Find the mode of the each of the following data collection.
5, 2, 7, 3, 5, 2, 9, 12, 13, 15, 2, 7, 3,5,7,6

Answer

To find the mode of the given data collection, we will follow these steps:

### Step-by-Step Solution:

1. **List the Data**: The given data collection is:
\[ 5, 2, 7, 3, 5, 2, 9, 12, 13, 15, 2, 7, 3, 5, 7, 6 \]

2. **Arrange the Data in Ascending Order**: We will sort the data from the smallest to the largest:
\[ 2, 2, 2, 3, 3, 5, 5, 5, 5, 6, 7, 7, 7, 9, 12, 13, 15 \]

3. **Count the Frequency of Each Number**: We will count how many times each number appears in the sorted list:
- 2 appears **3 times**
- 3 appears **2 times**
- 5 appears **4 times**
- 6 appears **1 time**
- 7 appears **3 times**
- 9 appears **1 time**
- 12 appears **1 time**
- 13 appears **1 time**
- 15 appears **1 time**

4. **Create a Frequency Table**: We can summarize the frequency of each number in a table format:
\[ \begin{array}{|c|c|} \hline \text{Data} & \text{Frequency} \\ \hline 2 & 3 \\ 3 & 2 \\ 5 & 4 \\ 6 & 1 \\ 7 & 3 \\ 9 & 1 \\ 12 & 1 \\ 13 & 1 \\ 15 & 1 \\ \hline \end{array} \]

5. **Identify the Mode**: The mode is the number(s) that appear most frequently. From our frequency table:
- The highest frequency is **4**, which corresponds to the number **5**.

6. **Conclusion**: Therefore, the mode of the given data collection is:
\[ \text{Mode} = 5 \]