Question Video: Finding the Value of a Variable in a Data Set Using the Median Mathematics • 6th Grade

Video Transcript

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

Here, we are given three separate values. And in each value, there is an unknown component of 𝑥 that we need to determine. However, we are given the information that the median of these values is 13. Let’s 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 𝑥 doesn’t 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 𝑥 plus three. The second value in order would be 𝑥 plus nine. And finally, 𝑥 plus 15 would be the largest value. The middle value is therefore that of 𝑥 plus nine.

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

Although not required, by substituting 𝑥 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 𝑥 equals four must be correct.