Question
Raj polled 100 students in his class to compare the number of hours that teen boys and girls played video games each week. The results of his survey are shown below. Which gender shows greater variability in their playing time?
Hours of Video Game Time per Week for Teen Boys
A box-and-whisker plot. The number line goes from 0 to 28. The whiskers range from 0 to 28, and the box ranges from 9 to 17. A line divides the box at 14.5.
Hours of Video Game Time per Week for Teen Girls
A box-and-whisker plot. The number line goes from 0 to 28. The whiskers range from 0 to 28, and the box ranges from 3 to 15. A line divides the box at 6.
Boys show greater variability because the 3rd quartile for boys is 17 but only 15 for girls.
Boys show greater variability because the median playing time for boys is 14.5 but only 6 for girls.
Girls show greater variability because the interquartile range for girls is 12 for girls but only 8 for boys.
Girls show greater variability because the data for the girls is skewed toward the lower end of the box plot.
Hours of Video Game Time per Week for Teen Boys
A box-and-whisker plot. The number line goes from 0 to 28. The whiskers range from 0 to 28, and the box ranges from 9 to 17. A line divides the box at 14.5.
Hours of Video Game Time per Week for Teen Girls
A box-and-whisker plot. The number line goes from 0 to 28. The whiskers range from 0 to 28, and the box ranges from 3 to 15. A line divides the box at 6.
Boys show greater variability because the 3rd quartile for boys is 17 but only 15 for girls.
Boys show greater variability because the median playing time for boys is 14.5 but only 6 for girls.
Girls show greater variability because the interquartile range for girls is 12 for girls but only 8 for boys.
Girls show greater variability because the data for the girls is skewed toward the lower end of the box plot.
Answers
GPT-4o mini
To determine which gender shows greater variability in their playing time, we can analyze the box-and-whisker plots provided.
1. **Boys' Data:**
- Minimum: 0
- Q1 (1st quartile): 9
- Median (Q2): 14.5
- Q3 (3rd quartile): 17
- Maximum: 28
- Interquartile Range (IQR) = Q3 - Q1 = 17 - 9 = 8
2. **Girls' Data:**
- Minimum: 0
- Q1 (1st quartile): 3
- Median (Q2): 6
- Q3 (3rd quartile): 15
- Maximum: 28
- Interquartile Range (IQR) = Q3 - Q1 = 15 - 3 = 12
Now we can analyze the options given:
- **Boys show greater variability because the 3rd quartile for boys is 17 but only 15 for girls.**
- This statement refers to the upper quartiles but doesn’t fully capture variability.
- **Boys show greater variability because the median playing time for boys is 14.5 but only 6 for girls.**
- While the median is higher for boys, it does not measure variability itself.
- **Girls show greater variability because the interquartile range for girls is 12 for girls but only 8 for boys.**
- This statement correctly identifies the IQR, which measures variability, and shows that girls have a higher IQR.
- **Girls show greater variability because the data for the girls is skewed toward the lower end of the box plot.**
- Skewness can influence perception but is not a direct measure of variability.
Given this, the statement that best assesses the variability based on calculated values is:
**Girls show greater variability because the interquartile range for girls is 12 for girls but only 8 for boys.**
1. **Boys' Data:**
- Minimum: 0
- Q1 (1st quartile): 9
- Median (Q2): 14.5
- Q3 (3rd quartile): 17
- Maximum: 28
- Interquartile Range (IQR) = Q3 - Q1 = 17 - 9 = 8
2. **Girls' Data:**
- Minimum: 0
- Q1 (1st quartile): 3
- Median (Q2): 6
- Q3 (3rd quartile): 15
- Maximum: 28
- Interquartile Range (IQR) = Q3 - Q1 = 15 - 3 = 12
Now we can analyze the options given:
- **Boys show greater variability because the 3rd quartile for boys is 17 but only 15 for girls.**
- This statement refers to the upper quartiles but doesn’t fully capture variability.
- **Boys show greater variability because the median playing time for boys is 14.5 but only 6 for girls.**
- While the median is higher for boys, it does not measure variability itself.
- **Girls show greater variability because the interquartile range for girls is 12 for girls but only 8 for boys.**
- This statement correctly identifies the IQR, which measures variability, and shows that girls have a higher IQR.
- **Girls show greater variability because the data for the girls is skewed toward the lower end of the box plot.**
- Skewness can influence perception but is not a direct measure of variability.
Given this, the statement that best assesses the variability based on calculated values is:
**Girls show greater variability because the interquartile range for girls is 12 for girls but only 8 for boys.**