Given;
[tex]3,7,6,5,4[/tex]STEP 1:
We need to find the mean of the data above
[tex]\begin{gathered} \text{Mean} \\ \bar{x}=\frac{3+7+6+5+4}{5}=\frac{25}{5}=5 \end{gathered}[/tex]STEP 2: We need to get the sum of the square of the difference of each data from the mean.
[tex]\begin{gathered} \Sigma(x-\bar{x})^2=(3-5)^2+(7-5)^2+(6-5)^2+(5-5)^2+(4-5)^2 \\ \Sigma(x-\bar{x})^2=(-2)^2+(2)^2+(1)^2+(0)^2+(-1)^2 \\ \Sigma(x-\bar{x})^2=10 \end{gathered}[/tex]STEP 3: We can find the standard deviation of the data using the formula below;
[tex]\begin{gathered} \text{standard deviation }\sigma=\sqrt[]{\frac{\Sigma(x-\bar{x})^2}{n}} \\ \text{Where n is the number of data = 5} \\ \sigma=\sqrt[]{\frac{10}{5}} \\ \sigma=\sqrt[]{2} \\ \sigma=1.41 \end{gathered}[/tex]Hence, the standard deviation for the group of data to the nearest hundredth is 1.41
