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

We have five value in the data-set

The third value will be 10 since we want the median to be 10

We want the mean to be 14

To find the mean of a data set, we divide the sum of the values by the number of values

Mean = Sum of values ÷ Number of values
14 = Sum of values ÷ 5
Sum of values = 14 × 5
Sum of values = 70

So we need 5 values that add up to 70, one of the value is 10, which is the median. We would want two values that are smaller than 10 and two values more than 10.

These four value must add up to 70 - 10 = 60

From here we can do trial and error:

Choose any two values less than 10, say 9 and 8
We now have in total 8 + 9 + 10 = 27

We have 70 - 27 = 43 left to find
Choose any two values that are bigger than 10 that add up to 43, for example, 20 and 23

Now we have our 5 values; 

8        9         10        20         23

Do the checking bit:

We can see from the set, the median is 10
Mean = [8+9+10+20+23] ÷ 5 = 70 ÷ 5 = 14

We can have values other than 8, 9, 20 and 23 as long as two values smaller than 10 and two values more than 10. All five values must add up to 70.