SLMNA3-11 EcoB 07 Correlation Goutam

8/14/2019 SLMNA3-11 EcoB 07 Correlation Goutam

1/22

A researcher finds that students who attend fewerclasses in the school get poor marks. What type ofcorrelation is this?

HintTypes


2/22

As the number of absence from the class increases,

the grades decline. The variables are changing in theopposite direction. Thus, it is a case of negativecorrelation.

Explanation


3/22


4/22

If the value of X is increasing, the value of Y will alsoincrease as there is a positive relation betweenvariables X and Y.

Explanation


5/22


6/22

The statement that the negative correlation exist betweenthe two is correct but it is not true to say that the value liesbetween -1.2 because the value of correlation of coefficient(r) always lies between1 to +1 ( 1 < r < + 1).

Explanation


7/22

Positive correlation can be of various degrees. Isthere any difference between perfect positivecorrelation and positive correlation? If yes, how?

HintProportionate change


8/22

When there is a proportionate change in the variablesin same direction it is called perfect positivecorrelation, whereas when the change in the variablesis in the same direction but in different proportion it iscalled positive correlation.

Y

OX

Y

XO

Explanation

Perfect positive correlation Positive correlation


9/22

In an internal exam, 5 students scored the followingmarks in mathematics and economics. Interpret theresult.

HintSpearmans correlation

Mathematics 90 80 70 60 50

Economics 90 70 80 60 50


10/22

Here, N = 5Spearmans rank correlation

2

3

6 D= 1 -

N N

kr

Mathematics Rank Economics Rank D D2

90

80

70

60

50

1

2

3

4

5

90

70

80

60

50

1

3

2

4

5

0

-1

1

0

0

0

1

1

0

0

2

2D

Explanation


11/22

The following table gives two kinds of assessment(internal and external) of 10 students performance inclass XII. Does the internal test effect the result ofexternal exam in any way? Find out with the help ofrelative performance of students in both the exams.

HintRank correlation

InternalTest

45 62 67 32 12 38 47 67 42 85

ExternalTest

39 48 65 32 20 35 45 77 30 62


12/22

2 3

1 1

3

3

3

1

12

12 2

12

10 10

6 D (m m )

= 1 -N N

,

6 10.5 ( )

= 1 -

k

k

r

Here

m n umber of items of equal ranks

N Number of items

r


13/22

16

12

1000 10

11

990

661990

1 06

94

6 10.5 ( )

= 1 -

6= 1 -

.

.

kr

Strong positive correlation shows that those who have scoredbetter in internal test have scored good in external test also.Therefore, the school should give emphasis on internal test forbetter performance in external exam.


14/22

On a trial basis, a farmer started using organic fertilizer

in his field to know its effects on productivity. Thefollowing data shows the use of organic fertilizer andthe productivity for different years. What type ofcorrelation exist between the two?

HintRelationship

Organic fertilizer(quintal)

15 18 20 24 30 35 40

Production(quintal)

85 93 95 105 120 130 150


15/22

2 2

2 2

2 2

14 431377

7

14 43546 3519

7 7

.

( ) ( )

( ) ( )

dx dy dx dy

Nrdx dy

dx dy N N


16/22

1291

22 75 57 05

1291

1297 88

99

. .

.

.

There is a strong correlation between organic fertilizerand productivity. He should continue using organicfertilizer to raise his production.


17/22

What kind of relationship do you find between X and Y inthe scatter diagram, if the points of the scatter diagramare (a) scattered (b) tend to cluster in a straight line

sloping downward (c) tend to cluster around a straightline sloping upward?

HintTypes


18/22

(a) No correlation: If the points or data plotted on a graph

are scattered, it is a case of no correlation. Norelationship is found between the two variables.

(b) Negative correlation: If the points tend to cluster on a

downward sloping straight line, it is a case of negativecorrelation. In negative correlation variables move inopposite direction. When one variable increases, otherdecreases and vice-versa.

(c) Positive correlation: If the points tend to cluster on adownward sloping straight line, it is a case of positivecorrelation. In positive correlation, variables movetogether in the same direction.

Explanation


19/22

HintMethods to measure

correlation

Following table shows marks in Economics and theaverage length of time that students spend travelling tocollege each morning. Draw an appropriate diagramand interpret the correlation.

Marks inEconomics

78 70 80 30 55 29 74 64 47 53

Time(Minutes)

12 35 19 30 30 15 22 10 17 16


20/22

(i) The scatter diagram shows thatthere is no correlation between thetime taken to travel to college andthe marks in Economics.

(ii) We cannot predict the marks ofany student based on how long ittakes him to get to college.

Marks

O

Time

10

20

30

40

50

60

70

80

5 10 15 20 2530 35

Explanation


21/22

After doing a survey, Mahesh told his teacher thatstudents who are more often absent show poorperformance in the class.

He asked the teacher the reason behind this kind of

correlation.

HintDegree of relationship


22/22

His teacher wants to convey that correlation should neverbe interpreted as cause and effect relation.

For example, there exist a relation when we say that the

students who attend less classes get poor marks. Butsometimes we see that a student who is not highlymotivated may also be absent more often.

Thus, correlation measures only degree and intensity of

relationship and not causation.

Explanation

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SLMNA3-11 EcoB 07 Correlation Goutam