Question

The 6 participants in a weight-loss class lost the following weights (in pounds) after three weeks of dieting.

Answer 1

Given data:

3, 0, 6, 6, 2, 1.

To find the standard deviation:

Let us find the mean.

$\begin{gathered} \mu=\frac{\sum ^{}_{}x}{N} \\ =\frac{3+0+6+6+2+1}{6} \\ =\frac{18}{6} \\ =3 \end{gathered}$

Using the standard deviation formula,

$\begin{gathered} \sigma=\sqrt[]{\frac{\sum ^{}_{}(x-\mu)^2}{N}} \\ =\sqrt[]{\frac{(3-3)^2+(0-3)^2+(6-3)^2+(6-3)^2+(2-3)^2+(1-3)^2}{6}} \\ =\sqrt[]{\frac{0^2+3^2+3^2+3^2+1^2+2^2}{6}} \\ =\sqrt[]{\frac{9+9+9+1+4}{6}} \\ =\sqrt[]{\frac{32}{6}} \\ =\sqrt[]{5.3333} \\ =2.3094 \\ \approx2.31 \end{gathered}$

Hence, the standard deviation is 2.31.