Find the median of : 34,47,41,52,53,56,35,49,55 and 42.

Answer

To find the median of the given data set: 34, 47, 41, 52, 53, 56, 35, 49, 55, and 42, 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.

**Sorted Data:** 34, 35, 41, 42, 47, 49, 52, 53, 55, 56

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

**Total Observations (n):** 10

### Step 3: Determine if the number of observations is even or odd.
Since there are 10 observations, which is an even number, we will use the formula for finding the median when the number of observations is even.

### Step 4: Apply the median formula for even numbers.
The formula for finding the median when the number of observations (n) is even is:
\[ \text{Median} = \frac{\text{(n/2)th term} + \text{(n/2 + 1)th term}}{2} \]

Here, \( n = 10 \), so:
- \( n/2 = 10/2 = 5 \)
- \( n/2 + 1 = 5 + 1 = 6 \)

### Step 5: Identify the 5th and 6th terms in the sorted data.
From our sorted data:
- The 5th term is 47.
- The 6th term is 49.

### Step 6: Calculate the median.
Now we substitute these values into the median formula:
\[ \text{Median} = \frac{47 + 49}{2} = \frac{96}{2} = 48 \]

### Final Answer:
The median of the given data set is **48**.

---