Question

Create a set of three numbers with a mean of 5 and a standard deviation of 5.

Answer 1

The set of 3 numbers with a mean of 5 and a standard deviation of 5 is given below

`0,5,10`

The mean of the set is

The standard deviation is calculated using the formula

`\sqrt{\frac{\sum_(i=1)^n\left(x_i-\bar{x}\right)^2}{n-1}}`
`\begin{gathered} \text{Standard deviation=}\sqrt[]{((0-5)^2+(5-5)^2+(10-5)^2)/(3-1)} \\ \text{Standard deviation=}\sqrt[]{\frac{25+0+25^{}}{2}}=\sqrt[]{(50)/(2)} \\ \text{Standard deviation=}\sqrt[]{25} \\ \text{Standard deviation=}5 \end{gathered}`

Thus, the data set is 0,5, and 10