Capital (in crores Rs.) 2 3 4 5 6 8 9 Profit (in Lakh Rs.) 6 5 7 7 8 9 10 Draw scatter diagram for the following data and identify the type of correlation.

Positive correlation with high degree

Positive correlation with low degree

The marks in History and Mathematics of twelve students in a public examination are given below. Calculate a coefficient of correlation by ranks. Student $$A$$ $$B$$ $$C$$ $$D$$ $$E$$ $$F$$ $$G$$ $$H$$ $$I$$ $$J$$ $$K$$ $$L$$ History $$69$$ $$36$$ $$39$$ $$71$$ $$67$$ $$76$$ $$40$$ $$20$$ $$85$$ $$65$$ $$55$$ $$34$$ Mathematics $$33$$ $$52$$ $$71$$ $$25$$ $$79$$ $$22$$ $$83$$ $$81$$ $$24$$ $$35$$ $$46$$ $$64$$ Interpret the result.

A bad student of history is even bad student in mathematics.

MCQ Questions for Class 11 Commerce Economics Correlation Quiz 2

State the following statement is true or false

The value of coefficient of correlation is always

$2$ .

0%
True
0%
False

Explanation

Value of coefficient of Correlation is always between

$-1$ and

$+1$ , depending on the strength and direction of a linear relationship between the variables.

Value of correlation coefficient lies between

$-1$ and

$+1$ .

Therefore, the given statement is FALSE.

If the value of any regression coefficient is zero, then two variables are:

0%
Qualitative
0%
Correlation
0%
Dependent
0%
Independent

Explanation

$\Rightarrow$ If the correlation coefficient of two variables is zero, it signifies that there is no linear relationship between the variables. However, this is only for a linear relationship; it is possible that the variables have a strong curvilinear relationship.

$\Rightarrow$ When the value of r is close to zero, generally between

$-0.1$ and

$+0.1,$ the variables are said to have no linear relationship or a very weak linear relationship.

$\Rightarrow$ For example, suppose the prices of coffee and of computers are observed and found to have a correlation of

$+.0008;$ this means that there is no correlation, or relationship, between the two variables.

$\therefore$ We can say that, if the value of any regression coefficient is zero, then two variables are

$Independent$ .

What is the correlation of this scatter diagram

0%
Perfect negative correlation
0%
Negative correlation with high degree
0%
Negative correlation with low degree
0%
Zero correlation

Regression is________________.

0%
independent of origin and scale
0%
independent of origin and not of scale
0%
independent of origin
0%
independent of scale

Write True/False in the following statement:
If regression coefficient are

$0.8$ and

$0.2$ then the value of corelation coefficient is

$+0.4$

0%
True
0%
False

Explanation

Given:-

Coefficient of regression are

$0.8$ and

$0.2$ .

Therefore,

Coefficient of correlation

$= \sqrt{0.8 \cdot 0.2} = \sqrt{0.16} = 0.4$

Hence the given statement is true.

What is the correlation of this scatter diagram

0%

Perfect positive correlation
0%
Positive correlation with high degree
0%
Positive correlation with low degree
0%
Zero correlation

What is the correlation of this scatter diagram

0%
Perfect negative correlation
0%
Negative correlation with high degree
0%
Negative correlation with low degree
0%
Zero correlation

Distance(Km)	80	120	160	200	240
Time(Hr)	2	3	4	5	6

A train travelled between two stations and distance and time were recorded as above,

Draw the scatter diagram and identify the type of correlation.

0%
Perfect positive correlation
0%
Positive correlation with high degree
0%
Positive correlation with low degree
0%
Zero correlation

What is the correlation of this scatter diagram

0%
Perfect negative correlation
0%
Negative correlation with high degree
0%
Negative correlation with low degree
0%
Zero correlation

What is the correlation of this scatter diagram

0%
Perfect positive correlation
0%
Positive correlation with high degree
0%
Positive correlation with low degree
0%
Zero correlation

Write True/False in the following statement:
The value of correlation coefficient lies between

$-2$ to

$+2$

0%
True
0%
False

Explanation

The value of correlation coefficient lies between

$-1$ to

$+1$ .

