Question
Kono gathers the heights of a random sample of sixth graders and seventh graders and displays the data in box plots. What can he say about the two data sets?
The median of the grade sample is greater than the median of the grade sample.
The grade sample has greater variability.
Convince Me!
How can you visually compare data from two samples that are displayed in box plots?
sample of sixth graders and seventh graders and displays the data in box plots. What can he say about the two data sets?
The median of the grade sample is greater than the median of the grade sample.
The grade sample has greater variability.
Convince Me!
How can you visually compare data from two samples that are displayed in box plots?
Two box plots. 6th grade students minimum is 56, 1st quartile is 58, median is 62, 3rd quartile is 64, maximum is 69. 7th grade student's minimum is 53, 1st quartile is 58, median is 63, 3rd quartile is 68, maximum is 74.
The median of the grade sample is greater than the median of the grade sample.
The grade sample has greater variability.
Convince Me!
How can you visually compare data from two samples that are displayed in box plots?
sample of sixth graders and seventh graders and displays the data in box plots. What can he say about the two data sets?
The median of the grade sample is greater than the median of the grade sample.
The grade sample has greater variability.
Convince Me!
How can you visually compare data from two samples that are displayed in box plots?
Two box plots. 6th grade students minimum is 56, 1st quartile is 58, median is 62, 3rd quartile is 64, maximum is 69. 7th grade student's minimum is 53, 1st quartile is 58, median is 63, 3rd quartile is 68, maximum is 74.
Answers
GPT-4o mini
To visually compare the two samples of box plots for sixth graders and seventh graders, we can look at a few important features: the medians, the range, the quartiles, and the overall variability.
### Key Observations
1. **Medians**:
- Sixth grade sample median: 62
- Seventh grade sample median: 63
**Comparison**: The median height of the **seventh grade** sample (63) is greater than the median height of the **sixth grade** sample (62). Thus, we can state that "the median of the seventh grade sample is greater than the median of the sixth grade sample."
2. **Quartiles**:
- **Sixth Grade**:
- 1st quartile (Q1): 58
- 3rd quartile (Q3): 64
- **Seventh Grade**:
- 1st quartile (Q1): 58
- 3rd quartile (Q3): 68
**Comparison**: The first quartile for both groups is the same (58), but the third quartile of the seventh grade sample (68) is greater than that of the sixth grade sample (64). This indicates that the middle 50% of the seventh graders tend to be taller compared to sixth graders.
3. **Range (Min and Max)**:
- Sixth grade sample range: 56 (min) to 69 (max)
- Seventh grade sample range: 53 (min) to 74 (max)
**Comparison**: The seventh grade sample has a larger maximum (74) compared to the sixth grade maximum (69). The minimum height of seventh graders (53) is lower than that of sixth graders (56). This indicates that the seventh grade sample includes a broader range of heights.
4. **Variability**:
- Variability can be inferred from the spread of the data represented by the interquartile range (IQR), which is the difference between Q3 and Q1:
- **Sixth Grade IQR**: 64 - 58 = 6
- **Seventh Grade IQR**: 68 - 58 = 10
**Comparison**: The IQR for the seventh grade sample (10) is greater than that of the sixth grade sample (6), indicating that the seventh grade sample has greater variability in heights.
### Conclusion
From our analysis based on the box plots:
- The median of the seventh grade sample is indeed greater than the median of the sixth grade sample.
- The seventh grade sample has greater variability as indicated by the broader interquartile range.
Therefore, Kono can confidently state that "the seventh grade sample has greater variability."
### Convincing Comparison
In summary, using box plots allows us to visually and quantitatively assess the central tendency (medians) and variability (ranges and quartiles) of different data sets succinctly. By analyzing these features, we can draw meaningful comparisons about the two groups of students based on height.
### Key Observations
1. **Medians**:
- Sixth grade sample median: 62
- Seventh grade sample median: 63
**Comparison**: The median height of the **seventh grade** sample (63) is greater than the median height of the **sixth grade** sample (62). Thus, we can state that "the median of the seventh grade sample is greater than the median of the sixth grade sample."
2. **Quartiles**:
- **Sixth Grade**:
- 1st quartile (Q1): 58
- 3rd quartile (Q3): 64
- **Seventh Grade**:
- 1st quartile (Q1): 58
- 3rd quartile (Q3): 68
**Comparison**: The first quartile for both groups is the same (58), but the third quartile of the seventh grade sample (68) is greater than that of the sixth grade sample (64). This indicates that the middle 50% of the seventh graders tend to be taller compared to sixth graders.
3. **Range (Min and Max)**:
- Sixth grade sample range: 56 (min) to 69 (max)
- Seventh grade sample range: 53 (min) to 74 (max)
**Comparison**: The seventh grade sample has a larger maximum (74) compared to the sixth grade maximum (69). The minimum height of seventh graders (53) is lower than that of sixth graders (56). This indicates that the seventh grade sample includes a broader range of heights.
4. **Variability**:
- Variability can be inferred from the spread of the data represented by the interquartile range (IQR), which is the difference between Q3 and Q1:
- **Sixth Grade IQR**: 64 - 58 = 6
- **Seventh Grade IQR**: 68 - 58 = 10
**Comparison**: The IQR for the seventh grade sample (10) is greater than that of the sixth grade sample (6), indicating that the seventh grade sample has greater variability in heights.
### Conclusion
From our analysis based on the box plots:
- The median of the seventh grade sample is indeed greater than the median of the sixth grade sample.
- The seventh grade sample has greater variability as indicated by the broader interquartile range.
Therefore, Kono can confidently state that "the seventh grade sample has greater variability."
### Convincing Comparison
In summary, using box plots allows us to visually and quantitatively assess the central tendency (medians) and variability (ranges and quartiles) of different data sets succinctly. By analyzing these features, we can draw meaningful comparisons about the two groups of students based on height.