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

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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


\begin{gathered} \text{mean}=(0+5+10)/(3)=(15)/(3)=5 \\ \operatorname{mean}=5 \end{gathered}

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

User Futbolpal
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