Question

Question 4 (5 points) Calculate the standard deviation of the following data set. {1, 3, 5, 7.9) Round your answer to the ncarcst hundredth. A Question 5 (5 points) The standard deviation will always be less than the mean ofa data sct. True False

Answer 1

We have the following:

1.

the standard deviation is calculated using the formula:

`\sigma=\sqrt[]{\frac{\sum^{}_{}(x_i-\bar{x})^2}{n}}`

now, the mean:

`\begin{gathered} \bar{x}=\frac{\sum ^{}_{}x_i}{n}=(1+3+5+7+9)/(5)=(25)/(5) \\ \bar{x}=5 \end{gathered}`

therefore:

`\begin{gathered} \sum ^{}_{}(x_i-\bar{x})^2=(1-5)^2_{}+(3-5)^2_{}+(5-5)^2_{}+(7-5)^2_{}+(9-5)^2_{} \\ \sum ^{}_{}(x_i-\bar{x})^2=4^2_{}+2^2_{}+0^2_{}+2^2_{}+4^2_{} \\ \sum ^{}_{}(x_i-\bar{x})^2=16+4+0+16+4=40 \end{gathered}`

replacing:

`\begin{gathered} \sigma=\sqrt[]{\frac{40^{}}{5}} \\ \sigma=\sqrt[]{8}=2\sqrt[]{2} \\ \sigma=2.82 \end{gathered}`

2. Although in this case the mean is greater than the standard deviation, it is not necessarily the case, if there are vamps that are far apart, the standard deviation may be greater.

Therefore, is FALSE