Question

How many distinct sets of three positive integers have a mean of 6,a median of 7,and no mode?

Answer 1

Find answer in image below

Answer 2

Given mean=6, median=7, no mode

Let the three positive integers be x, x+1, x+2

Now mean = (x+x+1+x+2)/3 = (3x+3)/3 = x+1

But here x+1=6 i.e., x=5 ... which means we have 5 sets of numbers whose mean is 6. (But this is just for knowing the number of sets, we can't use it further) , and also from definition of mean

Mean= sum/ total number of integers... i.e.,

we get that sum= mean*total no. Of integers = 6*3=18

As median given is 7 and we have only 3 intergers in the set .. we can know that middle number is 7 ..i.e., the number set is :

0+7+11=18

1+7+10=18

2+7+9=18

3+7+8=18

5+7+6=18

As there is no mode we cant get the set (4+7+7)