The sum and sum of squares corresponding to length $X$ (in cm ) and weight $y$
(in gm) of $50$ plant products are given below:
$i = l \sum 50 X_{i} = 212, i = l \sum 50 X_{i}^{2} = 902.8, i = l \sum 50 y_{i} = 261, i = l \sum 50 y_{i}^{2} = 1457.6$
Which is more varying the length or weight ?

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:

i = l \sum 50 X_{i} = 212, i = l \sum 50 X_{i}^{2} = 902.8, i = l \sum 50 y_{i} = 261, i = l \sum 50 y_{i}^{2} = 1457.6

Which is more varying the length or weight ?

Filo · Accepted Answer

i=1∑50​Xi​=212,i=1∑50​Xi2​=902.8,  Here, N=50Mean Xˉ=N∑i=150​​=50212​=4.24Variance  (σ12​ )=N1​i=1∑50​(Xi​−Xˉ)2  =501​i=1∑50​(Xi​−4.24)2  =501​i=1∑50​[Xi2​−8.48Xi​+17.97]  =501​[i=1∑50​Xi2​−8.48i=1∑50​Xi​+17.97×50]  =501​[902.8−8.48×(212)+898.5]  =501​[1801.3−1797.76]  =501​×3.54  =0.07  Also, given i=1∑50​yi​=261,i=1∑50​yi2​=1457.6Mean yˉ​=N1​i=1∑50​yi​=501​×261=5.22Variance (σ22​)=N1​i=1∑50​(yi​−yˉ​)2  =501​i=1∑50​(yi​−5.22)2  =501​i=1∑50​[y12​−10.44yi​+27.24]  =501​[i=1∑50​yi2​−10.44yi​+27.24×50 ]  =501​[1457.6−10.44×(261)+1362]  =501​[2816.6−2724.84]  =501​×94.76  =1.89Since, variance of weights (yi​)  is greater than the variance of lengths (Xi​) i.e  σ2​>σ1​ So, weight vary more  than the lengths .

Question Text	The sum and sum of squares corresponding to length $X$ (in cm ) and weight $y$ (in gm) of $50$ plant products are given below: $i = l \sum 50 X_{i} = 212, i = l \sum 50 X_{i}^{2} = 902.8, i = l \sum 50 y_{i} = 261, i = l \sum 50 y_{i}^{2} = 1457.6$ Which is more varying the length or weight ?
Answer Type	Text solution:1
Upvotes	150

The sum and sum of squares corresponding to length $X$ (in cm ) and weight $y$
(in gm) of $50$ plant products are given below:
$i = l \sum 50 X_{i} = 212, i = l \sum 50 X_{i}^{2} = 902.8, i = l \sum 50 y_{i} = 261, i = l \sum 50 y_{i}^{2} = 1457.6$
Which is more varying the length or weight ?

Text solutionVerified

Practice questions from similar books

The sum and sum of squares corresponding to length X (in cm ) and weight y (in gm) of 50 plant products are given below: i=l∑50​Xi​=212,i=l∑50​Xi2​=902.8,i=l∑50​yi​=261,i=l∑50​yi2​=1457.6 Which is more varying the length or weight ?

Text solutionVerified

Practice questions from similar books

The sum and sum of squares corresponding to length $X$ (in cm ) and weight $y$
(in gm) of $50$ plant products are given below:
$i = l \sum 50 X_{i} = 212, i = l \sum 50 X_{i}^{2} = 902.8, i = l \sum 50 y_{i} = 261, i = l \sum 50 y_{i}^{2} = 1457.6$
Which is more varying the length or weight ?