Hence the given statement is false.

What is the correlation of this scatter diagram

0%
Perfect positive correlation
0%
Positive correlation with high degree
0%
Positive correlation with low degree
0%
Zero correlation

Capital (in crores Rs.)	2	3	4	5	6	8	9
Profit (in Lakh Rs.)	6	5	7	7	8	9	10

Draw scatter diagram for the following data and
identify the type of correlation.

0%
Perfect positive correlation
0%
Positive correlation with high degree
0%
Positive correlation with low degree
0%
Zero correlation

Choose the statement which consists of two correlated variables.

0%
Increase in the intensity of cold results in greater sale of woollen clothes
0%
Increase in temperature of delhi has led to congestion
0%
Increase in weight of children s accompanied by increase in weight of their mother
0%
None of the above

$n=10, \sum x=4,\sum y=3, \sum x^2=8,\sum y^2=9$ and

$\sum xy=3,$ then the coefficient of

$r_{x,y}$ is

0%
$\frac{3}{4}$
0%
$\frac{1}{5}$
0%
$\frac{1}{6}$
0%
$\frac{1}{4}$

Explanation

Correlation coefficient

${ r }_{ x,y }=\dfrac { n\sum { xy } -\sum { x } \sum { y } }{ \sqrt { \left[ n\sum { { x }^{ 2 }-{ \left( \sum { x } \right) }^{ 2 } } \right] \left[ n\sum { { y }^{ 2 }-{ \left( \sum { y } \right) }^{ 2 } } \right] } }$

$=\displaystyle\frac { 30-12 }{ \sqrt { 64\times 81 } }$

$\Rightarrow r_{x,y}=\dfrac{1}{4}$

Choose the statement which consists of two positively correlated variables.

0%
Increase in temperature leads to increase in sales of air conditioners.
0%
Increase in temperature leads to decrease in traffic on road.
0%
Decrease in temperature is accompanied by increase in sales of ice creams
0%
None of the above

If the value of correlation

$\displaystyle r=\frac{1}{2}$ or

$\displaystyle r= - \frac{1}{2}$ , then correlation is called

0%
High negative
0%
High positive
0%
Low positive
0%
Moderate.

Explanation

When correlation between two series or variables is neither large nor
small, then it is called moderate degree correlation. It may be positive
moderate or negative moderate. For positive moderate, correlation the
value of

$\displaystyle r=\frac{1}{2}$ & for negative moderate
correlation the value of

$\displaystyle r=-\frac{1}{2}$
so choice (d) is correct

Calculate the correlation coefficient between the corresponding values of X and Y in the following table:

X	2	4	5	6	8	11
Y	18	12	10	8	7	5

0%
$-0.65$
0%
$-0.82$
0%
$-0.92$
0%
$-0.48$

Explanation

$X\\ 2\\ 4\\ 5\\ 6\\ 8\\ 11\\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \sum { x } =36$

$Y\\ 18\\ 12\\ 10\\ 08\\ 07\\ 05\\ \_ \_ \_ \_ \_ \_ \_ \\ \sum { y } =60$

$x=x-\overline { x } \\ -4\\ -2\\ -1\\ \quad 0\\ \quad 2\\ \quad 5\\ \_ \_ \_ \_ \_ \_ \\ \quad 0$

$Y=y-\overline { y } \\ \quad 8\\ \quad 2\\ \quad 0\\ -2\\ -3\\ -5\\ \_ \_ \_ \_ \_ \\ \quad 0$

$XY\\ -32\\ -4\\ \quad 0\\ \quad 0\\ -6\\ -25\\ \_ \_ \_ \_ \_ \_ \\ -67$

${ X }^{ 2 }\\ 16\\ 4\\ 1\\ 0\\ 4\\ 25\\ \_ \_ \_ \_ \_ \\ \quad 50$

${ Y }^{ 2 }\\ 64\\ 4\\ 0\\ 4\\ 9\\ 25\\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \sum { { Y }^{ 2 }=106 }$

