a research study was conducted to measure the time students focus on a task before being distracted. the box plots show the distributions of attention spans of high school and college students. students attention spans (minutes) college high school 0 2 4 6 8 10 12 14 16 18 20 22 24 which statements are true regarding the data sets? select two options. the median attention span of college students is greater than the median attention span of high school students. the range of attention span of college students is greater than the range of attention spans of high school students. the interquartile range of attention spans of college students is greater than the interquartile range of attention spans of high school students.

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# Brief Explanations:
1. **Median Analysis**: In a box - plot, the median is represented by the line inside the box. For college students, the median line is at a higher value (around 18 - 20 range) compared to high school students (around 14 - 16 range). So the median attention span of college students is greater than that of high school students.
2. **Range Analysis**: The range is calculated as the maximum value minus the minimum value. For high school students, the minimum is 0 and the maximum is around 20. For college students, the minimum is around 8 and the maximum is around 22. The range for high school: $20 - 0=20$, for college: $22 - 8 = 14$. Wait, no, maybe I misread the plot. Wait, looking at the plot again: High school's whiskers go from 0 to 20, college's from 8 to 22. Wait, no, maybe the left whisker for high school is 0, right is 20. College left is 8, right is 22. So range for high school is $20 - 0=20$, college is $22 - 8 = 14$. But that contradicts? Wait, maybe I made a mistake. Wait, the box - plot for high school: the left whisker starts at 0, right whisker at 20. College: left whisker at 8, right whisker at 22. Wait, but the other option about interquartile range: the box for college is wider? Wait, no, let's re - evaluate. Wait, the first option: median of college (line in college's box) is higher than high school's median (line in high school's box). So first option is correct. Now, the interquartile range (IQR) is the length of the box (Q3 - Q1). The college's box looks longer than high school's box. So IQR of college is greater than IQR of high school. Wait, maybe I messed up the range. Let's check again. High school: min = 0, max = 20, range = 20. College: min = 8, max = 22, range = 14. So range of college is less than high school. So the second option is wrong. The third option: IQR (college) > IQR (high school) is correct? Wait, no, let's see the boxes. High school's box is from, say, 10 to 16 (so IQR = 6). College's box is from 12 to 20 (IQR = 8). So IQR of college is greater. And median of college (18) is greater than high school (14). So the correct options are the first and the third? Wait, no, the problem says "Select two options". Wait, let's re - check the options:

Option 1: "The median attention span of college students is greater than the median attention span of high school students." - Correct, as college's median line is at a higher value.

Option 2: "The range of attention span of college students is greater than the range of attention spans of high school students." - Range of high school: max - min = 20 - 0 = 20. Range of college: 22 - 8 = 14. So this is incorrect.

Option 3: "The interquartile range of attention spans of college students is greater than the interquartile range of attention spans of high school students." - IQR is Q3 - Q1. The college's box is wider (longer) than high school's box, so IQR of college is greater. So this is correct.

Wait, but maybe my initial range calculation was wrong. Wait, maybe the left whisker for high school is not 0? Wait, the x - axis starts at 0, and the high school's left whisker is at 0, right at 20. College's left at 8, right at 22. So range for high school: 20 - 0 = 20, college: 22 - 8 = 14. So range of college is less than high school. So option 2 is wrong. So the two correct options are the first and the third? Wait, no, maybe I made a mistake. Wait, the problem's box - plot: let's assume that the high school's box is from 10 to 16 (Q1 = 10, Q3 = 16, IQR = 6), median at 14. College's box is from 12 to 20 (Q1 = 12, Q3 = 20, IQR = 8), median at 18. So median of college (18) > median of high school (14) - correct. IQR of college (8) > IQR of high school (6) - correct. Range of high school: 20 - 0 = 20, college: 22 - 8 = 14 - so range of college is less than high school, so option 2 is wrong. So the two correct options are the first and the third. Wait, but the options are:

1. The median attention span of college students is greater than the median attention span of high school students.

2. The range of attention span of college students is greater than the range of attention spans of high school students.

3. The interquartile range of attention spans of college students is greater than the interquartile range of attention spans of high school students.

So the correct two options are the first and the third. Wait, but maybe I misread the plot. Alternatively, maybe the range of college is greater? Wait, no, 22 - 8 = 14, 20 - 0 = 20. 14 < 20. So option 2 is wrong. So the correct options are:

A. The median attention span of college students is greater than the median attention span of high school students.

C. The interquartile range of attention spans of college students is greater than the interquartile range of attention spans of high school students.

# Answer:
A. The median attention span of college students is greater than the median attention span of high school students, C. The interquartile range of attention spans of college students is greater than the interquartile range of attention spans of high school students

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