Find the sum of the mode and the median of the given data
2, 4, 3, 4, 6, 2, 5, 1, 3, 2, 1

Options

A. 6
B. 5
C. 8
D. 10

Answer

To solve the problem of finding the sum of the mode and the median of the given data set, we will follow these steps:

### Step 1: Identify the Data
The given data is:
2, 4, 3, 4, 6, 2, 5, 1, 3, 2, 1

### Step 2: Find the Mode
The mode is the number that appears most frequently in the data set.

1. **Count the frequency of each number:**
- 1 appears 2 times
- 2 appears 3 times
- 3 appears 2 times
- 4 appears 2 times
- 5 appears 1 time
- 6 appears 1 time

2. **Identify the highest frequency:**
- The number 2 has the highest frequency (3 times).

Thus, the mode is **2**.

### Step 3: Find the Median
The median is the middle value when the data is arranged in ascending order.

1. **Arrange the data in ascending order:**
- The ordered data is: 1, 1, 2, 2, 2, 3, 4, 4, 5, 6

2. **Count the number of observations:**
- There are 11 observations (which is an odd number).

3. **Find the median position:**
- The median position is given by the formula: (n + 1) / 2
- Here, n = 11, so (11 + 1) / 2 = 12 / 2 = 6.

4. **Identify the 6th observation in the ordered data:**
- The 6th observation is **3**.

Thus, the median is **3**.

### Step 4: Calculate the Sum of Mode and Median
Now, we add the mode and the median:
- Mode = 2
- Median = 3

Sum = Mode + Median = 2 + 3 = **5**.

### Final Answer
The sum of the mode and the median is **5**.

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