The median of observations 11, 12, 14, 18, x+ 2, 20, 22, 25, 61 arranged in ascending order is 21. Find the value of x.

Answer

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

### Step 1: Understand the Median
The median is the middle value of a data set when it is arranged in ascending order. For an odd number of observations, the median is given by the formula:
\[ \text{Median} = \frac{N + 1}{2} \]
where \( N \) is the number of observations.

### Step 2: Count the Observations
In this case, the observations are:
11, 12, 14, 18, \( x + 2 \), 20, 22, 25, 61.
Counting these, we find there are 9 observations.

### Step 3: Calculate the Position of the Median
Since there are 9 observations (which is odd), we can find the position of the median:
\[ \text{Position} = \frac{9 + 1}{2} = \frac{10}{2} = 5 \]
This means the median is the 5th term in the ordered list.

### Step 4: Identify the 5th Term
Now, we need to arrange the observations in ascending order. The 5th term is \( x + 2 \). According to the problem, this median value is given as 21:
\[ x + 2 = 21 \]

### Step 5: Solve for \( x \)
To find \( x \), we will isolate it:
\[ x = 21 - 2 \]
\[ x = 19 \]

### Conclusion
The value of \( x \) is 19.

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