Question

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

test	score
1	91
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 91 and 94

Explanation:

Step1: Arrange original scores in ascending order

68, 70, 75, 76, 79, 90, 91. The median of 7 - data - set is the 4th value, so the median is 76. The mean of the original scores is $\frac{91 + 68+76 + 90+79+70+75}{7}=\frac{549}{7}\approx78.43$.

Step2: Analyze option A

If the scores are 77 and 78, the new data - set in ascending order is 68, 70, 75, 76, 77, 78, 79, 90, 91. The median is still 76. The new mean is $\frac{549+77 + 78}{9}=\frac{704}{9}\approx78.22$, which is less than the original mean, so A is incorrect.

Step3: Analyze option B

If the scores are 58 and 80, the new data - set in ascending order is 58, 68, 70, 75, 76, 79, 80, 90, 91. The median is 76. The new mean is $\frac{549+58 + 80}{9}=\frac{687}{9}\approx76.33$, which is less than the original mean, so B is incorrect.

Step4: Analyze option C

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

Step5: Analyze option D

If the scores are 91 and 94, the new data - set in ascending order is 68, 70, 75, 76, 79, 90, 91, 91, 94. The median is 79, which is not the same as the original median, so D is incorrect.

Answer:

C. 75 and 100