Find the median of the give data :
10, 16, 13, 15, 22, 18, 19

Answer

To find the median of the given data set: 10, 16, 13, 15, 22, 18, 19, 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:**
10, 13, 15, 16, 18, 19, 22

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

**Number of Observations (n):**
There are 7 numbers in total.

### Step 3: Determine if the number of observations is odd or even.
Since we have 7 observations, which is an odd number, we will use the formula for finding the median in an odd set of data.

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

**Calculating the position:**
\[ \frac{7 + 1}{2} = \frac{8}{2} = 4 \]
So, we need to find the 4th term in the sorted data.

### Step 5: Identify the 4th term in the sorted data.
Looking at our sorted data:
1. 10 (1st term)
2. 13 (2nd term)
3. 15 (3rd term)
4. 16 (4th term)

The 4th term is 16.

### Conclusion:
Thus, the median of the given data set is **16**.

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