Introduction

Understanding and calculating the mean of a set of numbers is a fundamental concept in mathematics, and it is often used in various real-world applications, including data analysis, sports statistics, and even recreational challenges like solving mysteries in golf tournaments. In this article, we will explore how to find the value of (x) when the mean of the numbers 5, 3, (x), 7, and 8 is 5. This involves a step-by-step process that can be applied to similar problems in different contexts.

What is the Mean?

The mean, also known as the arithmetic mean, is a measure of central tendency that represents the average value of a set of numbers. It is calculated by summing up all the numbers in the set and then dividing by the count of the numbers. The mean provides a useful summary of the data and is often used to understand the typical value in a dataset.

Formulating the Problem

Given Data

We have a set of numbers: 5, 3, (x), 7, and 8. We are told that the mean of these numbers is 5. Our task is to find the value of (x). We can write this in a mathematical equation as follows:

Mean Sum of values / Number of values

Setting Up the Equation

Using the given mean and the values provided, we can set up the equation as follows:

Mean (5 3 x 7 8) / 5 5

Simplifying the Sum:

First, we simplify the sum of the known numbers:

5 3 7 8 23

This simplifies our equation to:

(23 x) / 5 5

We can now solve for (x) by following these steps:

Solving for (x)

Multiply both sides of the equation by 5 to eliminate the fraction: 23 x 25 Subtract 23 from both sides to isolate (x): x 2

Therefore, the value of (x) is 2.

Verification

To ensure that our solution is correct, we can substitute (x 2) back into the original set of numbers and calculate the mean:

(5 3 2 7 8) / 5 (25) / 5 5

This confirms that our solution is indeed correct.

Real-World Applications

The concept of mean is widely used in various fields, including:

Sports Analysis: In golf, for example, understanding the mean score can help determine a player's overall performance. Financial Analysis: In finance, the mean is used to understand the average performance of an investment over time. Healthcare: In medical statistics, the mean can be used to understand the average recovery time or treatment outcomes.

By mastering the basics of calculating and understanding the mean, we can make informed decisions and draw meaningful insights from data.

Summary

In conclusion, by setting up and solving the given equation, we were able to determine the value of (x) in the set of numbers 5, 3, (x), 7, and 8, given that their mean is 5. The value of (x) is 2.