Question

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

Answer 1

Answer:

The possible sets are (1,7,10),(2,7,9),(3,7,8).

Step-by-step explanation:

Given : Sets of three positive integers have a mean of 6, a median of 7, and no mode.

To find : How many distinct sets are there ?

Solution :

Let the set be a,b,c

Where, a<b<c

We have given,

Median is 7

i.e. b=7

Mean is 6

i.e. $M=\frac{\sum x_n}{n}$

$6=\frac{a+b+c}{3}$

$18=a+7+c$

$a+c=11$

There is no mode so no number repeats.

Now, We have different values of a and c which satisfy the equation.

i.e. The value of a is 1,2 or 3.

The value of c is 10,9 or 8

As we don't take further number because the next number is 7 and it repeats in the data set which cannot be possible.

Therefore, The possible sets are (1,7,10),(2,7,9),(3,7,8).

Answer 2

Answer:

Mean=6

∴ Sum=6×3=18

Median=7

It must be the numbers less than 7 and greater than 7 and 7 must be included.

Examples:{1,7,10}

{2,7,9} and {3,7,8}

So there are three sets.