The mode of five numbers is 1,the median is 4 and the mean is.What are the numbers?

1 Answer
Dec 2, 2017

Only the following two combinations are possible:

#1" " , 1" ", 4" ", 5" "9#

#1" " , 1" ", 4" ", 6" "8#

Explanation:

I will assume that both the median and the mean are #4#.

The median is the value in the middle of a set of data arranged in order. There are #5# numbers, so the third one has to be #4#

#--- , ---, 4 ---, ---" "larr# the median is #4#

The mode is the value that occurs the most often. The mode is #1#. There are only two possible spaces for #1#, so there must be two of them.

#1" " , 1" ", 4 ---, ---" "larr# the mode is #1#

If the mean is #4# and there are five numbers, it means that the total of the five numbers is #5 xx 4 =20#

We already have a total of #6#, so the sum of the remaining teo numbers must be #20-6 =14#

Any combination of numbers bigger than 4 will do, except they cannot both be equal to #7#, because then there would be two modes.

Only the following two combinations are possible:

#1" " , 1" ", 4" ", 5" "9#

#1" " , 1" ", 4" ", 6" "8#

The following are not possible:

#1" " , 1" ", 4" ", 4" "10" "larr# there are two modes

#1" " , 1" ", 4" ",7" "7" "larr# there are two modes

#1" " , 1" ", 3" ", 4" "11" "larr# the median is not #4#

#1" " , 1" ", 2" ", 4" "12" "larr# the median is not #4#