Question
The given box plots show the number of text messages Paul and Sally received each day on their cell phones.
A number line plots daily text messages received by Paul and Sally. Paul received 15 through 18 and 18 through 26 messages. Sally received 18 through 24 and 24 through 28 messages.
Select the true statement.
A.
The median of Paul's data is equal to the median of Sally's data.
B.
The median of Paul's data is greater than the median of Sally's data.
C.
Paul's data has a larger overall spread than Sally's data.
D.
The interquartile range of Paul's data is less than the interquartile range of Sally's data.
A number line plots daily text messages received by Paul and Sally. Paul received 15 through 18 and 18 through 26 messages. Sally received 18 through 24 and 24 through 28 messages.
Select the true statement.
A.
The median of Paul's data is equal to the median of Sally's data.
B.
The median of Paul's data is greater than the median of Sally's data.
C.
Paul's data has a larger overall spread than Sally's data.
D.
The interquartile range of Paul's data is less than the interquartile range of Sally's data.
Answers
GPT-4o mini
To evaluate the statements about Paul's and Sally's text messages received, we need to determine the median and interquartile ranges (IQR) of their data based on the provided intervals.
### Step 1: Find the Medians
- **Paul's Data:**
- Paul received 15 through 18 messages (which represents 4 values: 15, 16, 17, 18).
- Paul received 18 through 26 messages (which includes values: 18, 19, 20, 21, 22, 23, 24, 25, 26).
Combining these, we have:
- Total values for Paul: 15, 16, 17, 18, 18, 19, 20, 21, 22, 23, 24, 25, 26.
To find the median:
- The total number of values: 13
- The median is the middle value, which is the 7th value: **20**.
- **Sally's Data:**
- Sally received 18 through 24 messages (which includes values: 18, 19, 20, 21, 22, 23, 24).
- Sally received 24 through 28 messages (which includes values: 24, 25, 26, 27, 28).
Combining these, we have:
- Total values for Sally: 18, 19, 20, 21, 22, 23, 24, 24, 25, 26, 27, 28.
To find the median:
- The total number of values: 12
- The median is the average of the 6th and 7th values: \( \frac{23 + 24}{2} = 23.5 \).
### Step 2: Comparisons of Medians
- Median of Paul: 20
- Median of Sally: 23.5
Thus, the true statement regarding the medians is:
- **B**: The median of Paul's data is less than the median of Sally's data.
### Step 3: Determine Interquartile Ranges (IQR)
- **Paul's Data:**
- Lower quartile (Q1): 17 (the average of 4th and 5th values).
- Upper quartile (Q3): 24 (the average of 10th and 11th values).
- IQR = Q3 - Q1 = 24 - 17 = 7.
- **Sally's Data:**
- Lower quartile (Q1): 21 (the average of 6th and 7th values).
- Upper quartile (Q3): 25.5 (the average of 10th and 11th values).
- IQR = Q3 - Q1 = 25.5 - 21 = 4.5.
### Final Comparisons
- IQR of Paul: 7
- IQR of Sally: 4.5
For the interquartile ranges, the true statement is:
- **D**: The interquartile range of Paul's data is greater than the interquartile range of Sally's data.
### Conclusion:
Based on the analysis:
- **True statement is:**
**B: The median of Paul's data is less than the median of Sally's data.**
### Step 1: Find the Medians
- **Paul's Data:**
- Paul received 15 through 18 messages (which represents 4 values: 15, 16, 17, 18).
- Paul received 18 through 26 messages (which includes values: 18, 19, 20, 21, 22, 23, 24, 25, 26).
Combining these, we have:
- Total values for Paul: 15, 16, 17, 18, 18, 19, 20, 21, 22, 23, 24, 25, 26.
To find the median:
- The total number of values: 13
- The median is the middle value, which is the 7th value: **20**.
- **Sally's Data:**
- Sally received 18 through 24 messages (which includes values: 18, 19, 20, 21, 22, 23, 24).
- Sally received 24 through 28 messages (which includes values: 24, 25, 26, 27, 28).
Combining these, we have:
- Total values for Sally: 18, 19, 20, 21, 22, 23, 24, 24, 25, 26, 27, 28.
To find the median:
- The total number of values: 12
- The median is the average of the 6th and 7th values: \( \frac{23 + 24}{2} = 23.5 \).
### Step 2: Comparisons of Medians
- Median of Paul: 20
- Median of Sally: 23.5
Thus, the true statement regarding the medians is:
- **B**: The median of Paul's data is less than the median of Sally's data.
### Step 3: Determine Interquartile Ranges (IQR)
- **Paul's Data:**
- Lower quartile (Q1): 17 (the average of 4th and 5th values).
- Upper quartile (Q3): 24 (the average of 10th and 11th values).
- IQR = Q3 - Q1 = 24 - 17 = 7.
- **Sally's Data:**
- Lower quartile (Q1): 21 (the average of 6th and 7th values).
- Upper quartile (Q3): 25.5 (the average of 10th and 11th values).
- IQR = Q3 - Q1 = 25.5 - 21 = 4.5.
### Final Comparisons
- IQR of Paul: 7
- IQR of Sally: 4.5
For the interquartile ranges, the true statement is:
- **D**: The interquartile range of Paul's data is greater than the interquartile range of Sally's data.
### Conclusion:
Based on the analysis:
- **True statement is:**
**B: The median of Paul's data is less than the median of Sally's data.**