Determine the mode for the following observations : 10,11,10,12,11,10,11,11,11,12,13,11,12.

Answer

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

### Step 1: Write down the observations
The observations given are:
10, 11, 10, 12, 11, 10, 11, 11, 11, 12, 13, 11, 12.

### Step 2: Arrange the observations in ascending order
We will arrange the observations from the smallest to the largest:
10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 13.

### Step 3: Count the frequency of each observation
Now we will count how many times each number appears in the ordered list:
- 10 appears **3 times**.
- 11 appears **6 times**.
- 12 appears **3 times**.
- 13 appears **1 time**.

### Step 4: Identify the mode
The mode is the number that appears most frequently in the dataset. From our counts:
- 10: 3 times
- 11: 6 times
- 12: 3 times
- 13: 1 time

Since 11 appears the most frequently (6 times), we conclude that the mode is:
**Mode = 11**

### Final Answer
The mode of the given observations is **11**.

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