Question

The sum and sum of squares corresponding to length $x$ (in cm) and weight $y$ (in gm) of 50 plant products are given below :

${\sum }_{i=1}^{50}{x}_i=212,{\sum }_{i=1}^{50}{x}_i^2=902.8,{\sum }_{i=1}^{50}{y}_i=261,{\sum }_{i=1}^{50}{y}_i^2=1457.6$

Which is more varying, the length or the weight ?

Answer 1

Here ${\sum }_{i=1}^{50}{x}_i=212,{\sum }_{i=1}^{50}{x}_i^2=902.8,{\sum }_{i=1}^{50}{y}_i=261,{\sum }_{i=1}^{50}{y}_i^2=1457.6$

Now, $\overline{x}=\frac{212}{50}=4.24$

${\sigma }_x^2=\frac{1}{50\times 902.8}-{\left(\frac{212}{50}\right)}^2$

= 18.056 - 17.978 = 0.078

${\sigma }_x=\sqrt{0.078=0.28}$

Also $\overline{y}=\frac{261}{50}=5.22$

${\sigma }_y^2=\frac{1}{50}\times 1457.6-{\left(\frac{261}{50}\right)}^2$

= $29.152-27.248=1.904$

${\sigma }_y=\sqrt{1.904}=1.38$

C.V. of length = $\frac{0.28}{4.24}\times 100=6.6$

C.V. of weight = $\frac{1.38}{5.22}\times 100=26.45$

C.V. of weight > C.V of length