If the median of 59, 62, 65, x, x + 2, 72, 85 and 94 is 69, then the value of x is

Options

A. 68
B. 67
C. None of these
D. 69

Answer

To find the value of \( x \) such that the median of the numbers \( 59, 62, 65, x, x + 2, 72, 85, \) and \( 94 \) is \( 69 \), we can follow these steps:

### Step 1: List the numbers in ascending order
The numbers given are \( 59, 62, 65, x, x + 2, 72, 85, 94 \). We need to arrange them in ascending order.

### Step 2: Determine the total number of values
There are a total of 8 values in the list.

### Step 3: Find the median formula for an even number of values
Since there are 8 values (an even number), the median is calculated as the average of the 4th and 5th values in the ordered list.

### Step 4: Identify the 4th and 5th values
The 4th value is \( x \) and the 5th value is \( x + 2 \).

### Step 5: Set up the median equation
We know that the median is given as \( 69 \). Therefore, we can set up the equation:
\[ \text{Median} = \frac{\text{4th value} + \text{5th value}}{2} = \frac{x + (x + 2)}{2} = \frac{2x + 2}{2} \]
This simplifies to:
\[ x + 1 \]

### Step 6: Set the median equal to 69
Now we set the equation from Step 5 equal to \( 69 \):
\[ x + 1 = 69 \]

### Step 7: Solve for \( x \)
To find \( x \), we subtract \( 1 \) from both sides:
\[ x = 69 - 1 = 68 \]

### Conclusion
Thus, the value of \( x \) is \( 68 \).