Miguel takes 5 tests. Each score is a whole number between 0 and 100, inclusive. The mean of his scores is 80, the median is 81, and there is just one mode and it is 88. What is the least possible score Miguel could have received on any one test?
1 Answer
Possible lowest score = 63
Miguel's Scores: 63, 80, 81, 88, 88
Explanation:
To simplify thing, the given are the following:
 There are five tests, with scores of 0 to 100



Reviewing the meaning of the measures of central tendencies:
 Mean: Average of the scores
 Median: Middle score
 Mode: The score with the highest frequency
So let Miguel's scores arranged in ascending order be:
Since we know that the median (the middle score) is 81, and we have a total of five scores, then we know that
in this case Miguel's scores would be:
Now, we know that the mode is 88, this means that at least two of Miguel's scores are 88. But as we can see in our given, there may only be two values greater than 81 in order to satisfy the condition
Lastly, in order to get the values of
Considering that the
So working on this,
Hence Miguel's scores are: 63, 80, 81, 88, 88
Checking if all conditions are satisfied:
(since it is the middle score)
(since two of Miguel's scores are 88, and no other score has a frequency of 2 or more)