Question

What is the standard deviation of the following data set rounded to the nearest tenth

Answer 1

The general formula for the standard deviation is:

`\sigma=\sqrt{(\Sigma(x_i-\mu)^2)/(N)}`

in which, N is the number of data, and μ is the sample's mean.

Start by calculating the sample's mean

`\begin{gathered} \mu=(7.7+8.4+9+8+6.9)/(5) \\ \mu=8 \end{gathered}`

then, apply the standard deviation formula

`\begin{gathered} \sigma=\sqrt{((7.7-8)^2+(8.4-8)^2+(9-8)^2+(8-8)^2+(6.9-8)^2)/(5)} \\ \\ \sigma=\sqrt{((-0.3)^2+(0.4)^2+(1)^2+(0)^2+(-1.1)^2)/(5)} \\ \\ \sigma=\sqrt{(2.46)/(5)} \\ \\ \sigma=√(0.492) \\ \sigma=0.701\approx0.7 \end{gathered}`

Answer:

The standard deviation is 0.7