For the data given below, find the sum of mode, median and mean.
6, 3, 8, 4, 3 11 7, 4,5, 4.

Options

A. 13.5
B. 13
C. 14
D. 14.5

Answer

To solve the problem, we need to find the sum of the mode, median, and mean for the given data set: 6, 3, 8, 4, 3, 11, 7, 4, 5, 4.

### Step 1: Arrange the data in ascending order
First, we will arrange the data in ascending order:
- The original data: 6, 3, 8, 4, 3, 11, 7, 4, 5, 4
- Arranged in ascending order: 3, 3, 4, 4, 4, 5, 6, 7, 8, 11

### Step 2: Calculate the Mean
The mean is calculated using the formula:
\[ \text{Mean} = \frac{\text{Sum of all terms}}{\text{Number of terms}} \]
- Sum of the terms: \(3 + 3 + 4 + 4 + 4 + 5 + 6 + 7 + 8 + 11 = 55\)
- Number of terms: 10

Now, we can calculate the mean:
\[ \text{Mean} = \frac{55}{10} = 5.5 \]

### Step 3: Calculate the Median
To find the median, we need to determine the middle value(s) of the ordered data set. Since there are 10 terms (an even number), the median will be the average of the 5th and 6th terms.
- The 5th term is 4 and the 6th term is 5.

Now, we can calculate the median:
\[ \text{Median} = \frac{4 + 5}{2} = \frac{9}{2} = 4.5 \]

### Step 4: Calculate the Mode
The mode is the number that appears most frequently in the data set.
- In our ordered data: 3 appears 2 times, 4 appears 3 times, and all other numbers appear less frequently.
- Therefore, the mode is 4 (as it appears the most).

### Step 5: Calculate the Sum of Mode, Median, and Mean
Now, we will add the mode, median, and mean together:
\[ \text{Sum} = \text{Mean} + \text{Median} + \text{Mode} = 5.5 + 4.5 + 4 = 14 \]

### Final Answer
The sum of mode, median, and mean is **14**.

---