Given that the mean of values four, 𝑥, five, eight, and eighteen is ten, find the
value of 𝑥.
For this problem, we’re already given the mean of the values; we know that the mean is
ten. The mean of five values is ten, but we’re missing one of those five values. We
don’t know what 𝑥 is, but we know that when you add four plus 𝑥 plus five plus
eight plus eighteen and then find the mean, you have ten. Let’s set up an equation to
help us solve this problem.
We know that the mean equals the sum of the values divided by the number of values in
the set. What we should do from here is plugging all the information that we know
into this formula. Starting off, we’ll plug in ten for the mean. Then, we’ll add the
sum of all the values we know. We know four, five, eight, and eighteen, and the
missing value is 𝑥. We also know that the total number of values in our set is five.
From here, we can do a little simplification to solve for 𝑥. We should just do a
little addition: adding four plus five plus eight plus eighteen; that equals
thirty-five. We’ll bring down our 𝑥 because we don’t know what 𝑥 is yet. Also bring
down our five. To get rid of the five in the denominator here, I’m going to multiply
this side of the equation by five over one.
But if I multiplied one side of the equation by five over one, I’ve to multiply both
sides of the equation by five over one to keep our equation balanced. When we
simplify that, we’re left with fifty equals thirty-five plus 𝑥. I then subtract
thirty-five from both sides to isolate our 𝑥-value. When I take away thirty-five
from fifty, I’m left with fifteen. 𝑥 equals fifteen; that’s our missing value.