### Video Transcript

Given that the median of the values
π₯ plus nine, π₯ plus three, and π₯ plus 15 is 13, determine the value of π₯.

Here, we are given three separate
values. And in each value, there is an
unknown component of π₯ that we need to determine. However, we are given the
information that the median of these values is 13. Letβs recall that the median of a
data set is the middle value when the data is given in ascending or descending
order.

So in order to find the median, we
need to check if the values are already in order. Notice that because π₯ doesnβt
change between the values, then the values themselves will change because of the
plus nine, plus three, and plus 15. So the lowest value must be π₯ plus
three. The second value in order would be
π₯ plus nine. And finally, π₯ plus 15 would be
the largest value. The middle value is therefore that
of π₯ plus nine.

Now, we were given that the median
is 13. But we also know that this middle
value, the median, is also π₯ plus nine. So we have that π₯ plus nine is
equal to 13. And by subtracting nine from both
sides, we have that π₯ equals four. And thatβs our answer for the value
of π₯.

Although not required, by
substituting π₯ equals four, we can work out that the original values must be 13,
12, and 19. In ascending order these would be
12, 13, and 19. So we can confirm that the median
is indeed 13. And so the value of π₯ equals four
must be correct.