Question Video: Calculating a Missing Value in a Data Set given the Mean | Nagwa Question Video: Calculating a Missing Value in a Data Set given the Mean | Nagwa

# Question Video: Calculating a Missing Value in a Data Set given the Mean Mathematics

Given the mean of the values 8, 22, 4, 12, and 𝑥 is 15, find the value of 𝑥.

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### 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.

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