Find the median of :
233 , 173 , 189 , 208 , 194 , 204 , 194 , 185 ,200 and 220

Answer

To find the median of the given data set: 233, 173, 189, 208, 194, 204, 194, 185, 200, and 220, we will follow these steps:

### Step 1: Count the number of data points (n)
First, we need to count how many numbers are in the data set.

**Data Points:** 233, 173, 189, 208, 194, 204, 194, 185, 200, 220

**Count (n):** There are 10 data points.

### Step 2: Arrange the data in ascending order
Next, we will sort the numbers in ascending order.

**Ascending Order:** 173, 185, 189, 194, 194, 200, 204, 208, 220, 233

### Step 3: Determine if n is odd or even
Since n = 10 (which is even), we will use the formula for finding the median in an even set of numbers.

### Step 4: Find the positions of the median
For an even number of data points, the median is the average of the two middle numbers. The positions of these numbers can be found using the formula:
- Middle positions: n/2 and (n/2) + 1

**Calculating Positions:**
- n/2 = 10/2 = 5
- (n/2) + 1 = 5 + 1 = 6

So, we need to find the 5th and 6th numbers in our sorted list.

### Step 5: Identify the 5th and 6th numbers
From our sorted list:
- 5th number = 194
- 6th number = 200

### Step 6: Calculate the median
Now, we will calculate the median by taking the average of the 5th and 6th numbers.

**Median Calculation:**
\[ \text{Median} = \frac{\text{5th number} + \text{6th number}}{2} = \frac{194 + 200}{2} = \frac{394}{2} = 197 \]

### Final Answer:
The median of the given data set is **197**.

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