document.write( "Question 864851: Katie Campbell's Business professor lost his grade book, which contained Katie's five test scores. Each of which was an integer from 0 to 100. A summary of the scores indicates:\r
\n" ); document.write( "\n" ); document.write( "The mean was 88.
\n" ); document.write( "The median was 87.
\n" ); document.write( "The mode was 92.
\n" ); document.write( "The data set was not bimodal. What is the least possible number among the missing scores? \n" ); document.write( "

Algebra.Com's Answer #521325 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Hint: The median is 87. So that's a given number in the set of 5 (because the median is always part of a set with an odd number of numbers). This means you have 2 values above the median of 87 and two values below it. The two values above the median must be 92 since this is the only mode. There cannot be just one copy of 92 or else you wouldn't have a mode. You cannot have more than two copies of 92 or else that would bump the median of 87 down (and not make 87 the median)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So our data set looks like this: x, y, 87, 92, 92\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now add up the values and divide by 5 to get the mean of 88: $\"%28x%2By%2B87%2B92%2B92%29%2F5+=+88\"$ . From here, solve for y and get it in terms of x. You'll have a linear equation and you can graph it to find ordered pairs on it that are possible (x,y) values. Keep in mind that x < 87 and y < 87. If either x = 87 or y = 87, then you'd have another mode, but this set is not bimodal.
\n" ); document.write( " \n" ); document.write( "

\n" );