Question

Suppose that a set of data 3, 3, 4, 5, 6 and 7 indicating the number of students graduated from their doctorate degree by a random sample of 6 universities in Malaysia. Find the standard deviation of the aforementioned dataset.

Answer 1

$$mean=\bar{x}=\dfrac{3+3+4+5+6+7}{6}=\dfrac{14}{3}$$

$$Var(X)=s^2=\dfrac{1}{6-1}((3-\dfrac{14}{3})^2 +(3-\dfrac{14}{3})^2+$$

$$+(4-\dfrac{14}{3})^2+(5-\dfrac{14}{3})^2+(6-\dfrac{14}{3})^2$$

$$+(7-\dfrac{14}{3})^2)=\dfrac{8}{3}$$

$$s=\sqrt{s^2}=\sqrt{\dfrac{8}{3}}=\dfrac{2\sqrt{6}}{3}\approx1.632993$$

The standard deviation of the aforementioned dataset is s=1.632993.