Question
Given the dataset 15, 10, 12, 11, 5, 8, 25, 30, 9, and 6, what parts of the five-number summary would change if a new data point of 15 was added?(1 point)
Responses
median
median - no response given
median, Q1, Q3, maximum, and minimum
median, Q1, Q3, maximum, and minimum - no response given
Q1, Q3
Q1, Q3 - no response given
median, Q3
Responses
median
median - no response given
median, Q1, Q3, maximum, and minimum
median, Q1, Q3, maximum, and minimum - no response given
Q1, Q3
Q1, Q3 - no response given
median, Q3
Answers
GPT-4o mini
To determine how the five-number summary (minimum, Q1, median, Q3, and maximum) is affected by adding a new data point of 15 to the dataset, we first need to calculate the five-number summary for the original dataset, which includes the values: 5, 6, 8, 9, 10, 11, 12, 15, 25, 30.
1. **Ordering the original dataset:**
- 5, 6, 8, 9, 10, 11, 12, 15, 25, 30
2. **Calculating the five-number summary of the original dataset:**
- Minimum: 5
- Maximum: 30
- Median (middle value): (10 + 11) / 2 = 10.5
- Q1 (lower quartile): Average of the 1st half (5, 6, 8, 9) = (6 + 8) / 2 = 7
- Q3 (upper quartile): Average of the 2nd half (11, 12, 15, 25, 30) = (15 + 25) / 2 = 20
3. **Adding the new data point (15) to the dataset:**
- New dataset: 5, 6, 8, 9, 10, 11, 12, 15, 15, 25, 30
- Ordering: 5, 6, 8, 9, 10, 11, 12, 15, 15, 25, 30
4. **Calculating the five-number summary for the new dataset:**
- Minimum: 5
- Maximum: 30
- Median: (11 + 12) / 2 = 11.5 (now between the 6th and 7th value)
- Q1: Average of the 1st half (5, 6, 8, 9, 10) = 8
- Q3: Average of the 2nd half (12, 15, 15, 25, 30) = (15 + 25) / 2 = 20
5. **Points of change:**
- Median changes from 10.5 to 11.5.
- Q1 changes from 7 to 8.
- Q3 remains 20, and maximum (30) and minimum (5) do not change.
### Conclusion:
The parts of the five-number summary that would change by adding a new data point of 15 are the **median and Q1**. Therefore, the correct response is:
**median, Q1, Q3, maximum, and minimum** (since median and Q1 changed) is incorrect since Q3, maximum, and minimum didn't change.
The best correct option from the provided responses is **median, Q3**, as Q3 remained the same but was incorrectly presented in the choices and may seem connected to the change calculated in context to median and Q1, if we are strict in quoting parts changed further than those mentioned as important parts M and Q1 .
1. **Ordering the original dataset:**
- 5, 6, 8, 9, 10, 11, 12, 15, 25, 30
2. **Calculating the five-number summary of the original dataset:**
- Minimum: 5
- Maximum: 30
- Median (middle value): (10 + 11) / 2 = 10.5
- Q1 (lower quartile): Average of the 1st half (5, 6, 8, 9) = (6 + 8) / 2 = 7
- Q3 (upper quartile): Average of the 2nd half (11, 12, 15, 25, 30) = (15 + 25) / 2 = 20
3. **Adding the new data point (15) to the dataset:**
- New dataset: 5, 6, 8, 9, 10, 11, 12, 15, 15, 25, 30
- Ordering: 5, 6, 8, 9, 10, 11, 12, 15, 15, 25, 30
4. **Calculating the five-number summary for the new dataset:**
- Minimum: 5
- Maximum: 30
- Median: (11 + 12) / 2 = 11.5 (now between the 6th and 7th value)
- Q1: Average of the 1st half (5, 6, 8, 9, 10) = 8
- Q3: Average of the 2nd half (12, 15, 15, 25, 30) = (15 + 25) / 2 = 20
5. **Points of change:**
- Median changes from 10.5 to 11.5.
- Q1 changes from 7 to 8.
- Q3 remains 20, and maximum (30) and minimum (5) do not change.
### Conclusion:
The parts of the five-number summary that would change by adding a new data point of 15 are the **median and Q1**. Therefore, the correct response is:
**median, Q1, Q3, maximum, and minimum** (since median and Q1 changed) is incorrect since Q3, maximum, and minimum didn't change.
The best correct option from the provided responses is **median, Q3**, as Q3 remained the same but was incorrectly presented in the choices and may seem connected to the change calculated in context to median and Q1, if we are strict in quoting parts changed further than those mentioned as important parts M and Q1 .