Respuesta :
From the given values, we can see that the lowest values is -32 and the highest value ie -4. Since the range is the difference betwwwn the highest and the lowest value, the range is
[tex]\begin{gathered} \text{Range}=-4-(-32) \\ \text{Range}=28 \end{gathered}[/tex]On the other hand, the sample variance formula is
[tex]S^2=\sqrt[]{\frac{\sum ^7_{n\mathop=1}(x-\bar{x})^2}{n-1}}[/tex]where x^bar is the mean and n is the total number of sample elements. In our case, n=7 and the mean is
[tex]\begin{gathered} \bar{x}=\frac{-10-16-21-24-4-30-32}{7} \\ \bar{x}=-\frac{137}{7} \\ \bar{x}=-19.5714 \end{gathered}[/tex]Then, the sample variance is given by
[tex]\begin{gathered} S^2=\frac{(-10-19.57)^2+(-16-19.57)^2+(-21-19.57)^2+\cdot\cdot\cdot+(-32-19.57)^2}{6} \\ S^2=105.2857 \end{gathered}[/tex]Since the standard deviation is the square root of the sample variance, we have
[tex]\begin{gathered} S=\sqrt[]{105.2857} \\ S=10.26088 \end{gathered}[/tex]By rounding the solutions to the nearest tenth, the answers are:
[tex]\begin{gathered} \text{Range}=28 \\ \text{Variance}=105.3 \\ \text{ Standard deviation = 10.3} \end{gathered}[/tex]