Answer to Question #200721 in Statistics and Probability for Joana

Question

teacher jane randomly selected the grades in statistics and probability of 7 grade 11 students. calculate the mean grade, variance and standard deviation of the given set of data.

Answer 1

$$\def\arraystretch{1.5} \begin{array}{c:c:c} x & x-\bar{x} & (x-\bar{x})^2 \\ \hline 94 & 8 & 64 \\ 88 & 2 & 4\\ 79 & -7 & 49 \\ 89 & 3 & 9 \\ 91 & 5 & 25 \\ 84 & -2 & 4 \\ 77 & -9 & 81 \\ \hdashline \sum_i x_i=602 & & \sum_i (x_i-\bar{x})^2=236 \\ \end{array}$$

$$mean=\bar{x}=\dfrac{1}{n}\sum_ix_i=\dfrac{1}{7}(602)=86$$

$$Var(X)=s^2=\dfrac{1}{n-1}\sum_i(x_i-\bar{x})^2$$

$$=\dfrac{1}{7-1}(236)=\dfrac{118}{3}\approx39.333333$$

$$s=\sqrt{s^2}=\sqrt{\dfrac{118}{3}}\approx6.271629$$