Find the median of the given data
11, 16, 12, 15, 20, 17, 19

Answer

To find the median of the given data set: 11, 16, 12, 15, 20, 17, 19, we will follow these steps:

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

- The smallest number is 11.
- The next smallest is 12.
- Then we have 15, followed by 16, 17, 19, and finally 20.

So, the arranged data in ascending order is:
**11, 12, 15, 16, 17, 19, 20**

### Step 2: Count the number of elements in the data set.
Now we will count how many numbers are in our arranged list.

- The numbers are: 11, 12, 15, 16, 17, 19, 20
- There are a total of **7 elements**.

### Step 3: Determine if the number of elements is odd or even.
Since we have 7 elements, we note that 7 is an **odd number**.

### Step 4: Use the formula for the median of an odd number of elements.
The formula for finding the median when the number of elements (n) is odd is:
\[ \text{Median} = \frac{n + 1}{2} \]

- Here, \( n = 7 \).
- So, we calculate:
\[ \text{Median position} = \frac{7 + 1}{2} = \frac{8}{2} = 4 \]

### Step 5: Find the value at the median position.
Now, we need to find the 4th observation in our arranged data set.

- The arranged data is: 11, 12, 15, **16**, 17, 19, 20
- The 4th observation is **16**.

### Final Answer:
Thus, the median of the given data is **16**.

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