Problem 2 - Basic College Mathematics

Question

For each set of numbers, find the minimum, the maximum, and the range. $$ 1,6,15,97 $$

Step-by-Step Solution

Answer

The minimum is 1, the maximum is 97, and the range is 96.

Step 1 - List the Numbers

First, write down all the numbers given in the set: 1, 6, 15, 97.

Step 2 - Find the Minimum

To find the minimum, look for the smallest number in the set. The smallest number in this set is 1.

Step 3 - Find the Maximum

To find the maximum, look for the largest number in the set. The largest number in this set is 97.

Step 4 - Calculate the Range

The range is calculated by subtracting the minimum value from the maximum value. Therefore, the range is given by 97 - 1 = 96.

Key Concepts

Minimum

In any set of numbers, the minimum is the smallest value. To find it, simply compare all the numbers in the set and identify the one with the lowest value. For example, in the set \(1, 6, 15, 97\), the minimum is 1. This concept is crucial because it helps in understanding the lower bound of data in a dataset. Minimum values often serve as a reference point in various statistical calculations and analysis.

Maximum

The maximum in a set of numbers is the largest value. Finding it involves comparing all the numbers and identifying the highest one. In our example set \(1, 6, 15, 97\), the maximum is 97. Knowing the maximum is important for understanding the upper limit of a dataset. It can also influence decisions and analyses, providing key insights into the extent and scale of the numbers involved.

Set of Numbers

A set of numbers is simply a collection of distinct values. Sets can be finite or infinite, but in most practical scenarios like the given problem, we deal with finite sets. For instance, our set contains four numbers: \(1, 6, 15, 97\). Sets are fundamental in mathematics because they help organize and analyze numbers, and they underpin many mathematical concepts and operations. Within sets, you can identify other properties like mean, median, mode, and range.

Basic Arithmetic

Basic arithmetic refers to simple mathematical operations including addition, subtraction, multiplication, and division. In this problem, we primarily deal with subtraction. When calculating the range, you subtract the minimum value from the maximum value. Here, the range is calculated as follows: \(97 - 1 = 96\). Understanding basic arithmetic is essential because it is the foundation for more complex mathematical concepts and operations. It allows us to perform calculations that can lead to insightful data analysis and problem-solving.