Find the mode of the observations 12, 8, 4, 8, 1, 8, 9, 11, 9, 10, 12, 8.

Answer

To find the mode of the observations 12, 8, 4, 8, 1, 8, 9, 11, 9, 10, 12, 8, we will follow these steps:

### Step 1: List the Observations
Write down all the observations clearly.
- Observations: 12, 8, 4, 8, 1, 8, 9, 11, 9, 10, 12, 8

### Step 2: Identify Unique Values
Identify the unique values from the observations.
- Unique Values: 1, 4, 8, 9, 10, 11, 12

### Step 3: Count the Frequency of Each Value
Count how many times each unique value appears in the list.
- 1 appears 1 time
- 4 appears 1 time
- 8 appears 4 times
- 9 appears 2 times
- 10 appears 1 time
- 11 appears 1 time
- 12 appears 2 times

### Step 4: Determine the Maximum Frequency
Identify which value has the highest frequency.
- The frequencies are:
- 1 (1 time)
- 4 (1 time)
- 8 (4 times)
- 9 (2 times)
- 10 (1 time)
- 11 (1 time)
- 12 (2 times)

The maximum frequency is 4, which corresponds to the value 8.

### Step 5: State the Mode
The mode is the value that appears most frequently in the observations.
- Therefore, the mode is **8**.

### Summary:
The mode of the observations 12, 8, 4, 8, 1, 8, 9, 11, 9, 10, 12, 8 is **8**.

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