Observations 11, 12, 14, 18, x + 2, x + 4, 30, 32, 35, 41 have been arranged in ascending order. If median is 24, then the value of x will be

Options

A. 22
B. 21
C. 24
D. None of these

Answer

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

### Step 1: Identify the number of observations
We have the observations: \( 11, 12, 14, 18, x + 2, x + 4, 30, 32, 35, 41 \). There are a total of 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 in the ordered list.

### Step 3: Set up the equation for the median
According to the problem, the median is given as 24. Therefore, we can set up the equation:
\[ \text{Median} = \frac{\text{5th term} + \text{6th term}}{2} = 24 \]
This implies:
\[ \text{5th term} + \text{6th term} = 48 \]

### Step 4: Identify the 5th and 6th terms
In the ordered list, the 5th term is \( x + 2 \) and the 6th term is \( x + 4 \). Thus, we can write:
\[ (x + 2) + (x + 4) = 48 \]

### Step 5: Simplify the equation
Combine like terms:
\[ 2x + 6 = 48 \]

### Step 6: Solve for \( x \)
Subtract 6 from both sides:
\[ 2x = 48 - 6 \]
\[ 2x = 42 \]
Now, divide by 2:
\[ x = \frac{42}{2} = 21 \]

### Conclusion
The value of \( x \) is \( 21 \).