Question

question #3
simon takes seven tests in social studies class. the table shows his scores.

test	score
2	68
3	76
4	90
5	79
6	70
7	75

after taking two more tests, the mean of simons test - score data increases but the median remains the same. which values could be the scores of the two additional tests?
a 77 and 78
b 58 and 80
c 75 and 100
d 90 and 94

Explanation:

Step1: Arrange original scores

Arrange 91, 68, 76, 90, 79, 70, 75 in ascending - order: 68, 70, 75, 76, 79, 90, 91. The median of 7 numbers is the 4th - number, so the median is 76.

Step2: Analyze option A

If the two scores are 77 and 78, the new set of scores in ascending - order is 68, 70, 75, 76, 77, 78, 79, 90, 91. The median is 76. The original mean is $\frac{91 + 68+76 + 90+79+70+75}{7}=\frac{549}{7}\approx78.43$. The new mean is $\frac{549 + 77+78}{9}=\frac{704}{9}\approx78.22$, the mean decreases, so option A is incorrect.

Step3: Analyze option B

If the two scores are 74 and 80, the new set of scores in ascending - order is 68, 70, 74, 75, 76, 79, 80, 90, 91. The median is 76. The new mean is $\frac{549+74 + 80}{9}=\frac{703}{9}\approx78.11$, the mean decreases, so option B is incorrect.

Step4: Analyze option C

If the two scores are 75 and 100, the new set of scores in ascending - order is 68, 70, 75, 75, 76, 79, 90, 91, 100. The median is 76. The new mean is $\frac{549+75 + 100}{9}=\frac{724}{9}\approx80.44$, the mean increases, so option C is correct.

Step5: Analyze option D

If the two scores are 90 and 94, the new set of scores in ascending - order is 68, 70, 75, 76, 79, 90, 90, 91, 94. The median is 79, the median changes, so option D is incorrect.

Answer:

C. 75 and 100