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 smallest to largest.

**Sorted Data:** 18, 25, 27, 28, 30, 31, 33, 36, 37, 39, 40

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

**Count of Observations (n):** 11

### Step 3: Determine if n is odd or even.
Since we have counted the observations, we see that n = 11, which is an odd number.

### Step 4: Use the median formula for odd n.
For an odd number of observations, the median can be found using the formula:
\[ \text{Median} = \frac{n + 1}{2} \]
Substituting the value of n:
\[ \text{Median} = \frac{11 + 1}{2} = \frac{12}{2} = 6 \]

### Step 5: Identify the median value.
The median is the value at the position we calculated (6th position) in the sorted data.

Counting to the 6th term in the sorted list:
1. 18 (1st)
2. 25 (2nd)
3. 27 (3rd)
4. 28 (4th)
5. 30 (5th)
6. 31 (6th)

Thus, the 6th term is 31.

### Final Answer:
The median of the given data set is **31**.

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