The sum of mean, mode and median of the data 6, 3, 9, 5, 1, 2, 3, 6, 5, 1, 3 is

Options

A. 12
B. 13
C. 10
D. 11

Answer

To find the sum of the mean, mode, and median of the given data set \(6, 3, 9, 5, 1, 2, 3, 6, 5, 1, 3\), we will follow these steps:

### Step 1: Organize the Data
First, we need to arrange the data in ascending order.

**Data in ascending order:**
1, 1, 2, 3, 3, 3, 5, 5, 6, 6, 9

### Step 2: Calculate the Mean
The mean is calculated by taking the sum of all the values and dividing it by the number of values.

**Sum of the data:**
\[ 1 + 1 + 2 + 3 + 3 + 3 + 5 + 5 + 6 + 6 + 9 = 44 \]

**Number of terms:**
There are 11 terms in the data.

**Mean calculation:**
\[ \text{Mean} = \frac{\text{Sum of data}}{\text{Number of terms}} = \frac{44}{11} = 4 \]

### Step 3: Calculate the Median
To find the median, we need to identify the middle value in the ordered data set. Since there are 11 terms (an odd number), the median is the value at position \((n + 1)/2\).

**Position of the median:**
\[ \text{Median position} = \frac{11 + 1}{2} = 6 \]

**Median value:**
The 6th value in the ordered list is 3.

### Step 4: Calculate the Mode
The mode is the value that appears most frequently in the data set.

**Frequency of values:**
- 1 appears 2 times
- 2 appears 1 time
- 3 appears 3 times
- 5 appears 2 times
- 6 appears 2 times
- 9 appears 1 time

**Mode:**
The most frequently occurring value is 3.

### Step 5: Sum of Mean, Mode, and Median
Now we can sum the mean, mode, and median.

**Sum calculation:**
\[ \text{Sum} = \text{Mean} + \text{Median} + \text{Mode} = 4 + 3 + 3 = 10 \]

### Final Answer
The sum of the mean, mode, and median of the data is **10**.

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