Problem 4 - Algebra Form and Function

Question

Find the mean of the data set. $$ -5,-2,0,5,2 $$

Step-by-Step Solution

Answer

Answer: The mean of the given data set is 0.

Step 1: Write the given data set

The data set is given as: $$ -5, -2, 0, 5, 2 $$

Step 2: Find the total number of values in the data set

We have a total of 5 values in the data set.

Step 3: Calculate the sum of the data set

Add all the values in the data set together: $$ (-5) + (-2) + 0 + 5 + 2 $$

Step 4: Simplify the sum

Combine the numbers to get the sum: $$ -5 - 2 + 5 + 2 = 0 $$

Step 5: Divide the sum by the total number of values

Now, divide the sum of the data set (0) by the total number of values (5) to find the mean: $$ \frac{0}{5} $$

Step 6: Simplify the result

The final result, when simplified, is: $$ \frac{0}{5} = 0 $$ The mean of the given data set is 0.

Key Concepts

Understanding a Data Set

A data set is simply a collection of numbers, which in this exercise happens to be

• -5
• -2
• 0
• 5
• 2

Each number in this collection is called a data point.
Together, they form the full data set that we are working with.
Data sets can vary in size and complexity, sometimes containing just a few numbers or even thousands.
But in every case, the process of analyzing or summarizing the data can start by understanding what constitutes the entirety of the data set. Data sets are crucial because they contain the raw information that we need to make informed conclusions.
This might involve calculating the central tendency, such as the mean (or average), which is a powerful indicator of the overall trend of the data.
By grasping what a data set is, you can begin effectively working with statistics.

Calculating the Sum of Values

The sum of values in a data set is an essential step in many statistical analyses, including calculating the mean.
To find the sum, each number in the data set is added together, which involves combining both positive and negative numbers.
Here, our values are

• -5
• -2
• 0
• 5
• 2

When these numbers are added, you start by pairing numbers that cancel each other out:

• -5 and 5 give 0
• -2 and 2 also give 0

The remaining value is 0, leading to a total sum of 0.
Understanding how to find the sum of a data set allows us to move on to the final step: calculating the mean.

Finding the Average (Mean)

The average, often referred to as the mean, is a measure of central tendency.
It tells us what we might consider as a typical value in a data set.
To calculate the mean, the sum of all the values in the data set is divided by the number of values.
In the given exercise, the total sum is 0, as calculated, and there are five numbers in the set.
We then compute the mean using the formula:\[\text{Mean} = \frac{\text{Sum of values}}{\text{Total number of values}}\]\[\text{Mean} = \frac{0}{5} = 0\]
This result tells us that the average or mean of this data set is 0.
Calculating the mean can help you quickly grasp what a typical or expected value in a data set is.
It's crucial in statistics because it provides insight into the overall behavior of the data.