The mean of median and mode of the data 7, 6, 7, 9, 8, 8, 10, 8 is

Options

A. 8.5
B. 9
C. 5.5
D. 8

Answer

To find the mean of the median and mode of the given data set \(7, 6, 7, 9, 8, 8, 10, 8\), we will follow these steps:

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

**Data in ascending order**:
\[6, 7, 7, 8, 8, 8, 9, 10\]

### Step 2: Find the Median
To find the median, we need to determine the middle value of the ordered data. Since there are 8 values (an even number), the median will be the average of the 4th and 5th terms.

- **4th term**: 8
- **5th term**: 8

**Median Calculation**:
\[ \text{Median} = \frac{\text{4th term} + \text{5th term}}{2} = \frac{8 + 8}{2} = \frac{16}{2} = 8 \]

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

In the ordered data:
- 6 appears 1 time
- 7 appears 2 times
- 8 appears 3 times
- 9 appears 1 time
- 10 appears 1 time

The number that appears the most is 8, which appears 3 times.

**Mode**: 8

### Step 4: Calculate the Mean of Median and Mode
Now that we have both the median and mode, we can find the mean of these two values.

**Mean Calculation**:
\[ \text{Mean} = \frac{\text{Median} + \text{Mode}}{2} = \frac{8 + 8}{2} = \frac{16}{2} = 8 \]

### Final Answer
The mean of the median and mode of the data is **8**.

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