Can you find sets of positive integers that satisfy the following? 1. Three numbers with mean 3 and mode 2

2. Three numbers with mean 7 and mode 10

3. Three numbers with mean 8, median 10 and range 8

4. Four numbers with mean 7.5, mode 6 and median 7

5. Four numbers with mean 6, median 6.5 and range 11

6. Five numbers with mean 4, mode 3 and range 9

{ 6 ,6 , 6, 7 , 10 } , { 5 , 6 , 6 , 8 , 10 }  ,  { 4 , 6 , 6 , 9 , 10 } , etc. (There's a lot more)

Explanation:

Mean of a set is equal to the terms added divided by the number of terms.

Median is the middle number when you order out the terms in the set in the increasing order from left to out.

Mode is the most occurring term.

Now, since the mean of five number  

{ v , w , x , y , z }  is  7 , we have:  v + w + x + y + z 5 = 7  => v + w + x + y + z = 35

Now, the middle term, the median, is 6.

Now we have:  

{ v , w , 6 , y, z }

Since the mode is 6, there has to be at least two 6.

There isn't enough limitations to have one answer.

For example, you could have this:

{ 4 , 5 , 6 , 6 , 14 }

The values add up to 35, the middle term is 6, and 6 is the most occurring.

You will find many other sets possible.

Step-by-step explanation:

Use this way to solve the rest.

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step-by-step explanation:

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