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

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

### Step 2: Count the number of observations.
Next, we need to determine how many numbers are in our sorted list.

**Total Observations (n):** 10

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

### Step 4: Use the median formula for an even number of observations.
The formula for 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 list.
From our sorted data:
- 5th term = 194
- 6th term = 200

### Step 6: Calculate the median.
Now, we can plug these values into the median formula:
\[ \text{Median} = \frac{194 + 200}{2} = \frac{394}{2} = 197 \]

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

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