Problem 3 - Basic College Mathematics

Question

For each set of numbers, find the minimum, the maximum, and the range. $$ 12,16,38,112,5 $$

Step-by-Step Solution

Answer

Minimum: 5, Maximum: 112, Range: 107

Step 1: Identify the Numbers

List out all the numbers given in the set: 12, 16, 38, 112, 5.

Step 2: Find the Minimum Value

Look for the smallest number in the set. From the list 12, 16, 38, 112, 5, the minimum value is 5.

Step 3: Find the Maximum Value

Look for the largest number in the set. From the list 12, 16, 38, 112, 5, the maximum value is 112.

Step 4: Calculate the Range

Subtract the minimum value from the maximum value to determine the range. The range is calculated as: \[ \text{{Range}} = \text{{Maximum}} - \text{{Minimum}} \]Substitute the values: \[ \text{{Range}} = 112 - 5 = 107 \]

Key Concepts

minimum value

In any set of numbers, the minimum value is the smallest number in that set. Finding the minimum value is a crucial step in various mathematical calculations, including range calculation. To identify the minimum value, you simply compare each number in the set with others.
For example, consider the numbers 12, 16, 38, 112, and 5.
When we compare these, we see that 5 is the smallest. Therefore, the minimum value in this set is 5.

• Minimum value is useful for calculations and understanding data.
• It's always a single unique number in any finite set.

maximum value

The maximum value in a set of numbers is the largest number present. Identifying the maximum value is also necessary for many mathematical problems. Just like finding the minimum, you need to compare all numbers in the set to find the maximum value.
Let's use the same example: 12, 16, 38, 112, and 5.
By comparing each number, we determine that 112 is the largest. So, the maximum value in this set is 112.

• Knowing the maximum value helps in assessing the range and other statistical measures.
• Like the minimum value, the maximum value is always a unique number in a finite set.

range calculation

The range of a set of numbers gives you an idea of how spread out the numbers are. To calculate the range, you subtract the minimum value from the maximum value.
Using our example set: 12, 16, 38, 112, and 5

First, we identified the minimum value as 5 and the maximum value as 112.

Next, we use the formula:
The calculation follows: \[\text{Range} = \text{Maximum} - \text{Minimum}\]Substitute our values: 112 (max) and 5 (min)
\[\text{Range} = 112 - 5 = 107\]

• Range gives a sense of the data spread.
• It helps in understanding the variability between values in a set.