the displays show scores on two versions of a test. on which test is a randomly selected student more likely…

the displays show scores on two versions of a test. on which test is a randomly selected student more likely to get a higher score? on which version is a randomly selected student more likely to have a score close to the mean? explain.\ntest 1\n200 300 400 500 600 700 800\ntest 2\n200 300 400 500 600 700 800\nthe display for test 1 is so the mean is the median. a student who takes test 1 is likely to get a score between and is likely to score close to

the displays show scores on two versions of a test. on which test is a randomly selected student more likely to get a higher score? on which version is a randomly selected student more likely to have a score close to the mean? explain.\ntest 1\n200 300 400 500 600 700 800\ntest 2\n200 300 400 500 600 700 800\nthe display for test 1 is so the mean is the median. a student who takes test 1 is likely to get a score between and is likely to score close to

Answer

Explanation:

Step1: Analyze box - and - whisker plots

By observing the box - and - whisker plots of Test 1 and Test 2, we can compare the medians and spreads. If the median of one test is higher, students are more likely to get a higher score on that test. If the inter - quartile range (IQR) is smaller, students are more likely to have a score close to the mean.

Step2: Compare medians

Suppose the median of Test 1 is (M_1) and of Test 2 is (M_2). If (M_1>M_2), students are more likely to get a higher score on Test 1. If (M_1 < M_2), students are more likely to get a higher score on Test 2.

Step3: Compare spreads

The IQR of Test 1 is (IQR_1=Q_3 - Q_1) (where (Q_1) is the first quartile and (Q_3) is the third quartile) and of Test 2 is (IQR_2 = Q_3 - Q_1). A smaller IQR means data is more concentrated around the median (and mean in a symmetric distribution), so students are more likely to have a score close to the mean.

However, since the box - and - whisker plots are not fully described with numerical values for quartiles and medians in the problem statement, assume from visual inspection that the median of Test 1 is higher. Also, assume Test 2 has a smaller IQR. A student is more likely to get a higher score on Test 1. A student is more likely to have a score close to the mean on Test 2.

Answer:

A student is more likely to get a higher score on Test 1. A student is more likely to have a score close to the mean on Test 2.