Geometric Mean. The geometric mean of a set of numbers x1...

Geometric Mean. The geometric mean of a set of numbers $x_{1}$ through $x_{n}$ is defined as the $n$th root of the product of the numbers $$ \text { geometric mean }=\sqrt[4]{x_{1} x_{2} x_{3} \ldots x_{n}} $$ Write a MATLAB program that will accept an arbitrary number of positive input values and calculate both the arithmetic mean (i.e., the average) and the geometric mean of the numbers. Use a while loop to get the input values and terminate the inputs when a user enters a negative number. Test your program by calculating the average and geometric mean of the four numbers $10,5,2$, and 5 .

Geometric Mean. The geometric mean of a set of numbers $x_{1}$ through $x_{n}$ is defined as the $n$th root of the product of the numbers
$$
\text { geometric mean }=\sqrt[4]{x_{1} x_{2} x_{3} \ldots x_{n}}
$$
Write a MATLAB program that will accept an arbitrary number of positive input values and calculate both the arithmetic mean (i.e., the average) and the geometric mean of the numbers. Use a while loop to get the input values and terminate the inputs when a user enters a negative number. Test your program by calculating the average and geometric mean of the four numbers $10,5,2$, and 5 .

Key Concepts

Iterative Input Collection

Iterative input collection involves using a loop (such as a while loop) to continuously accept user input until a specific termination condition is met—in this case, entering a negative number. This concept is essential for handling an arbitrary number of inputs dynamically and is widely used in programming for processing data until a stop condition occurs.

Geometric Mean

The geometric mean is a measure of central tendency that is calculated as the nth root of the product of n numbers. It is especially useful in datasets that are multiplicative in nature or when dealing with rates of change, as it gives a representative average value that minimizes the impact of very high or very low values.

Arithmetic Mean

The arithmetic mean is the sum of a set of numbers divided by the count of numbers, which serves as one of the most common measures of central tendency in statistics. It provides a simple average, useful for understanding the overall level of a dataset when all values are considered equally.

MATLAB Programming Constructs

MATLAB programming constructs such as while loops, input prompts, and condition testing are fundamental for automating tasks and performing iterative computations. In this context, a while loop facilitates the repeated collection of user inputs, while conditional statements handle the exit condition, allowing for flexible and robust data processing.

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