What is the mode of the observation 5, 7, 8, 5, 7, 6, 9, 5, 10, 6

Answer

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

### Step-by-Step Solution:

1. **List the Observations**:
The given observations are: 5, 7, 8, 5, 7, 6, 9, 5, 10, 6.

2. **Count the Frequency of Each Observation**:
- Count how many times each number appears in the list:
- **5** appears **3 times** (1, 2, 3)
- **7** appears **2 times** (1, 2)
- **8** appears **1 time**
- **6** appears **2 times** (1, 2)
- **9** appears **1 time**
- **10** appears **1 time**

3. **Identify the Highest Frequency**:
- From the counts:
- 5: 3 times
- 7: 2 times
- 8: 1 time
- 6: 2 times
- 9: 1 time
- 10: 1 time
- The highest frequency is **3**, which corresponds to the number **5**.

4. **Conclude the Mode**:
- Since 5 appears most frequently (3 times), the mode of the given observations is **5**.

### Final Answer:
The mode of the observations is **5**.

---