Question

Find the mean of each pair of numbers. 5 and \(-6\)

Short answer

The mean of 5 and -6 is -0.5.

Step-by-step solution

Understand the Mean

The mean (also known as the average) of a set of numbers is found by adding the numbers together and then dividing by the count of the numbers.

Sum the Numbers

Add the two numbers together: \[ 5 + (-6) = 5 - 6 = -1 \]

Count the Numbers

Determine how many numbers are being averaged. In this case, there are two numbers: 5 and -6.

Divide the Sum by the Number of Values

Divide the sum of the numbers by the count of the numbers:\[ \text{Mean} = \frac{-1}{2} = -0.5 \]

Key concepts

Mean

The mean is a common mathematical concept used to find the central point of a set of numbers. It is often used to provide a single value that represents the entire collection. To calculate the mean, you follow a simple process: add all the numbers in the set together to find the sum, and then divide this sum by the total number of values you have. This gives you the mean, which can also be called the average.

• Add up all the numbers in the list.
• Count how many numbers are in the list.
• Divide the total sum by this count.

For example, with the numbers 5 and -6, the sum is -1 after adding them. Since there are two numbers, you divide -1 by 2, resulting in a mean of -0.5. This approach helps to simplify the dataset by giving a single value that sums up the overall tendency of the numbers.

Average

The term 'average' is frequently used interchangeably with 'mean,' but it is important to recognize that there are different types of averages in mathematics. The most common type, and the one often referred to as the mean, is what people usually mean when they mention average without specifying further.

• The arithmetic mean (or simply mean) is calculated by adding all the values and dividing by their count.
• The median is another type of average that involves finding the middle number in a set when it is ordered from least to greatest.
• The mode is the number that appears most frequently in a set of numbers.

In everyday situations, people most often calculate the arithmetic mean when asked to find the average of a set of numbers, like in our exercise here with 5 and -6, resulting in an average of -0.5.

Negative Numbers

Negative numbers are an essential part of the number system. They are numbers less than zero and are used to represent values below a defined point, often in the context of temperatures, debt, or elevation below sea level. Working with negative numbers follows the same basic principles as positive numbers with a few additional rules.

• When adding a negative number, it is like subtracting the absolute value of that number.
• Subtracting a negative number is equivalent to adding its absolute value.
• Negative multiplied by a negative gives a positive.
• Negative multiplied by a positive results in a negative.

In our example, when you add 5 and -6, it's like saying you have 5 and you take away 6. The outcome is -1, which illustrates how negative numbers can affect the overall result when calculating means or performing other arithmetic operations.