Therefore,

$\overline { a } =\cfrac { 36 }{ 6 } \\ \quad =6$

$\overline { y } =\cfrac { 60 }{ 6 } \\ \quad =10$

Therefore,

$=\quad \cfrac { \sum { XY } }{ \sqrt { \sum { { X }^{ 2 } } \sum { { Y }^{ 2 } } } } \\ =\cfrac { -67 }{ \sqrt { 50*106 } } \\ =-0.92$

If x, y are independent variable, then

0%
$Cov\left ( x, y \right )=1$
0%
$r_{xy}=0$
0%
$r_{xy}=1$
0%
$Cov\left ( x, y \right )=0$

Explanation

Fact. If the variables are uncorrelated or independent then covariance
and coefficient of correlation between the variable both are equal to 0
i.e.

$r_{xy}=Cov\left ( x, y \right )=0$

The data in which of the following scatterplots would be best modeled by a quadratic function in which the

$x^2$ term has a negative coefficient?

Explanation

The option 1 is correct for the quadratic equation having negative coefficient of

$x^2$ term.
Example:

$y = -x^2$
So, the value is decreasing.
When you graph the points of x and y you will get the first graph as answer for quadratic equation having negative coefficient of

$x^2$ term.
y: 1 2 3

$x^2$ : -1 -4 -9

A strong positive association between x and y is depicted by which of the following graphs?

Explanation

A strong association implies that there must be seen a concentrated set of points in the

$x-y$ plane.

Also, a positive association implies that the points must be going upwards, meaning that as

$x$ increases, correspondingly

$y$ increases too.

This kind of set is visible in option D.

The marks obtained by nine students in physics and Mathematics are given below:

Physics	48	60	72	62	56	40	39	52	30
Mathematics	62	78	65	70	38	54	60	32	31

calculate spearman's coefficient.

0%
$r=0.66$
0%
$r=0.32$
0%
$r=0.53$
0%
$r =0.28$

Explanation

Descending order arranged data will be as follows:

Physics:

$72,62,60,56,52,48,40,39,30$

MAthematics:

$78,70,65,62,60,54,38,32,31$

Thus data will be

Physics $(P)$

Mathematics $(M)$

Rank $(P)$

$|d|$

$d^2$

$n=9,\quad \sum d^2=40$

$r=1-\cfrac{6\sum d^2}{n(n^2-1)}=1-\cfrac{40\times 6}{9(9^2-1)}=1-\cfrac{240}{720}=0.66$

The coefficient of correlation is always between

0%
$0\ and \ 1$
0%
$-1\ and \ 1$
0%
$-\infty \ and \ \infty$
0%
$-10\ and \ 10$

Explanation

$\Rightarrow$ Correlation coefficients are expressed as values between

$-1$ and

$+1$ .

$\Rightarrow$ A coefficient of

$+1$ indicates a perfect positive correlation: A change in the value of one variable will predict a change in the same direction in the second variable.

$\Rightarrow$ A coefficient of

$-1$ indicates a perfect negative correlation: A change in the value of one variable predicts a change in the opposite direction in the second variable.

FInd the rank correlation from the following data:

S. No.	1	2	3	4	5	6	7	8	9	10
Rank Differences	-2	-4	-1	3	2	0	-2	3	3	-2

0%
0.64
0%
0.50
0%
0.45
0%
0.34

Explanation

Sl.No

Rank Difference $(d)$

$d^2$

10.

-2

-4

-1

-2

$\sum d^2=60,\quad n=10$

$r=1-\cfrac{6\sum d^2}{n(n^2-1)}$

$r=1-\cfrac{6(60)}{10(10^2-1)}$

$r=1-\cfrac{360}{990}$

$r=0.6363....\approx 0.64$

Rank correlation depends on________________.

0%
a specific distribution
0%
the ranks of observations
0%
the ranks of unknown value
0%
the ranks of known value

Rank correlation co-efficient was developed by___________.

