Question

Five items was taken from the output of factory. The length and weight of 5 items are given

below.

Length (meter): 5 6 7 9 12

Weight (KG): 13 15 18 19 20

State which of the two characteristics of two items is more variable?

Answer 1

$$mean_x=\mu_x=\dfrac{5+6+7+9+12}{5}=7.8$$

$$\sigma_x^2=\dfrac{\Sigma(x_i-\bar{x})^2}{n}=\dfrac{1}{5}(7.84+3.24+0.64$$ $$+1.44+17.64)=6.16$$

$$mean_y=\mu_y=\dfrac{13+15+18+19+20}{5}=17$$

$$\sigma_y^2=\dfrac{\Sigma(y_i-\bar{y})^2}{n}=\dfrac{1}{5}(16+4+1+4+9)$$ $$=6.8$$

Since $\sigma_y^2=6.8>6.16=\sigma_x^2,$ then characteristics of weight is more variable.