the table shows the summary statistics of scores on an exam for two random samples of high school…

the table shows the summary statistics of scores on an exam for two random samples of high school students.\n\nexam scores\n| |min|q1|q2|q3|max|\n|--|--|--|--|--|--|\n|red mountain high|51|67|75.5|83|99|\n|all prep academy|50|59.5|76.5|89|99|\n\nchoose all the statements that correctly compare the groups of students.\na. the range in statistics exam scores for all prep academy is smaller.\nb. students at all prep academy have a greater median statistic exam score.\nc. students at red mountain high have a smaller mean statistic exam score.\nd. the scores for students at red mountain high show a smaller interquartile range.\ne. the scores for students at all prep academy show greater variability about the median.

the table shows the summary statistics of scores on an exam for two random samples of high school students.\n\nexam scores\n| |min|q1|q2|q3|max|\n|--|--|--|--|--|--|\n|red mountain high|51|67|75.5|83|99|\n|all prep academy|50|59.5|76.5|89|99|\n\nchoose all the statements that correctly compare the groups of students.\na. the range in statistics exam scores for all prep academy is smaller.\nb. students at all prep academy have a greater median statistic exam score.\nc. students at red mountain high have a smaller mean statistic exam score.\nd. the scores for students at red mountain high show a smaller interquartile range.\ne. the scores for students at all prep academy show greater variability about the median.

Answer

Explanation:

Step1: Calculate range for each school

Range = Max - Min. For Red Mountain High, range = 99 - 51 = 48. For All Prep Academy, range = 99 - 50 = 49. So A is false.

Step2: Identify median

Median is Q2. For Red Mountain High, median = 75.5. For All Prep Academy, median = 76.5. So B is true.

Step3: Calculate inter - quartile range (IQR)

IQR = Q3 - Q1. For Red Mountain High, IQR = 83 - 67 = 16. For All Prep Academy, IQR = 89 - 59.5 = 29.5. So D is true.

Step4: Analyze variability about median

We can't determine variability about median just from five - number summary without more data. And we can't determine mean from five - number summary. So C and E are not determinable from given data.

Answer:

B. Students at All Prep Academy have a greater median statistic exam score. D. The scores for students at Red Mountain High show a smaller interquartile range.