Math, asked by mohitdodeja007, 11 months ago

The following table provides the distribution of items according to size groups and also the
number of defectives:
Size group:
9-11
11-13
13-15 15-17 17-19
No. of items:
350
400
300
150
No. of defective items: 25
70
60
45
The correlation coefficient between size and defectives is
(a) 0.25
(b) 0.12 (c) 0.14 B (d) 0.07
250
20​

Answers

Answered by amitnrw
3

Given :  distribution of items according to size groups and also the

number of defectives:  

To Find :  The correlation coefficient between size and defectives is

 The correlation coefficient between items and defectives is

Solution:

a = x - Mean of x  ,  ( mean of x = ∑x/5 = 1450/5= 290)

b =y - Mean of y  ,  ( mean of y  = ∑y/5 = 220/5= 44)

 x y a b a²         b²  ab

250 25 -40 -19 1600 361  760

350 70 60 26 3600 676  1560

400 60 110 16 12100 256   1760

300 45 10 1 100         1   10

150 20 -140 -24 19600 576   3360

1450 220       37000 1870   7450

Correlation coefficient   between items and defectives is

=  ∑ab/√∑a² * √∑b²

=  7450 / ( √37000 * √1870)

= 0.8956

The correlation coefficient between size and defectives is

a = x - Mean of x  ,  ( mean of x = ∑x/5 = 70/5= 14)

b =y - Mean of y  ,  ( mean of y  = ∑y/5 = 220/5= 44)

 x y a b a²   b²  ab

10 25 -4 -19 16 361 76

12 70 -2 26 4 676 -52

14 60 0 16 0 256 0

16 45 2 1 4 1 2

18 20 4 -24 16 576 -96

70 220     40 1870 -70

The correlation coefficient between size and defectives is 0.25

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