Find the median of
(i) 7, 11, 25, 45, 23, 12, 11, 9, 10
(ii) 15, 14, 11, 9, 7, 12, 18, 20

Answer

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

### Part (i): Find the median of 7, 11, 25, 45, 23, 12, 11, 9, 10

**Step 1: Arrange the data in ascending order.**
- The given numbers are: 7, 11, 25, 45, 23, 12, 11, 9, 10.
- Arranging them in ascending order: 7, 9, 10, 11, 11, 12, 23, 25, 45.

**Step 2: Count the number of observations (n).**
- There are 9 numbers in total.
- \( n = 9 \) (which is odd).

**Step 3: Use the median formula for an odd number of observations.**
- The formula for the median when \( n \) is odd is:
\[ \text{Median} = \frac{n + 1}{2} \text{th term} \]
- Substituting \( n = 9 \):
\[ \text{Median} = \frac{9 + 1}{2} = \frac{10}{2} = 5 \]
- The 5th term in the ordered list is 11.

**Step 4: Conclusion for Part (i).**
- The median of the first set is **11**.

### Part (ii): Find the median of 15, 14, 11, 9, 7, 12, 18, 20

**Step 1: Arrange the data in ascending order.**
- The given numbers are: 15, 14, 11, 9, 7, 12, 18, 20.
- Arranging them in ascending order: 7, 9, 11, 12, 14, 15, 18, 20.

**Step 2: Count the number of observations (n).**
- There are 8 numbers in total.
- \( n = 8 \) (which is even).

**Step 3: Use the median formula for an even number of observations.**
- The formula for the median when \( n \) is even is:
\[ \text{Median} = \frac{\left(\frac{n}{2}\right) \text{th term} + \left(\frac{n}{2} + 1\right) \text{th term}}{2} \]
- Substituting \( n = 8 \):
\[ \text{Median} = \frac{\left(\frac{8}{2}\right) \text{th term} + \left(\frac{8}{2} + 1\right) \text{th term}}{2} = \frac{4\text{th term} + 5\text{th term}}{2} \]
- The 4th term is 12 and the 5th term is 14:
\[ \text{Median} = \frac{12 + 14}{2} = \frac{26}{2} = 13 \]

**Step 4: Conclusion for Part (ii).**
- The median of the second set is **13**.

### Summary of Results:
- Median of the first set: **11**
- Median of the second set: **13**