Problem 5 - Algebra Form and Function

Question

Find the mean of the data set. $$ 5,2,19,6,5,2 $$

Step-by-Step Solution

Answer

Answer: The mean of the data set is 6.5.

Step 1: Sum the values in the set

To find the sum, simply add all the values in the set together: $$ 5+2+19+6+5+2 = 39 $$

Step 2: Count the number of values in the set

The given data set contains 6 values, which can be confirmed by counting each of the values: 5, 2, 19, 6, 5, and 2.

Step 3: Divide the sum by the number of values

Now that we have the sum of the values (39) and the number of values (6), we can find the mean by dividing the sum by the number of values: $$ \text{Mean} = \frac{\text{Sum}}{\text{Number of values}} = \frac{39}{6} = 6.5 $$ So, the mean of the given data set is 6.5.

Key Concepts

Understanding the Data Set

A "data set" is simply a collection of numbers or values. These can represent any kind of observable data, such as test scores, temperatures, or counts. In our example, we have a data set:

• 5
• 2
• 19
• 6
• 5
• 2

This set contains six numbers. Data sets can vary in size, ranging from just a few values to thousands or even millions, depending on the context.
In data analysis, the mean is often used to find the central tendency, or average, of a data set. This helps to summarize the data with a single value that represents it well.

Calculating the Sum of Values

The "sum of values" refers to the total obtained when you add all the numbers in a data set together. This step is foundational for calculating the mean.
To calculate the sum in our example, you add each number one by one:

• Start with the first number: 5
• Add the second number: 5 + 2 = 7
• Continue adding: 7 + 19 = 26
• Add the next: 26 + 6 = 32
• Next: 32 + 5 = 37
• Finally: 37 + 2 = 39

So, the sum of the values is 39. This step ensures that you accurately compile the data, making it ready for the next steps in calculating the mean.

Identifying the Number of Values

The "number of values" simply refers to how many individual numbers you have in your data set. For our example data set 5, 2, 19, 6, 5, and 2, the number of values is 6.
This count is crucial because, when calculating the mean, you divide the sum of the values by this number. Dividing the sum by the count gives a sense of each number's contribution to the total.
To ensure accuracy, always double-check the number of values by counting them one by one, particularly in larger data sets. This practice helps to avoid small mistakes that could lead to incorrect results in the mean calculation.