Question

find the standard deviation of the data set that is obtained after subtracting three from each value 246, 387, 297, 276, 338, 281, 242

Answer 1

We have the following:

we calculate the new values

`\begin{gathered} 246-3=243 \\ 387-3=384 \\ 297-3=294 \\ 276-3=273 \\ 338-3=335 \\ 281-3=278 \\ 242-3=239 \end{gathered}`

now, we calculate the mean

`(243+384+294+273+335+278+239)/(7)=292.3`

the standard deviation of the data set is:

`\begin{gathered} s=\sqrt[]{(\Sigma(x_i)^2)/(n)-\bar{x}^2} \\ s=\sqrt[]{(243^2+384^2+294^2+273^2+335^2+278^2+239^2)/(7)-292.3^2} \\ s=\sqrt[]{(614100)/(7)-85439.3} \\ s=47.9 \end{gathered}`

The answer is the option C. 47.9