Question

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

Answer 1

Answer:

Step-by-step explanation: DISTINCT SET OF THREE POSITIVE INTEGERS HAVE MEAN 6MEDIAN ,MODE WILL 6+7= 13 MODE

Answer 2

Answer: 4 sets

Step-by-step explanation:

Let A , B , C are the sets of positive integers

Now n is 3 which is odd

Therefore as given Median is 7

In A, B, C ;   B is median

Therefore B = 7

Now mean = 6

$Mean = \dfrac{\text { Sum of observation} }{\text { Number of observation }} \\\\6 = \dfrac{A+B+C}{3} \\\\\Rightarrow A+B+C= 18 \\\\ \text {As B= 7 we have }\\\\\Rightarrow A+7+C= 18 \\\\\Rightarrow A+C= 11$

Possible combination of A+C= 11 is

A=1 C= 10

A= 2 C= 9

A= 3 C= 8

A= 4 C= 7

A= 5 C= 6

Now the function have no mode

therefore we exclude A= 4 and C= 7

The distinct sets are 1) 1, 7, 10 ;2) 2 , 7, 9 ; 3) 3, 7, 8 ; 4) 5, 7, 6

Hence, there are distinct 4 sets of three positive integers that have mean of 6 median 7 and no mode