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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