Respuesta :
The range of the data set is the maximum value minus the minimum value.
The maximum value is 35 and the minimum value is 4, so we have that:
[tex]\text{range}=35-4=31[/tex]In order to calculate the variance, first we need to find the mean of the data set:
[tex]x=\frac{5+10+6+9+8+4+4+8+9+35}{10}=\frac{98}{10}=9.8[/tex]Now, the variance can be calculated as:
[tex]\begin{gathered} \text{variance}=\frac{(x_1-x)^2+(x_2-x)^2+\cdots+(x_n-x)^2}{n} \\ \text{variance}=\frac{(5-9.8)^2+(10-9.8)^2+\cdots+(35-9.8)^2}{10} \\ \text{variance}=\frac{23.04+0.04+14.44+0.64+3.24+33.64+33.64+3.24+0.64+635.04}{10} \\ \text{variance}=\frac{747.6}{10}=74.76 \end{gathered}[/tex]Rounding to the nearest tenth, the variance is 74.8.
The standard deviation is the square root of the variance:
[tex]\text{stddev}=\sqrt{\text{variance}}=\sqrt{74.76}=8.646[/tex]Rounding to the nearest tenth, the standard deviation is 8.6
