. Find the median of the given data:
8, 9, 12, 7, 5, 4, 18, 20, 6,3

Answer

To find the median of the given data set: 8, 9, 12, 7, 5, 4, 18, 20, 6, 3, follow these steps:

### Step 1: Arrange the data in ascending order
First, we need to sort the numbers from the smallest to the largest.

- The given data: 8, 9, 12, 7, 5, 4, 18, 20, 6, 3
- Arranging in ascending order: 3, 4, 5, 6, 7, 8, 9, 12, 18, 20

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

- The sorted data has 10 numbers: 3, 4, 5, 6, 7, 8, 9, 12, 18, 20
- Therefore, the number of observations (n) = 10

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

### Step 4: Use the median formula
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 = 10
- n/2 = 10/2 = 5
- n/2 + 1 = 5 + 1 = 6

### Step 5: Identify the 5th and 6th observations
Now, we will find the 5th and 6th observations in the sorted data.

- The 5th observation is 7
- The 6th observation is 8

### Step 6: Calculate the median
Now, substitute the values into the median formula:

\[ \text{Median} = \frac{7 + 8}{2} = \frac{15}{2} = 7.5 \]

### Conclusion
Thus, the median of the given data set is **7.5**.

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