Problem 2 - Algebra Form and Function

Question

Find the mean of the data set. $$ 2,4,6,8,100 $$

Step-by-Step Solution

Answer

Answer: The mean of the given data set is 24.

Step 1: Identify the values in the data set

The values in the data set are: 2, 4, 6, 8, and 100.

Step 2: Calculate the sum of the values

To find the sum, add all the values together: $$ 2 + 4 + 6 + 8 + 100 = 120 $$

Step 3: Divide the sum by the number of values

Since there are 5 values in the data set, divide the sum by 5 to find the mean: $$ \frac{120}{5} = 24 $$ The mean of the given data set is 24.

Key Concepts

Data Set

In mathematics, a data set is a collection of numbers or values that are usually related in some way. In the example given, the data set consists of the numbers 2, 4, 6, 8, and 100. Each of these numbers is an element or a member of the data set. Data sets can vary in size, meaning they can have just a few numbers or many more. Identifying the elements in the data set is the first step towards calculating important measures like the mean.

Sum of Values

To find the sum of values in a data set, you simply add each number together. In our data set, the numbers 2, 4, 6, 8, and 100 need to be added.

• Adding 2, 4, 6, and 8 gives us 20.
• Then, add 100 to 20, resulting in a total sum of 120.

Calculating the sum of values is a crucial step when computing the mean because it provides us with a single number that represents the total of all data points. This sum is essential for the next step: division.

Division

After finding the sum of the values, the next operation is division. This step involves dividing the total sum by the count of values within the data set. In our set, there are five numbers altogether:

• The total sum is 120.
• We have 5 numbers in the data set.

So, divide 120 by 5, which gives 24. Division transforms the combined sum to its mean value by distributing it evenly across all elements in the set. This shows the central value or "average" of the set.

Arithmetic Mean

The term "mean" typically refers to the arithmetic mean. It is a way of finding the central average value in a data set. It reflects what is typically the "average" value among the numbers. The arithmetic mean is calculated by dividing the sum of all data points by the number of points. Here, with our calculated sum of 120 and 5 data points, dividing these gives a mean of 24.
The arithmetic mean is one of many ways to represent data, but it is widely used due to its simplicity and ease of calculation. It provides insight into the overall "level" of a set of values and is often the first measure considered when analyzing a data set.