The set of 3 numbers with a mean of 5 and a standard deviation of 5 is given below
[tex]0,5,10[/tex]The mean of the set is
[tex]\begin{gathered} \text{mean}=\frac{0+5+10}{3}=\frac{15}{3}=5 \\ \operatorname{mean}=5 \end{gathered}[/tex]The standard deviation is calculated using the formula
[tex]\sqrt{\frac{\sum_{i=1}^n\left(x_i-\bar{x}\right)^2}{n-1}}[/tex][tex]\begin{gathered} \text{Standard deviation=}\sqrt[]{\frac{(0-5)^2+(5-5)^2+(10-5)^2}{3-1}} \\ \text{Standard deviation=}\sqrt[]{\frac{25+0+25^{}}{2}}=\sqrt[]{\frac{50}{2}} \\ \text{Standard deviation=}\sqrt[]{25} \\ \text{Standard deviation=}5 \end{gathered}[/tex]Thus, the data set is 0,5, and 10
