### Video Transcript

Given the mean of the values eight,
22, 4, 12, and 𝑥 is 15, find the value of 𝑥.

In this question, we’re given a
data set which includes an unknown value 𝑥. We’re told that the mean of these
values is 15 and we need to find the unknown value of 𝑥. The mean of a data set is found by
calculating the sum of the data values and dividing by the total number of data
values. So, we can start by adding our
values eight plus 22 plus four plus 12 plus 𝑥. And as we know that there are five
data values, then we would be dividing by five.

Notice that even though we don’t
know what 𝑥 is yet, we still include it as one of the values. We’ve been given that the mean is
equal to 15. So, we can put this on the
left-hand side of our equation. At the minute, we don’t know the
value of 𝑥, but we can go ahead and add together the other values in our set. We can then simplify our
calculation as 15 equals 46 plus 𝑥 over five. We now need to rearrange this
equation in order to find the value of 𝑥.

Multiplying both sides of this
equation by five gives us 75 equals 46 plus 𝑥. Subtracting 46 then from both sides
of our equation, we have 75 minus 46 equals 𝑥. 29 equals 𝑥 then. And so, our answer is that 𝑥
equals 29. We can check our answer by
substituting the value of 𝑥 equals 29, summing with the rest of the values,
dividing by five, and checking that we get a value of 15. And thus confirming the value 𝑥
equals 29.