We have to calculate the mean and standard deviation of this set of numbers.
We can calculate the mean of a set of numbers with the equation:
[tex]\begin{gathered} M_{}=\dfrac{1}{n}\sum ^n_{i=1}\, x_i \\ M_{}=\dfrac{1}{7}(11+15+17+19+21+24+27) \\ M_{}=\dfrac{134}{7} \\ M_{}\approx19.14 \end{gathered}[/tex]
And the standard deviation can be calculated as:
[tex]\begin{gathered} s_{}=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M_2)^2} \\ s_{}=\sqrt{\dfrac{1}{6}((11-19.14)^2+(15-19.14)^2+(17-19.14)^2+. . . +(27-19.14)^2)} \\ s_{}=\sqrt{\dfrac{176.86}{6}} \\ s=\sqrt{29.48}\approx5.43 \end{gathered}[/tex]
Answer:
The mean of this sample is 19.14.
The standard deviation of this sample is 5.43.
