Question

select the correct answer.
the table lists the test scores william and andre received on five math assessments.

williams scores	andres scores
97	74
78	73
81	87
91	82

which statement best describes the difference of the mean of the two data sets?
a. it is equal to about 0.5 times the mean absolute deviation of either data set.
b. it is equal to about 1 times the mean absolute deviation of either data set.
c. it is equal to about 1.5 times the mean absolute deviation of either data set.
d. it is equal to about 2 times the mean absolute deviation of either data set.

Explanation:

Step1: Calculate William's mean

Mean = $\frac{89+97+78+81+91}{5} = \frac{436}{5} = 87.2$

Step2: Calculate Andre's mean

Mean = $\frac{90+74+73+87+82}{5} = \frac{406}{5} = 81.2$

Step3: Find mean difference

Difference = $87.2 - 81.2 = 6$

Step4: Calculate William's MAD

Deviations from 87.2: $|89-87.2|=1.8$, $|97-87.2|=9.8$, $|78-87.2|=9.2$, $|81-87.2|=6.2$, $|91-87.2|=3.8$
MAD = $\frac{1.8+9.8+9.2+6.2+3.8}{5} = \frac{30.8}{5} = 6.16 \approx 6$

Step5: Calculate Andre's MAD

Deviations from 81.2: $|90-81.2|=8.8$, $|74-81.2|=7.2$, $|73-81.2|=8.2$, $|87-81.2|=5.8$, $|82-81.2|=0.8$
MAD = $\frac{8.8+7.2+8.2+5.8+0.8}{5} = \frac{30.8}{5} = 6.16 \approx 6$

Step6: Compare difference to MAD

Mean difference (6) ≈ 1×MAD (≈6)

Answer:

B. It is equal to about 1 times the mean absolute deviation of either data set.