Problem 1 - Basic College Mathematics

Question

For each set of numbers, find the minimum, the maximum, and the range. $$ 3,7,10,16,25,38 $$

Step-by-Step Solution

Answer

Minimum: 3, Maximum: 38, Range: 35

Step 1 - Identify the Numbers

First, list out all the numbers provided in the set: 3, 7, 10, 16, 25, and 38.

Step 2 - Find the Minimum Value

The minimum value is the smallest number in the set. Look through the list and identify the smallest number: 3.

Step 3 - Find the Maximum Value

The maximum value is the largest number in the set. Examine the list and find the largest number: 38.

Step 4 - Calculate the Range

The range of the set is found by subtracting the minimum value from the maximum value. \( \text{Range} = \text{Maximum} - \text{Minimum} \ \text{Range} = 38 - 3 = 35 \)

Key Concepts

minimum value

In mathematics, the minimum value of a set of numbers is the smallest number in that set. To find it, you look through the list of numbers and identify the one that is the least. For example, in the set \(3, 7, 10, 16, 25, 38\), the smallest number is 3. Therefore, the minimum value is 3. It's important to understand this concept because it helps us to determine the range and analyze the data set effectively.

maximum value

The maximum value is the largest number in a set of numbers. You determine this by scanning through your list of numbers and picking the highest one. In our example set \(3, 7, 10, 16, 25, 38\), the largest number is 38, so the maximum value is 38. Knowing the maximum value, like the minimum, is a basic aspect of analyzing number sets. It helps to provide insight into the spread and range of the data.

range calculation

The range is a measure of how spread out the numbers in a set are. It is calculated by subtracting the minimum value from the maximum value. This gives you an idea of the distance between the smallest and largest numbers. Using our set \(3, 7, 10, 16, 25, 38\), the minimum value is 3, and the maximum value is 38. So, the range is \[38 - 3 = 35\]. This simple calculation helps to quickly understand the variability in the dataset.

step-by-step solution

Here is a more detailed look at the step-by-step solution:

Step 1 - Identify the Numbers: List all numbers given: 3, 7, 10, 16, 25, 38.

Step 2 - Find the Minimum Value: Look for the smallest number in the list. Here, it's 3.

Step 3 - Find the Maximum Value: Look for the largest number in the list. In this set, it's 38.

Step 4 - Calculate the Range: Subtract the minimum value from the maximum value. So, \[38 - 3 = 35\]. This clear sequence helps ensure an ordered and accurate approach to finding the minimum, maximum, and range.

basic arithmetic

Basic arithmetic forms the foundation of finding minimum, maximum, and range. It involves simple operations like:

• Addition: Combining numbers.
• Subtraction: Finding the difference between numbers.

In our case, subtraction is key. By subtracting one number from another, we can find the range. For example, we subtract 3 (minimum) from 38 (maximum) to get 35. Understanding these simple arithmetic operations is crucial to solving a wide range of mathematical problems efficiently.