Question

With the aid of a table, find the sample Standard Deviation of the following dataset:

X = {2.2, 4.7, 6.3, 5.8, 5.7, 7.2, 2.6, 2.4, 6.1, 6.8}

Answer 1

Sample mean is  

$$\bar{x}=\dfrac{1}{10}(2.2+ 4.7+6.3+ 5.8+5.7$$ $$+7.2+2.6+2.4+6.1+6.8)=4.98$$

Sample Variance

$$s^2=\dfrac{\Sigma(x_i-\bar{x})^2}{n-1}$$ $$=\dfrac{1}{10-1}((2.2-4.98)^2+(4.7-4.98)^2$$

$$+(6.3-4.98)^2+(5.8-4.98)^2+(5.7-4.98)^2$$

$$+(7.2-4.98)^2+(2.6-4.98)^2+(2.4-4.98)^2$$

$$+(6.1-4.98)^2+(6.8-4.98)^2)=\dfrac{32.556}{9}$$

Sample Standard Deviation

$$s=\sqrt{s^2}=\sqrt{\dfrac{32.556}{9}}\approx1.902$$