Question

the mean of the following set of numbers is 6. find x. 4, 2, 5, 9, 8, x

Explanation:

Step1: Recall the formula for the mean

The formula for the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(n\) is the number of data points and \(\sum_{i=1}^{n}x_{i}\) is the sum of the data points. Here \(n = 6\) and \(\bar{x}=6\). So, \(\sum_{i = 1}^{6}x_{i}=n\times\bar{x}\).

Step2: Calculate the sum of the known numbers

The sum of the known numbers is \(4 + 2+5 + 9+8=28\). Let the unknown number be \(x\). Then the sum of all the numbers is \(28 + x\).

Step3: Set up the equation using the mean formula

Since \(\sum_{i = 1}^{6}x_{i}=n\times\bar{x}\), we have \(28 + x=6\times6\).

Step4: Solve the equation for \(x\)

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Answer:

\(x = 8\)