Question

Find the mean, variance, and standard deviation of the scores of the students in an English test: 8, 9, 12, 18, 11, 16, 25, and 19

Answer 1

$$mean=\mu$$

$$=\dfrac{8+9+12+18+11+16+25+19}{8}=14.75$$

$$Var(X)=\sigma^2=\dfrac{1}{8}((8-14.75)^2+(9-14.75)^2$$

$$+(12-14.75)^2+(18-14.75)^2+(11-14.75)^2$$

$$+(11-14.75)^2+(16-14.75)^2+(25-14.75)^2$$

$$+(19-14.75)^2)=29.4375$$

$$\sigma=\sqrt{\sigma^2}=\sqrt{29.4375}=5.4256$$