The scores of a dart game are 46, 25, 33, 56, 31, 46, 49, 55, a, b, and c. If 33 is the only mode, 46 is the median, and a>c, what is the possible range of values for a?

Answer 1

Put the values into ascending order:

46, 25, 33, 56, 31, 46, 49, 55, a, b, and c

___ 25 ___ 31 ___ 33 ___ 46 46 ___ 49 ___ 55 ___ 56 ___ [note: a,b,c go in the underlines]

Given:

a>c

33 is the only mode

46 is the median

If "33 is the only mode (the value that occurs most often)." then there must be 2 or 3 more 33's (to outnumber the two 46's]. a,b,c cannot all be 33 because a>c. Therefore b=33 and c=33.

Now we have:

25 31 33 33 33 46 46 ___ 49 ___ 55 ___ 56 ___ [note: a goes in the underlines]

For 46 to be the median (the middle value), we now have five below and five above it:

25 31 33 33 33 46 46 ___ 49 ___ 55 ___ 56 ___ [note: a goes in the underlines]

The value for a is in the range [46, maxdartboardvalue]

Answer 2

25, 31, 33, 46, 46, 49, 55, 56, c,b,a

for the mode to be 33, then c=b=33.

25, 31, 33, 33,33 , 46, 46, 49, 55, 56<--- median is 46 for a>=47