Find the median of the observation 17,14,13,12,18,19,16,14,12,19,16,25,and 15.

Answer

To find the median of the given observations, we will follow these steps:

### Step 1: List the Observations
The given observations are:
17, 14, 13, 12, 18, 19, 16, 14, 12, 19, 16, 25, and 15.

### Step 2: Arrange the Observations in Ascending Order
We need to arrange the numbers from smallest to largest:
12, 12, 13, 14, 14, 15, 16, 16, 17, 18, 19, 19, 25.

### Step 3: Count the Number of Observations
Now, we count how many numbers we have:
1. 12
2. 12
3. 13
4. 14
5. 14
6. 15
7. 16
8. 16
9. 17
10. 18
11. 19
12. 19
13. 25

Total number of observations (N) = 13.

### Step 4: Determine if N is Odd or Even
Since N = 13, which is an odd number, we will use the formula for finding the median in the case of an odd number of observations.

### Step 5: Use the Median Formula
The formula for the median when N is odd is:
\[ \text{Median} = \frac{N + 1}{2} \]
Substituting the value of N:
\[ \text{Median} = \frac{13 + 1}{2} = \frac{14}{2} = 7 \]

### Step 6: Find the 7th Value in the Ordered List
Now, we need to find the 7th value in our ordered list:
1. 12
2. 12
3. 13
4. 14
5. 14
6. 15
7. 16 (This is the 7th value)

### Conclusion
Thus, the median of the observations is:
**Median = 16**

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