How do you write down 5 numbers where the mean is 7 and the median and mode are 6?

Feb 21, 2018

$6 , 6 , 6 , 7 , 10$

Explanation:

The mean is the average of the 5 numbers which is 7; considering this there is another aspect to take into account, we have to take into account the median being 6. A median means that if the numbers are going to be put in order, the mid-value has to be 6.

The total amount of numbers is 5. So, it should be:

$x , x , 6 , x , x$

Considering the x as the unknown numbers which we need to determine with the help of the mode property, or the numbers that appears most frequently we have:

$6 , 6 , 6 , x , x$

We need now to include one x=7 as the average is 7 and not an approximation as well an x=10 :

$6 , 6 , 6 , 7 , 10$

To check that this is correct:
median or mid-value: 6;
mode or most repeating number: 6

Now,we need to take the average. This is:

$\frac{6 + 6 + 6 + 7 + 10}{5} = 7$

Feb 23, 2018

$\left\{6 , 6 , 6 , 7 , 10\right\} , \left\{5 , 6 , 6 , 8 , 10\right\}$, $\left\{4 , 6 , 6 , 9 , 10\right\}$, 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 $\left\{v , w , x , y , z\right\}$ is $7$, we have:

$\frac{v + w + x + y + z}{5} = 7$

=>$v + w + x + y + z = 35$

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

Now we have: $\left\{v , w , 6 , y , z\right\}$ 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:

$\left\{4 , 5 , 6 , 6 , 14\right\}$ The values add up to 35, the middle term is 6, and 6 is the most occurring.

You will find many other sets possible.