Mean of median, mode and range of the data
1, 2, 3, 3, 2, 5, 6, 2, 2, 1, 4, 6, 6,5 is

Options

A. `7//3`
B. `10//3`
C. `11//3`
D. `5//3`

Answer

To find the mean of the median, mode, and range of the given data set, we will follow these steps:

### Step 1: Organize the Data
First, we need to arrange the data in ascending order. The given data is:
1, 2, 3, 3, 2, 5, 6, 2, 2, 1, 4, 6, 6, 5

Arranging this in ascending order gives us:
1, 1, 2, 2, 2, 2, 3, 3, 4, 5, 5, 6, 6, 6

### Step 2: Calculate the Median
To find the median, we need to determine the middle value of the ordered data. Since there are 14 numbers (an even count), we will take the average of the 7th and 8th values.

- The 7th term is 3.
- The 8th term is also 3.

Now, we calculate the median:
\[ \text{Median} = \frac{\text{7th term} + \text{8th term}}{2} = \frac{3 + 3}{2} = \frac{6}{2} = 3 \]

### Step 3: Calculate the Mode
The mode is the number that appears most frequently in the data set.

From the ordered data:
- The number 2 appears 4 times.
- The number 3 appears 2 times.
- The number 5 appears 2 times.
- The number 6 appears 3 times.

Thus, the mode is:
\[ \text{Mode} = 2 \]

### Step 4: Calculate the Range
The range is calculated by subtracting the smallest value from the largest value in the data set.

- The highest value is 6.
- The lowest value is 1.

Now, we calculate the range:
\[ \text{Range} = \text{Highest value} - \text{Lowest value} = 6 - 1 = 5 \]

### Step 5: Calculate the Mean of Median, Mode, and Range
Now that we have the median, mode, and range, we can find their mean.

- Median = 3
- Mode = 2
- Range = 5

Now, we calculate the mean:
\[ \text{Mean} = \frac{\text{Median} + \text{Mode} + \text{Range}}{3} = \frac{3 + 2 + 5}{3} = \frac{10}{3} \]

### Final Answer
The mean of the median, mode, and range of the data is:
\[ \frac{10}{3} \]

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