty associated with various events encountered in everyday life. It is concerned with analyzing uncertain phenomena and facilitating decision-making in the presence of unpredictability. Probability theory enables the quantification of the likelihood of different outcomes and supports informed decision-making…
IntroductionTime series analysis involves examining datasets that are collected over time to identify meaningful patterns and variations. These variations can be broadly classified into long-term and short-term components. Recognizing and analyzing these components is crucial for effective forecasting, which enables data-driven decision-making across various domains. 1. Components of Variation in Time Series Time series data…
Introduction Correlation and regression are essential statistical techniques used to examine the nature, strength, and form of the relationship between two or more variables. While correlation measures the direction and magnitude of association, regression provides an equation to predict the value of one variable based on another. Visual tools such as scatter diagrams assist in…
Introduction Measures of dispersion, also referred to as measures of variability, are statistical tools used to describe the extent to which data points in a dataset deviate from a central value. They provide insights into the distribution and consistency of data, helping to evaluate the spread of observations. Common measures of dispersion include the range,…
Mode:The mode refers to the value that appears most frequently in a given dataset. A dataset may be: Example: In the dataset {2, 3, 3, 4, 5, 5, 5, 6}, the mode is 5, as it occurs three times—more than any other value. Median and Quartiles:The median represents the middle value that divides a dataset…
Measures of central tendency, such as the arithmetic mean (AM), combined arithmetic mean, geometric mean (GM), and harmonic mean (HM) are all measures of central tendency, each used in different contexts. AM is the simple average. Combined AM calculates the average of combined datasets. GM is used for rates of change or when data is…
Skewness and kurtosis are important statistical measures that help describe the shape and characteristics of a data distribution. While skewness refers to the asymmetry of the distribution, kurtosis pertains to the “tailedness” or the peakedness of the distribution curve. Skewness Definition:Skewness quantifies the degree of asymmetry in a distribution relative to its mean. It helps…
Introduction In statistics, measures of central tendency and dispersion are essential tools used to describe and summarize the characteristics of a dataset. Measures such as the mean, median, and mode provide insights into the central location or ‘average’ value, while measures like range, variance, and standard deviation indicate the degree of spread or variability within…