Question

Katies business professor lost his computer memory, which contained her five test scores for the course. A summary of the scores (each of which was an integer from 0 to 100) indicates the following:

The mean was 88
The median was 87
The mode was 92
(The data set was not bimodal) What is the least possible number among the missing scores

Answer 1

The least possible number among the missing scores is 83.

Explanation:

If we arrange the test scores in non decreasing order then obviously
`87` will be at the third position since it is the median.

As it is not bimodal and the given mode is greater than the median the arrangement of test scores should be as given below.(assuming the unknown scores be
`x,y` and
`x<y`)

`x,y,87,92,92`

Now let us verify it with the mean;

`(x+y+87+92+92)/(5) = 88`

⇒
`x+y+271=440`

⇒
`x+y=169`

Now for
`x` to be least;
`y` must be maximum possible value here.

Therefore
`y` is equal to
`86`

⇒
`x=83`