Problem 6 - Basic College Mathematics

Question

For each set of numbers, find the minimum, the maximum, and the range. $$ 8,3,8,7,3,3,6 $$

Step-by-Step Solution

Answer

The minimum value is 3, the maximum value is 8, and the range is 5.

Step 1: Identify and write down the numbers

List all the numbers given in the set: \( 8, 3, 8, 7, 3, 3, 6 \)

Step 2: Find the minimum value

The minimum value is the smallest number in the set. Identify the smallest number: \( 3 \)

Step 3: Find the maximum value

The maximum value is the largest number in the set. Identify the largest number: \( 8 \)

Step 4: Calculate the range

Subtract the minimum value from the maximum value to find the range. Using the formula: \[ \text{Range} = \text{Maximum} - \text{Minimum} \] So, \( \text{Range} = 8 - 3 = 5 \)

Key Concepts

Minimum Value

In mathematics, the minimum value of a set of numbers is the smallest number within that set. To find the minimum value, you need to compare all the numbers in the dataset and identify the one that is the lowest.

For example, in the set of numbers \(8, 3, 8, 7, 3, 3, 6\), the minimum value is the number that is smallest compared to all others. Here’s how to identify it:

• Look at each number and compare them systematically.
• Starting from the first number: 8 is compared to 3 and 3 is smaller.
• Continue comparing 3 with the next number 8.
• 3 remains smaller when compared to 7, 3 (again), and 6.
• Thus, 3 is the minimum value in this set.

So, by following this method, you can determine that the minimum value in the provided set is \(3\).

Maximum Value

The maximum value in a set of numbers is the largest number within that set. To find the maximum value, you need to identify the number that is greater than all other numbers in the set.

Let’s look at how to find the maximum value in the set \(8, 3, 8, 7, 3, 3, 6\):

• Begin by comparing the first number, 8, with the next number in the set.
• 8 remains the largest compared to 3.
• Compare it with the next numbers: 8, 7, 3, 3, and 6.
• No number in the set is larger than 8.
• Thus, 8 is the maximum value in this set.

By systematically comparing each number, you find that the maximum value in the given set is \(8\).

Range Calculation

The range of a set of numbers is a measure of the spread of the numbers, calculated by finding the difference between the maximum and minimum values of the set. Understanding the range is important because it gives you an idea of the dispersion of the numbers.

To calculate the range for the set \(8, 3, 8, 7, 3, 3, 6\):

• First, determine the maximum value, which we found to be 8.
• Then, find the minimum value, which is 3.
• Use the range formula: \[ \text{Range} = \text{Maximum} - \text{Minimum} \]
• Substitute the values: \[ \text{Range} = 8 - 3 = 5 \]

So, the range of the set is \(5\). This tells us that there is a difference of 5 units between the smallest and largest numbers in the set.