Answer:
[tex]median=mean=\frac{R_{n-1}}{2}+9[/tex]
Step-by-step explanation:
The first thing to identify is that this one is a consecutive set, meaning that the increment between each number is the same, in this case, an increment of 3 between each number, when sets have this type of behavior, and only on these cases, the mean and the median are the same, let's look at some examples:
[2, 4, 6, 8, 10, 12]
The mean would be:
mean=[tex]\frac{2+4+6+8+10+12}{6}[/tex]=7
Since the number of elements is even, the median would be the average of the two middle terms:
median=[tex]\frac{6+8}{2}[/tex]=7
As you can see mean=median
There is one more thing to help you in this exercise, for consecutive sets, the mean can also be calculated by the formula:
[tex]mean=\frac{x_{1} + x_{n} }{2}[/tex]
Where [tex]x_{1}[/tex] is the first term of the set and [tex]x_{n}[/tex] is the last.
If we ran this formula with the set i used as an example:
mean=[tex]\frac{2+12}{2}=7[/tex].
So applying all of that to the set given we would have:
[tex]median=mean=\frac{15+R_{n-1}+3}{2} =\frac{R_{n-1}+18}{2} =\frac{R_{n-1}}{2}+9[/tex]
