Want to ask us a question? Click here
Browse Questions
 Ad
0 votes

The sum and sum of squares corresponding to length x (in cm) and weight (y) in gm of 50 plant products are given below: $\sum \limits _{i=1} ^{50} x_i=212, \qquad\sum \limits_{i=1}^{50}x_i^2 =902.8;\qquad \sum \limits _{i=1} ^{50} y_i=261, \qquad\sum \limits_{i=1}^{50}y_i^2 =1457.6$ Which is more varying , the length or weight?

Can you answer this question?

1 Answer

0 votes
Toolbox:
• The formula required to solve this problem are : Mean $\bar{x}= \large\frac{\sum x_i}{n}$
• Standard deviation $\sigma= \sqrt {\large\frac{\sum x_i^2}{\sum n} - \bigg( \large\frac{\sum x_i}{n} \bigg)^2 }$
• Coefficient variation $=\large\frac{\sigma}{\bar {x} }$$\times 100 For length, Mean \bar{x}= \large\frac{\sum x_i}{n} \qquad= \large\frac{212}{50} \qquad= 4.24 Standard deviation \sigma= \sqrt {\large\frac{\sum x_i^2}{\sum n} - \bigg( \large\frac{\sum x_i}{n} \bigg)^2 } \qquad= \sqrt { \large\frac{902.8}{50} -\bigg(\large\frac{212}{50}\bigg)^2} \qquad= \sqrt { \large\frac{902.8 \times 50-(212)^2}{50 \times 50}} \qquad= \large\frac{1}{50}$$ \sqrt { 45140-44944}$
$\qquad= \large\frac{14}{50} =\frac{7}{25} $$=0.28 Step 3: Coefficient of variation : =\large\frac{\sigma}{\bar {x}}$$\times 100$
$\qquad= \large\frac{0.28}{4.24} $$\times 100 \qquad= \large\frac{28}{4.24} \qquad= 6.604 For weight, Step 1: Mean \bar{x}= \large\frac{\sum x_i}{n} \qquad= \large\frac{261}{50} \qquad= 5.22 Step 2: Standard deviation \sigma= \sqrt {\large\frac{\sum x_i^2}{\sum n} - \bigg( \large\frac{\sum x_i}{n} \bigg)^2 } \qquad= \sqrt{\large\frac{1457.6}{50} \bigg( \large\frac{261}{50}\bigg)^2 } \qquad= \large\frac{1457.6 \times 50 -(261 \times 261)}{50 \times 50} \qquad= \large\frac{1}{50}$$\sqrt {72880 -68121}$
$\qquad= \large\frac{\sqrt {4759}}{50}$$=1.37 Step 3: Coefficient of variation : =\large\frac{\sigma}{\bar {x}}$$\times 100$
$\qquad= \large\frac{1.37}{5.22}$$\times 100$
$\qquad= \large\frac{137}{5.22}$
$\qquad= 26.24$
COMPARISON:
Variability depends upon coefficient of variation.
Higher the coefficient of variation, higher is the variability.
$\therefore$ coefficient of variation of weight is higher as compared to coefficient of variation of length.
$\therefore$ weight is more varying than length.
answered Jul 1, 2014 by

0 votes
1 answer

0 votes
1 answer

0 votes
1 answer

0 votes
1 answer

0 votes
1 answer

0 votes
1 answer

0 votes
1 answer