Question

Which box-and-whisker plot represents this data: 6, 7, 8, 10, 18, 20, 22, 25, 28, 30, 30
?


A box-and-whisker plot is shown. The number line goes from 2 to 38. The whiskers range from 6 to 30, and the box ranges from between 8 and 10 to 28 with a median between 20 and 22.


A box-and-whisker plot is shown. The number line goes from 2 to 38. The whiskers range from 6 to 30, and the box ranges from 18 to between 24 and 26 with no median value.


A box-and-whisker plot is shown. The number line goes from 2 to 38. The whiskers range from 6 to 30, and the box ranges from between 12 and 14 and between 26 and 28 with a median of 22.


A box-and-whisker plot is shown. The number line goes from 2 to 38. The whiskers range from 6 to 30, and the box ranges from between 12 and 14 to between 26 and 28 with a median between 20 and 22.

Answer 1

To determine which box-and-whisker plot represents the given data set: 6, 7, 8, 10, 18, 20, 22, 25, 28, 30, 30, we need to calculate the five-number summary, which includes:

1. Minimum (smallest value)
2. First quartile (Q1)
3. Median (Q2)
4. Third quartile (Q3)
5. Maximum (largest value)

### Given Data:
6, 7, 8, 10, 18, 20, 22, 25, 28, 30, 30

### 1. Minimum:
- The minimum value is **6**.

### 2. Maximum:
- The maximum value is **30**.

### 3. Median (Q2):
- The data set has 11 numbers. The median is the middle number, which is the 6th value when the data is arranged in ascending order.
- Median \( Q2 = 20 \).

### 4. First Quartile (Q1):
- To find Q1, we take the first half of the data (the first 5 values): 6, 7, 8, 10, 18.
- The median of this subset (5 values) is the 3rd value:
- \( Q1 = 8 \).

### 5. Third Quartile (Q3):
- For Q3, we take the second half of the data (the last 5 values): 20, 22, 25, 28, 30, 30.
- The median of this subset (5 values) is the 3rd value:
- \( Q3 = 25 \).

### Summary:
Now we have the five-number summary:
- Minimum = 6
- Q1 = 8
- Q2 (Median) = 20
- Q3 = 25
- Maximum = 30

### Box-and-Whisker Plot Interpretation:
1. The whiskers extend from 6 to 30.
2. The box will range from 8 (Q1) to 25 (Q3).
3. The median (Q2) is at 20.

### Analyzing Options:
1. **First Option**: Whiskers from 6 to 30, box from **8 to 10** to **28**, with median between 20 and 22. (Incorrect Q3)
2. **Second Option**: Whiskers from 6 to 30, box from 18 to **24** to **26**, no median. (No correct Q1, Q2, Q3)
3. **Third Option**: Whiskers from 6 to 30, box from **12 to 14** to **26 to 28**, with median 22. (Incorrect Q1 and Q2)
4. **Fourth Option**: Whiskers from 6 to 30, box from **12 to 14** to **26 to 28**, median between 20 and 22. (Incorrect Q1 and Q3)

### Conclusion:
None of the options completely match the calculated five-number summary and box-and-whisker plot characteristics.

However, you would expect the correct box-and-whisker plot to show:
- Whiskers from 6 to 30.
- Box from 8 to 25.
- Median at 20.

Therefore, the first option is the best choice, though it incorrectly states the upper box limit. The median is also described inaccurately.