0%
Karl Pearson
0%
C. Spearman
0%
Francis Cotton
0%
Carly

The marks in history and mathematics of twelve students in a public examination are given below. Calculate a coefficient of correlation by ranks.

Student	A	B	C	D	E	F	G	H	I	J	K	L
History	69	36	39	71	67	76	40	20	85	65	55	34
Mathematics	33	52	71	25	79	22	83	81	24	35	46	64

0%
-0.77
0%
-0.92
0%
0.77
0%
0.92

Explanation

Students

History $(H)$

Mathematics $(M)$

Rank $(H)$

Rank $(M)$

$|d|$

$d^2$

100

$n=12,\quad \sum d^2=508$

$r=1-\cfrac{6\sum d^2}{n(n^2-1)}=1-\cfrac{6\times 508}{12(12^2-1)}=1-\cfrac{3048}{1716}=-0.77$

If increase in value of one variable is not accompnied by the proportional decrease in second variable, then corrrelation between two variables is

0%
perfect positive
0%
perfect negative
0%
imperfect positive
0%
imperfect negative

The marks in History and Mathematics of twelve students in a public examination are given below. Calculate a coefficient of correlation by ranks.

Student	$A$	$B$	$C$	$D$	$E$	$F$	$G$	$H$	$I$	$J$	$K$	$L$
History	$69$	$36$	$39$	$71$	$67$	$76$	$40$	$20$	$85$	$65$	$55$	$34$
Mathematics	$33$	$52$	$71$	$25$	$79$	$22$	$83$	$81$	$24$	$35$	$46$	$64$

Interpret the result.

0%
A very good student of history is a very bad student in mathematics.
0%
A bad student of history is even bad student in mathematics.
0%
This is positive correlation
0%
None of the above

Explanation

Students

History $(H)$

Mathematics $(M)$

Rank $(H)$

Rank $(M)$

$|d|$

$d^2$

100

$n=12,\quad \sum d^2=508$

$r=1-\cfrac{6\sum d^2}{n(n^2-1)}=1-\cfrac{6\times 508}{12(12^2-1)}=1-\cfrac{3048}{1716}=-0.77$

Since $r<0,$ we can say that a very good student of history is a very bad student in mathematics.

Following are the rank obtained by 10 students in two subjects , Statistics and Mathematics . To what extent the knowledge of the students in the two subjects is related?

Statistics	1	3	3	4	5	6	7	8	9	10
Mathematics	2	4	1	5	3	9	7	10	6	8

0%
0.76
0%
0.66
0%
0.56
0%
0.48

Explanation

Statistic $(X)$

Mathematics $(Y)$

$XY$

$X^2$

$Y^2$

100

$\sum X=56,\quad \sum Y=55,\quad \sum XY=369,\quad \sum X^2=390,\quad \sum Y^2=385$

$N=10$

Cov $(x,y)=\cfrac{\sum XY}{N}-\cfrac{\sum X}{N}.\cfrac{\sum Y}{N}=\cfrac{369}{10}-\cfrac{56}{10}.\cfrac{55}{10}=6.1$

$\sigma_x=\sqrt{\cfrac{\sum X^2}{N}-\left(\cfrac{\sum X^2}{N}\right)^2}=\sqrt{\cfrac{390}{10}-\left(\cfrac{56}{10}\right)^2}=2.76$

$\sigma_y=\sqrt{\cfrac{\sum Y^2}{N}-\left(\cfrac{\sum Y^2}{N}\right)^2}=\sqrt{\cfrac{385}{10}-\left(5.5\right)^2}=2.87$

$r=\cfrac{Cov(x,y)}{\sigma_x.\sigma_y}=\cfrac{6.1}{2.87\times 2.76}=0.77$

CBSE Questions for Class 11 Commerce Economics Correlation Quiz 2 - MCQExams.com

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Practice Class 11 Commerce Economics Quiz Questions and Answers

CBSE Questions for Class 11 Commerce Economics Correlation Quiz 2 - MCQExams.com

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Practice Class 11 Commerce Economics Quiz Questions and Answers

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