Find the median of the given data : 25, 34, 31, 23, 22, 26, 35, 28, 20, 32

Answer

To find the median of the given data set: 25, 34, 31, 23, 22, 26, 35, 28, 20, 32, 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.

**Data in ascending order:**
20, 22, 23, 25, 26, 28, 31, 32, 34, 35

### Step 2: Determine the number of observations (n).
Count the total number of data points.

**Total observations (n):**
There are 10 numbers in the data set.

### Step 3: Identify if n is even or odd.
Since n = 10, which is an even number, we will use the formula for finding the median for even sets.

### Step 4: Use the median formula for even n.
The formula for the median when n is even is:
\[ \text{Median} = \frac{\text{(n/2)th observation} + \text{(n/2 + 1)th observation}}{2} \]

Here, n/2 = 10/2 = 5. Therefore, we will find the 5th and 6th observations.

### Step 5: Identify the 5th and 6th observations.
From the sorted data:
- The 5th observation is 26.
- The 6th observation is 28.

### Step 6: Calculate the median.
Now, we can substitute the values into the median formula:
\[ \text{Median} = \frac{26 + 28}{2} = \frac{54}{2} = 27 \]

### Final Answer:
The median of the given data set is **27**.

---