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:
250
350
400
300
150
No. of defective items:
25
70
60
45
20
The correlation coefficient between size and defectives is
(a) 0.25
(b) 0.12
(C) 0.14
(d) 0.07
Answers
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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