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.