Question

Find the value of x such that the data set has a mean of 105. 102, 121, 106, 113, 110

Answer 1

Step 1

Write an expression for the mean of a set of numbers

`\bar{x}(The\text{ mean) = }\frac{sum\text{ of set of numbers}}{nu\text{mber of set of numbers }}`

Sum of set number = 102 + 121 + 106 + 113 + 110 + x =552 + x

number of set of numbers = 6

mean = 105

Step 2

Substitute in the values and find the value of x

`\begin{gathered} 105=\frac{552\text{ + x}}{6} \\ 105=(552+x)/(6) \\ 105*6\text{ = 552 + x} \\ 630\text{ = 552 +x } \\ x\text{ = 630 - 552} \\ x\text{ =78} \\ \end{gathered}`

x = 78