Question

the table shows the test scores of students who
studied for a test as a group (group a) and students
who studied individually (group b).
student test scores (out of 100)
which would be the best measures of center and
variation to use to compare the data?
the scores of group b are skewed right, so the
mean and range are the best measures for
comparison.
both distributions are nearly symmetric, so the
mean and the standard deviation are the best
measures for comparison.
both distributions are nearly symmetric, so the
median and the interquartile range are the best
measures for comparison.
the scores of both groups are skewed, so the
median and standard deviation are the best
measures for comparison.

Explanation:

Step1: Analyze data distribution

If data is symmetric, mean and standard deviation are good measures. If skewed, median and inter - quartile range are better.

Step2: Check symmetry

Group A: 84, 60, 77, 96, 92, 88, 68, 84, 92, 100. Group B: 82, 68, 85, 87, 83, 85, 83, 70, 80, 88.
Sort Group A: 60, 68, 77, 84, 84, 88, 92, 92, 96, 100. Sort Group B: 68, 70, 80, 82, 83, 83, 85, 85, 87, 88.
Both distributions are nearly symmetric (Group A: mean \(\bar{x}_A=\frac{60 + 68+77+84+84+88+92+92+96+100}{10}=84.1\), median \(M_A=\frac{84 + 88}{2}=86\); Group B: mean \(\bar{x}_B=\frac{68+70+80+82+83+83+85+85+87+88}{10}=81.1\), median \(M_B=\frac{83+83}{2}=83\). The differences between mean and median are small).

Answer:

Both distributions are nearly symmetric, so the mean and the standard deviation are the best measures for comparison.