Question

find the range variance and standard deviation of 2.1,3.0,1.9,1.5,4.8

Answer 1

Sorted Data Set: $1.5, 1.9, 2.1, 3.0, 4.8$

$$Range=4.8-1.5=3.3$$

$$mean=\mu=\dfrac{1}{5}(1.5+1.9+2.1+3.0+4.8)$$

$$=2.66$$

$$Var(x)=\sigma^2=\dfrac{1}{5}((1.5-2.66)^2+(1.9-2.66)^2$$

$$+(2.1-2.66)^2+(3.0-2.66)^2+(4.8-2.66)^2)$$

$$=1.3864$$

$$\sigma=\sqrt{\sigma^2}=\sqrt{1.3864 }\approx1.177455$$