To determine the mode and the median from the given figures: 25, 15, 23, 40, 27, 25, 23, 25, 20, we can follow these steps:
### Step 1: Determine the Mode
1. **List the numbers**: 25, 15, 23, 40, 27, 25, 23, 25, 20.
2. **Count the frequency of each number**:
- 15 appears 1 time
- 20 appears 1 time
- 23 appears 2 times
- 25 appears 3 times
- 27 appears 1 time
- 40 appears 1 time
3. **Identify the number with the highest frequency**: The number 25 appears the most frequently (3 times).
4. **Conclusion**: The mode is 25.
### Step 2: Determine the Median
1. **Arrange the numbers in ascending order**:
- The sorted list is: 15, 20, 23, 23, 25, 25, 25, 25, 27, 40.
2. **Count the total number of observations (n)**: There are 9 numbers in total.
3. **Find the position of the median**:
- The median position is given by the formula (n + 1) / 2.
- Here, n = 9, so the position is (9 + 1) / 2 = 10 / 2 = 5.
4. **Locate the median**: The 5th number in the sorted list is 25.
5. **Conclusion**: The median is 25.
### Final Results:
- **Mode**: 25
- **Median**: 25
---
