Which data set has a median of 16 ?

Options

A. 16, 21, 26, 29, 32
B. 0, 4, 7, 10, 16, 16
C. 0, 9, 31, 17, 18, 22
D. 25, 14, 7, 16, 21

Answer

To determine which data set has a median of 16, we will analyze each option step by step.

### Step-by-Step Solution:

1. **Understand the Median Calculation**:
- The median is the middle value of a data set when it is arranged in order.
- If the number of observations (n) is odd, the median is the value at the position (n + 1) / 2.
- If n is even, the median is the average of the values at positions n / 2 and (n / 2) + 1.

2. **Analyze Option 1**:
- Data Set: 16, 21, 26, 29, 32
- Arrange the data: Already arranged as 16, 21, 26, 29, 32.
- Count of observations (n): 5 (odd).
- Median position: (5 + 1) / 2 = 3rd term.
- 3rd term = 26.
- **Conclusion**: Median is 26, not 16. Option 1 is incorrect.

3. **Analyze Option 2**:
- Data Set: 0, 4, 7, 10, 16, 16
- Arrange the data: Already arranged as 0, 4, 7, 10, 16, 16.
- Count of observations (n): 6 (even).
- Median position: (6 / 2) = 3rd term and (6 / 2) + 1 = 4th term.
- 3rd term = 7, 4th term = 10.
- Median = (7 + 10) / 2 = 17 / 2 = 8.5.
- **Conclusion**: Median is 8.5, not 16. Option 2 is incorrect.

4. **Analyze Option 3**:
- Data Set: 0, 9, 17, 18, 22, 31
- Arrange the data: Already arranged as 0, 9, 17, 18, 22, 31.
- Count of observations (n): 6 (even).
- Median position: (6 / 2) = 3rd term and (6 / 2) + 1 = 4th term.
- 3rd term = 17, 4th term = 18.
- Median = (17 + 18) / 2 = 35 / 2 = 17.5.
- **Conclusion**: Median is 17.5, not 16. Option 3 is incorrect.

5. **Analyze Option 4**:
- Data Set: 7, 14, 16, 21, 25
- Arrange the data: Already arranged as 7, 14, 16, 21, 25.
- Count of observations (n): 5 (odd).
- Median position: (5 + 1) / 2 = 3rd term.
- 3rd term = 16.
- **Conclusion**: Median is 16. Option 4 is correct.

### Final Answer:
The data set that has a median of 16 is **Option 4**.