The general formula for the standard deviation is:
[tex]\sigma=\sqrt{\frac{\Sigma(x_i-\mu)^2}{N}}[/tex]in which, N is the number of data, and μ is the sample's mean.
Start by calculating the sample's mean
[tex]\begin{gathered} \mu=\frac{7.7+8.4+9+8+6.9}{5} \\ \mu=8 \end{gathered}[/tex]then, apply the standard deviation formula
[tex]\begin{gathered} \sigma=\sqrt{\frac{(7.7-8)^2+(8.4-8)^2+(9-8)^2+(8-8)^2+(6.9-8)^2}{5}} \\ \\ \sigma=\sqrt{\frac{(-0.3)^2+(0.4)^2+(1)^2+(0)^2+(-1.1)^2}{5}} \\ \\ \sigma=\sqrt{\frac{2.46}{5}} \\ \\ \sigma=\sqrt{0.492} \\ \sigma=0.701\approx0.7 \end{gathered}[/tex]Answer:
The standard deviation is 0.7