Qm Nithin.docx

PROBLEMS

45.Calculate Karl Pearson’s coefficient of correlation from the following data:

(1) Sum of deviation of X=5 (2) Sum of deviation of Y=4 (3) Sum of squares of deviations of X=40 (4) Sum of squares of deviation of Y=50 (5) Sum of products of deviation of X and Y=32 (6) No. Of pairs of observations =10 ANSWER:

r=

∑𝑑𝑥∗𝑑𝑦 √∑𝑑𝑥²−∑𝑑𝑦²

r= r= r=

32 √40∗50 32 √2000 32 √44.7913595499

r=𝟎 ∙ 𝟕𝟏𝟓𝟓

BIT COLLEGE BANGLORE

NITHIN KUNCHOOR

PROBLEMS

48. Given n=10; ∑x=100; ∑y=150; ∑(x-10)2=180; ∑(y-15)2=25; ∑(x-10)(y-15)=60; Obtain Karl Pearson’s correlation coefficient. ANSWER:

N=10 ∑x=100 ∑y=150 ∑(x-10)2=180 ∑(y-15)2=25 ∑(x-10) (y-15)=60

̅̅̅= 𝑥

∑𝑥 𝑛

100

=

10

𝑥̅ =10 ∑𝑦

𝑦̅=

𝑛

150

=

10

𝑦̅=15 ∑(𝑥−𝑥̅ )(𝑦−𝑦̅)

r=

√∑(𝑥−𝑥̅ )2 ∑(𝑦−𝑦̅)²

r=

60

√(180)(25)

BIT COLLEGE BANGLORE

NITHIN KUNCHOOR

PROBLEMS

r=

60

√4500

r=

60

67∙0820

r =0∙8944

BIT COLLEGE BANGLORE

NITHIN KUNCHOOR