Find the median of : 18, 30, 39, 36, 28, 27, 31, 40, 33, 25 and 37.

Answer

To find the median of the given data set: 18, 30, 39, 36, 28, 27, 31, 40, 33, 25, and 37, we will follow these steps:

### Step 1: Arrange the data in ascending order
First, we need to sort the numbers from the smallest to the largest.

- Given data: 18, 30, 39, 36, 28, 27, 31, 40, 33, 25, 37
- Arranged data: 18, 25, 27, 28, 30, 31, 33, 36, 37, 39, 40

### Step 2: Count the number of observations
Next, we count how many numbers are in the data set.

- Total observations: 11

### Step 3: Determine if the number of observations is odd or even
Since we have 11 observations, we note that this is an odd number.

### Step 4: Find the median position
For an odd number of observations, the median is found at the position given by the formula:
\[ \text{Median position} = \frac{n + 1}{2} \]
where \( n \) is the number of observations.

- Here, \( n = 11 \)
- Median position: \( \frac{11 + 1}{2} = \frac{12}{2} = 6 \)

### Step 5: Identify the median value
Now, we need to find the 6th term in our arranged data.

- Arranged data: 1st: 18, 2nd: 25, 3rd: 27, 4th: 28, 5th: 30, 6th: 31

Thus, the 6th term is 31.

### Final Answer
The median of the given observations is **31**.

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