The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x.
29, 32, 48, 50, x, x + 2, 72, 78, 84, 95

Answer

To find the value of \( x \) in the given observations, we will follow these steps:

### Step 1: Identify the number of observations
The given observations are:
\[ 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95 \]

Counting these, we find there are 10 observations.

### Step 2: Determine the position of the median
Since there are 10 observations (an even number), the median is calculated as the average of the 5th and 6th terms.

### Step 3: Write the formula for the median
The formula for the median in this case is:
\[ \text{Median} = \frac{\text{5th term} + \text{6th term}}{2} \]
Given that the median is 63, we can set up the equation:
\[ 63 = \frac{\text{5th term} + \text{6th term}}{2} \]

### Step 4: Identify the 5th and 6th terms
From the ordered list:
- The 5th term is \( x \)
- The 6th term is \( x + 2 \)

### Step 5: Substitute the terms into the median formula
Substituting the 5th and 6th terms into the median formula gives:
\[ 63 = \frac{x + (x + 2)}{2} \]

### Step 6: Simplify the equation
This simplifies to:
\[ 63 = \frac{2x + 2}{2} \]
\[ 63 = x + 1 \]

### Step 7: Solve for \( x \)
To find \( x \), we can rearrange the equation:
\[ x = 63 - 1 \]
\[ x = 62 \]

### Conclusion
Thus, the value of \( x \) is \( 62 \).

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