Video Transcript
Given that the mean of the values
four, 𝑥, five, eight, and 18 is 10, find the value of 𝑥.
We’ve been given the mean of a set
of values and all but one of the values themselves. The mean of a data set is
calculated by finding the sum of all the data values and dividing this total by how
many values there are. We know that the mean of the values
is 10. And looking at the list, we can
identify that there are five values in the data set. We therefore know that the sum of
all the data values divided by five is equal to 10. Multiplying both sides of this
equation by five, we find that the sum of all the data values is 50. We’re now able to form an equation
that will allow us to determine the value of 𝑥.
Summing the five data values and
equating this expression with 50 gives the equation four plus 𝑥 plus five plus
eight plus 18 equals 50. Simplifying on the left-hand side
gives 𝑥 plus 35 equals 50. And finally, subtracting 35 from
each side of the equation gives 𝑥 equals 15. We’ve found that the value of 𝑥,
the missing value in this data set, is 15.
