To identify the mode in the given set of data, we need to follow a few key steps. Let's break the process down step-by-step for clarity.
The data set provided is:
[tex]\[ 8, 4, 10, 8, 7, 4, 8, 9 \][/tex]
### Step 1: Tally the Frequency of Each Number
First, we need to determine how many times each number appears in the data set. Below is the frequency of each number:
- The number 8 appears 3 times.
- The number 4 appears 2 times.
- The number 10 appears 1 time.
- The number 7 appears 1 time.
- The number 9 appears 1 time.
### Step 2: Create a Frequency Distribution
We can represent the frequency distribution as follows:
[tex]\[
\begin{array}{c|c}
\text{Number} & \text{Frequency} \\
\hline
8 & 3 \\
4 & 2 \\
10 & 1 \\
7 & 1 \\
9 & 1 \\
\end{array}
\][/tex]
### Step 3: Determine the Mode
The mode is the number that appears most frequently in the data set. From our frequency distribution:
- The number 8 has the highest frequency, which is 3.
Therefore, the mode of the data set [tex]\(\{8, 4, 10, 8, 7, 4, 8, 9\}\)[/tex] is:
[tex]\[ \boxed{8} \][/tex]
