Corr- Session 4

8/8/2019 Corr- Session 4

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Correlation

Prepared by:

Prof. Shuchi Mathur


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Definitions

Correlation analysis deals with the associationbetween two or more variables.- Simpson & Kafka

Correlation analysis attempts to determine the degreeof relationship between variables.- Ya Lun Chou

When the relationship is of quantitative nature, theappropriate statistical tool for discovering & measuring

the relationship & expressing it in brief formula is knownas correlation.:- Croxton & Cowden


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Types of correlation

Positive & Negative

Simple, Multiple & Partial

Linear & Non linear

X 10 12 15 18 20

Y 15 20 22 25 37

X 80 70 60 40 30

Y 50 44 31 20 10


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Methods of studying Correlation

Karl Pearsons Coefficient of correlation

Spearmans Rank Correlation coefficient


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Q1) Find out the coefficient of correlation between

the sales & expenses of the following 10 firms (000

Rs.)

Firms 1 2 3 4 5 6 7 8 9 10

Sales 50 50 55 60 65 65 65 60 60 50

Expenses 11 13 14 16 16 15 15 14 13 13

Ans : r= 0.786


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Q2) Calculate Coefficient of Correlation between the values

of X & Y given below:

Values of X 65 66 67 67 68 69 70 72

Values of Y 67 68 65 68 72 72 69 71

Ans: r= 0.6030


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Q3) The following table gives the distribution of items of production & also the

relatively defective items among them, according to size of groups. Find the

correlation coefficient between size & defect in quality.

Size group No. of items No. of defective items

15-16 200 150

16-17 270 162

17-18 340 170

18-19 360 180

19-20 400 180

20-21 300 114

Ans: r= -0.949


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Ranks are given

Q4) The values of the same 15 students in two subjects

A & B are given below, the two numbers within

the brackets denoting the ranks of the same student

in A & B respectively:

(1,10), (2,7), (3,2), (4,6), (5,4),(6,8), (7,3),(8,1),

(9,11),( 10,15),(11,9),(12,5),(13,14), (14,12), (15,13)

Ans: 0.51


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Q5) Ten competitors in a beauty contest are

ranked by 3judges in the following order:

1st Judge 1 6 5 10 3 2 4 9 7 8

2nd Judge 3 5 8 4 7 10 2 1 6 9

3rd Judge 6 4 9 8 1 2 3 10 5 7

Use the rank correlation coefficient determines which pair of judges

has the nearest approach to common tastes in beauty.

Ans: R= - 0.212

R= - 0.297

R= 0-636


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Ranks are not given

Q6) Calculate the coefficient of rank correlation from the following data:

X 60 34 40 50 45 41 22 43 42 66 64 46

Y 75 32 34 40 45 33 12 30 36 72 41 57

Ans: r= 0.82


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Q7) Calculate Spearmans coefficient of correlation between marks

assigned to 10 students by judges X & Y in a certain competitive

test given below:

S.No. 1 2 3 4 5 6 7 8 9 10

Marks by Judge X 52 53 42 60 45 41 37 38 25 27

Marks by Judge Y 65 68 43 38 77 48 35 30 25 50

Ans: 0.539


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Equal ranksQ8) Obtain the rank correlation coefficient between the

variables X & Y from the following pairs of observed values.

X 50 55 65 50 55 60 50 65 70 75

Y 110 110 115 125 140 115 130 120 115 160

Ans: 0.155


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Q9)Find out the rank correlation coefficient from

the following:

A 115 109 112 87 98 98 120 100 98 118

B 75 73 85 70 76 65 82 73 68 80

Ans : 0.7272


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Thank You

Corr- Session 4

Documents

Transcript of Corr- Session 4