Question

Find the value of x such that the data set has the given mean.98, 121, 104, 113, 107, x; mean 116

Answer 1

Mean : The "mean" is the "average" , for which add up all the numbers and then divide by the number of numbers.

`\text{ Mean =}\frac{\text{ Sum of all numbers in the data}}{Total\text{ number of data}}`

The given set of data; 98, 121, 104, 113, 107, x

Sum of all data : 98 + 121 + 104 + 113 + 107 + x = 543 + x

Total numbers of data : 6

Mean of the data : 116

Substitute the value in the expression of mean;

`\begin{gathered} \text{ Mean =}\frac{\text{ Sum of all numbers in the data}}{Total\text{ number of data}} \\ 116=(543+x)/(6) \end{gathered}`

Simplify the expression for x;

`\begin{gathered} 116=(543+x)/(6) \\ 543+x=116*6 \\ 543+x=696 \\ x=696-543 \\ x=153 \end{gathered}`

So, the number is 153

Answer : x = 153