Question

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.
all of the college students in the study had greater attention spans than the high school students.
the minimum attention span of high school students is greater than the minimum attention span of college students.

Explanation:

Step1: Identify median from box - and - whisker plot

The line inside the box represents the median. For college students, the median is around 16 and for high - school students, it is around 14. So, the median attention span of college students is greater than that of high - school students.

Step2: Calculate range

Range = Maximum - Minimum. For college students, range is approximately \(22 - 8=14\). For high - school students, range is approximately \(18 - 6 = 12\). So, the range of attention span of college students is greater than that of high - school students.

Step3: Calculate inter - quartile range (IQR)

IQR = \(Q_3 - Q_1\). For college students, \(Q_1\approx12\), \(Q_3\approx18\), \(IQR_{college}=18 - 12 = 6\). For high - school students, \(Q_1\approx10\), \(Q_3\approx14\), \(IQR_{high - school}=14 - 10 = 4\). The inter - quartile range of college students is greater than that of high - school students.

Step4: Check minimum values

The minimum value for high - school students is 6 and for college students is 8. So, the minimum attention span of college students is greater than that of high - school students, not the other way around. Also, not all college students had greater attention spans than high - school students as there is an overlap in the data.

Answer:

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.