Define 'algorithm'.

An algorithm is defined as a step-by-step problem-solving procedure that provides a set of instructions to achieve a specific goal or solve a particular problem. It is a systematic method that outlines how to reach a solution by breaking down the process into smaller, manageable parts. This structured approach can be applied in various fields, including mathematics, computer science, and daily decision-making.

The importance of algorithms lies in their ability to provide clear directives that can be followed to obtain a desired result, making them essential for programming and software development. In coding, for instance, algorithms serve as the foundational blueprint guiding the logic and structure of programs.

In contrast, other concepts do not accurately encompass the definition of an algorithm. A random guessing method does not involve a structured approach or guarantee a logical outcome. A formula for data analysis pertains to a specific mathematical expression used to analyze data, rather than a procedure to solve problems step-by-step. Lastly, a software programming language refers to the syntax and grammar used to write code, not the methodical approach to solve problems or compute results. Thus, the choice representing an algorithm as a systematic procedure is the most accurate and relevant definition.