Belinda took three tests. If her median score was 55 , her mean score was 66 , and the range was 39 , what were her three test scores?
A) 47 , 66 , 85
B) 27 , 55 , 66
C) 36 , 55 , 74
D) 52 , 55 , 91
E) 55 , 66 , 94

Question

Quizplus · Accepted Answer

We know the median is 55, so one of her scores must be 55.
We know the mean is 66, so the sum of her scores must be 66 * 3 = 198.
We know the range is 39, so the difference between her highest and lowest score is 39.
Let x be her lowest score. Then her highest score is x + 39. 
We know the median is the middle number when the scores are listed in order, so either her lowest or highest score must be 55. 
If her lowest score is 55, then her highest score is 55 + 39 = 94. The sum of her scores is 55 + x + 94 = 149 + x, and the mean is (149 + x)/3. We can solve the equation (149 + x)/3 = 66 to find x = 91. This gives us the scores 55, 91, and 94, which has a range of 39 and a median of 55, as required.
If her highest score is 55, then her lowest score is 55 - 39 = 16. The sum of her scores is 16 + x + 55 = 71 + x, and the mean is (71 + x)/3. We can solve the equation (71 + x)/3 = 66 to find x = 93. This gives us the scores 16, 55, and 93, which has a range of 77 and a median of 55, which is not possible. 
Therefore, the only possible answer is D) 52, 55, 91.

Belinda Took Three Tests