Question

Find the mean of each pair of numbers. \(-2\) and 6

Short answer

The mean is 2.

Step-by-step solution

Understand the Problem

We are asked to find the mean of two numbers, -2 and 6. The mean, also known as the average, is calculated by adding the numbers together and then dividing the sum by the quantity of numbers.

Calculate the Sum of the Numbers

Add the two numbers together. Calculate \(-2 + 6\):\[-2 + 6 = 4\]

Divide the Sum by the Number of Terms

Since there are two numbers, we divide the sum by 2:\[\frac{4}{2} = 2\]

Verify the Calculation

Double-check the calculation by confirming each step was followed correctly. Sum is \(4\), and dividing by the number of terms (2) gives \(2\).

Key concepts

Understanding the Average

When we talk about the average, we're referring to a value that represents the central point of a data set. It's a measure of central tendency used to summarize a set of numbers into a single value. The purpose of finding an average is to get a general idea of the "center" of the numbers we're dealing with. It can be very useful in everyday life, such as understanding your test scores or calculating the average temperature over a period of time.

There are different types of averages, including mean, median, and mode, but the most common is the arithmetic mean. Whenever someone says "average," they often mean the arithmetic mean, unless stated otherwise. Understanding the average helps in making informed predictions and decisions based on numerical data.

What is Arithmetic Mean?

The arithmetic mean, also known simply as the mean, is the most widely used type of average. To calculate the arithmetic mean, you sum up all the numbers in your data set and then divide this sum by the count of numbers in the set.

Let's say you're given the numbers

• -2
• 6

To find their arithmetic mean, you would add these two numbers, a. -2 + 6 = 4

Then, divide the resulting sum by the number of values, which is 2 in this case:b. \[\frac{4}{2} = 2\]

So, the arithmetic mean of -2 and 6 is 2.

This calculation provides a balanced midpoint value, representing where the total sum would "balance out," if you thought of these numbers on a number line. It's a simple yet powerful tool for summarizing data.

Detailed Step-by-Step Solution

Following a step-by-step solution is crucial for grasping the concept of calculating the arithmetic mean. Let’s look at how to break down the process:

First, understand what is being asked. You need to identify the numbers whose mean you will calculate. In our example, these numbers are -2 and 6. Next, add these numbers to find their total sum.

• \(-2 + 6 = 4\)

Once the sum is calculated, divide it by the number of values you have. This number tells you how to distribute the summed value evenly across each individual number involved.

Divide the sum by 2, since there are two numbers:

• \(\frac{4}{2} = 2\)

Double-check each step to ensure accuracy. Verification helps prevent minor mistakes and ensures your final mean is correct. First, check your addition: is 4 truly what -2 and 6 add up to? Then, confirm how you divided by 2. This methodical approach helps in building confidence when working with numbers and ensures that you're using the correct procedures in all scenarios.