Question

What is the standard deviation of the data?Some teenagers collected trash for a beach cleanup.The data for the number of pounds of trash collected byeach teenager are shown below.26, 26, 21, 22, 20, 25, 35O pounds4.66 pounds5.03 poundso 25.33 pounds

Answer 1

`\begin{gathered} \text{The standard deviation for the observed data is given as;} \\ \sigma=\sqrt[]{(\Sigma(x-\mu)^2)/(N)} \\ \text{Where }\sigma=s\tan dard\text{ deviation, } \\ x=\text{the values observed (26,26,21,22,20,25,35)} \\ \mu=the\text{ population mean} \\ \text{The mean is derived as } \\ \text{Mean}=((26+26+21+22+20+25+35))/(7) \\ \text{Mean}=(175)/(7) \\ \text{Mean}=25 \\ \Sigma(x-\mu)=(26-25)+(26-25)+(21-25)+(22-25)+(20-25)+(25-25)+(35-25) \\ \Sigma(x-\mu)=1+1+\lbrack-4\rbrack+\lbrack-3\rbrack+\lbrack-5\rbrack+0+10 \\ \Sigma(x-\mu)=1+1-4-3-5+10 \\ \Sigma(x-\mu)=0 \\ \text{Back to the formular;} \\ \sigma=\sqrt[]{(\Sigma(x-\mu)^2)/(N)} \\ \sigma=\sqrt[]{(0^2)/(7)} \\ \sigma=\sqrt[]{0} \\ \sigma=0 \end{gathered}`