If the arithmetic mean of 6,8,5,7,p and 4 is 7 then the value of p

Options

A. 10
B. 12
C. 15
D. 20

Answer

To find the value of \( p \) given that the arithmetic mean of the numbers 6, 8, 5, 7, \( p \), and 4 is 7, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the formula for Arithmetic Mean (AM)**:
The arithmetic mean of a set of numbers is calculated by dividing the sum of the numbers by the total count of the numbers.

\[ \text{AM} = \frac{\text{Sum of all values}}{\text{Number of values}} \]

2. **Set up the equation**:
In this case, the numbers are 6, 8, 5, 7, \( p \), and 4. The total count of these numbers is 6. According to the problem, the arithmetic mean is 7.

\[ \frac{6 + 8 + 5 + 7 + p + 4}{6} = 7 \]

3. **Calculate the sum of the known numbers**:
First, we will calculate the sum of the known numbers:

\[ 6 + 8 + 5 + 7 + 4 = 30 \]

4. **Substitute the sum into the equation**:
Now, substitute the sum back into the equation:

\[ \frac{30 + p}{6} = 7 \]

5. **Multiply both sides by 6 to eliminate the fraction**:
To solve for \( p \), multiply both sides by 6:

\[ 30 + p = 42 \]

6. **Isolate \( p \)**:
Now, subtract 30 from both sides to find \( p \):

\[ p = 42 - 30 \]

\[ p = 12 \]

### Final Answer:
The value of \( p \) is \( 12 \).

---