Question

Calculate the standard deviation of the following data;

45, 50, 67, 68, 75, 80, 70, 65, 70,90

Answer 1

$n=10$

$$\mu=\dfrac{\displaystyle\sum_{i=1}^nx_i}{n}=\dfrac{1}{10}(45+50+67+68+75+80$$

$$+70+65+70+90)=68$$

$$\sigma^2=\dfrac{\displaystyle\sum_{i=1}^n(x_i-\mu)^2}{n}=\dfrac{1}{10}((45-68)^2+(50-68)^2$$

$$+(67-68)^2+(68-68)^2+(75-68)^2$$

$$+(80-68)^2+(70-68)^2+(65-68)^2$$

$$+(70-68)^2+(90-68)^2)=154.8$$

$$\sigma=\sqrt{\sigma^2}=\sqrt{154.8}\approx12.4419$$