Question

The standard deviation of the observations 1, 3, 5, 7 and 9​

Answer 1

Answer:

standard deviation =6.324

Step-by-step explanation:

Answer 2

Answer:

The standard deviation of observations 1, 3, 5, 7, and 9​ is 2.828

Step-by-step explanation:

• Standard deviation is defined as the deviation of the number from the mean of the group.

         $\sigma=\sqrt{\frac{ \Sigma(x-mean)^{2}}{n} }$

• mean is defined as the average of the group of numbers.

       $mean=\frac{sum \ of \ the \ numbers}{Total \ numbers}$

Step 1 of 1:

• The mean of the given numbers1,3,5,7,9 is given by

        $mean=\frac{1+3+5+7+9}{5} \\mean=\frac{25}{5}\\ mean=5$

• The standard deviation of the numbers is calculated as

        $\sigma=\sqrt{\frac{ \Sigma(x-mean)^{2}}{n} }$

        $\sigma=\sqrt{\frac{ (1-5)^{2}+(3-5)^2+(5-5)^2+(7-5)^2+(9-5)^2}{5} }\\ \sigma=\sqrt{\frac{ (-4)^{2}+(-2)^2+(0)^2+(2)^2+(4)^2}{5} }\\\sigma=\sqrt{\frac{ 16+4+0+4+16^2}{5} }\\\sigma=\sqrt{\frac{ 40}{5} }\\\sigma=\sqrt{8 }\\\sigma=2.828}$

Conclusion:

The standard deviation of observations 1, 3, 5, 7, and 9​ is 2.828