We have the scores: 13, 7, 6, 6, 10, 12, 3, 1, 3.
We have to calculate its mean and standard deviation.
We will start with the mean:
And the standard deviation can be calculated as:
![\begin{gathered} s=\sqrt[]{(1)/(n-1)\sum ^n_(i=1)\, (x_i-M)^2} \\ \\ s=\sqrt[]{(1)/(8)((13-6.78)^2+(7-6.78)^2+(6-6.78)^2+(6-6.78)^2+(10-6.78)^2+(12-6.78)^2+(3-6.78)^2+(1-6.78)^2+(3-6.78)^2)} \\ \\ s=\sqrt[]{(139.56)/(8)} \\ \\ s=√(17.44)=4.18 \end{gathered}]()
The sample mean is 6.78 hits.
The sample standard deviation is 4.18 hits.