Question

Create a set of five positive numbers (Repeats allowed) that have a median of $10$ and a mean of $14$ what thought process did you use to create your numbers? i have no clue

Answer 1

Find the numbers:

Given that the mean of $5$ numbers is $14$.

Therefore the sum of those five numbers is $14\times 5=70$

Also The median of those $5$ numbers is $10$

Therefore it can be concluded that the third number of the set is $10$.

Now the first two numbers of the set will be less than $10$.

So let us assume that the two numbers be $6\mathrm{and}8$

Now there are three numbers in the data set which are $6,8,10.$

Now sum of these three numbers is $24$.

Also the sum of 5 numbers in the data set is $70.$

Hence, The sum of remaining two numbers can be given as $70-24=46$

So select any two numbers whose addition is $46$.

Therefore the two numbers be $22,24$.

Hence, The set of 5 numbers is $\mathbf{6}\mathbf{,}\mathbf{8}\mathbf{,}\mathbf{10}\mathbf{,}\mathbf{22}\mathbf{,}\mathbf{24}\mathbf{.}$