Video Transcript
Noah has the following data: 18,
𝑚, 11, 15. If the mean is 13, find the value
of 𝑚.
Noah’s data set contains four
values, three of which are known and one of which is unknown. We are also told that the mean of
these values is 13. The mean of a data set is
calculated by finding the sum of all the values in the data set and dividing it by
how many values there are.
We know that the mean is 13 and the
number of values is four. So we can form an equation. 13 is equal to the sum of all the
values divided by four. Multiplying both sides of this
equation by four, we find that the sum of all the values is 52. We’re now able to form an equation
that will enable us to determine the value of 𝑚. Summing the four values gives 18
plus 𝑚 plus 11 plus 15, and we can equate this expression to 52. Simplifying on the left-hand side
gives 𝑚 plus 44 equals 52. And then subtracting 44 from each
side gives 𝑚 equals eight.
So, by first using the definition
of the mean to find the sum of all the values in the data set, we’ve found that the
missing value, 𝑚, is eight.
