Question

Find the Mean and Standard Deviation for the following situation.Hits in a Round of Hacky Sack137 66 1012313MeanStandard Deviaion

Answer 1

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:

$\begin{gathered} M=\dfrac{1}{n}\sum ^n_{i=1}\, x_i \\ M=\dfrac{1}{9}(13+7+6+6+10+12+3+1+3) \\ M=\dfrac{61}{9} \\ M=6.78 \end{gathered}$

And the standard deviation can be calculated as:

$\begin{gathered} s=\sqrt[]{\dfrac{1}{n-1}\sum ^n_{i=1}\, (x_i-M)^2} \\ \\ s=\sqrt[]{\dfrac{1}{8}((13-6.78)^2+(7-6.78)^2+(6-6.78)^2+(6-6.78)^2+(10-6.78)^2+(12-6.78)^2+(3-6.78)^2+(1-6.78)^2+(3-6.78)^2)} \\ \\ s=\sqrt[]{\dfrac{139.56}{8}} \\ \\ s=\sqrt{17.44}=4.18 \end{gathered}$

The sample mean is 6.78 hits.

The sample standard deviation is 4.18 hits.