Question

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.

Explanation:

1. Median Analysis: In a box - plot, the median is represented by the line inside the box. For college students' box - plot, the median line is at a higher value (let's assume from the plot, say around 16 - 18 range) compared to high school students' median (around 12 - 14 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 college students, the minimum is around 6 and the maximum is around 22, so the range is \(22 - 6=16\). For high school students, the minimum is around 0 and the maximum is around 20, so the range is \(20 - 0 = 20\). Wait, no, maybe I misread. Wait, looking at the plot: College students' whiskers: minimum around 6, maximum around 22. High school students' whiskers: minimum around 0, maximum around 20. Wait, no, maybe the high school's minimum is around 0, maximum around 20, college's minimum around 6, maximum around 22. Then range of college is \(22 - 6 = 16\), range of high school is \(20 - 0=20\)? No, that can't be. Wait, maybe the high school's maximum is around 20, college's maximum around 22. High school's minimum: let's see the left whisker of high school starts at 0? Wait, the x - axis is from 0 to 24. High school's box: left whisker from 0 to 10, box from 10 to 16, median at 14? College's box: left whisker from 6 to 12, box from 12 to 20, median at 16? Wait, no, the plot: High school: left whisker (minimum) at 0, box from 10 to 16, median at 14. College: left whisker at 6, box from 12 to 20, median at 16. Then range of high school: \(20 - 0 = 20\) (wait, no, the right whisker of high school: is it up to 20? College's right whisker up to 22. Then range of college: \(22 - 6=16\), range of high school: \(20 - 0 = 20\). So range of college is not greater than high school. Wait, maybe I made a mistake. Wait, the interquartile range (IQR) is Q3 - Q1. For high school: Q1 is 10, Q3 is 16, so IQR = 16 - 10 = 6. For college: Q1 is 12, Q3 is 20, so IQR = 20 - 12 = 8. So IQR of college is greater than IQR of high school. And median of college (16) is greater than median of high school (14). So the true statements are: "The median attention span of college students is greater than the median attention span of high school students" and "The interquartile range of attention spans of college students is greater than the interquartile range of attention spans of high school students". Wait, but the option about range: "The range of attention span of college students is greater than the range of attention spans of high school students" is false. So the two true options are:

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

Answer:

• The median attention span of college students is greater than the median attention span 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.