The marks obtained by nine students in Physics and Mathematics are given below: Physics $$48$$ $$60$$ $$72$$ $$62$$ $$56$$ $$40$$ $$39$$ $$52$$ $$30$$ Mathematics $$62$$ $$78$$ $$65$$ $$70$$ $$38$$ $$54$$ $$60$$ $$32$$ $$31$$ Interpret the result.

This indicates a moderate positive relationship between marks in Physics and Mathematics.

This indicates a high positive relationship between marks in Physics and Mathematics.

This indicates a negative relationship between marks in Physics and Mathematics.

Match the following items in List - I with most suitable options in List - II: List-I List-II (a) Fisher Inverse probability (b) Karl Pearson Normal Distribution (c) Thomas Baye's Correlation Coefficient (d) Karl Gauss Index Numbers

$$(a) - 4, (b) - 3, (c) - 1, (d) - 2$$

$$(a) - 4, (b) - 3, (c) - 2, (d) - 1$$

$$(a) - 4, (b) - 2, (c) - 3, (d) - 1$$

$$(a) - 4, (b) - 2, (c) - 1, (d) - 3$$

MCQ Questions for Class 11 Commerce Economics Correlation Quiz 4

Rank correlation is useful where____________.

0%
we place things in an order of merit
0%
the number of variables is more than 30
0%
there is a need to calculate the co-efficient of frequency distribution
0%
none of the above

When the number of items is small, the correlation co-efficient can be found out by _________.

0%
karl pearson's method
0%
spearman's method
0%
product moment correlation
0%
concurrent deviation method

Karl Pearson's method helps to__________.

0%
give direction and degree of relationship between the two variables.
0%
calculate the unknown value from a known value.
0%
both (A) and (B).
0%
calculate the known value from an unknown value.

The angle between the two lines will be wider when the correlation between two variable is___________.

0%
less
0%
more
0%
equal
0%
very high

Correlation is______________.

0%
independent of change of origin
0%
independent of change of scale
0%
independent of origin and not of scale
0%
both (A) and (B)

The original formula that Pearson developed is commonly known as___________.

0%
Probable error
0%
the product moment method
0%
concurrent deviation method
0%
short-cut method

The coefficient of correlation when coefficients of regression are

$0.2$ and

$1.8$ is

0%
$0.36$
0%
$0.2$
0%
$0.6$
0%
$0.9$

Explanation

$Given\quad { b }_{ xy }=0.2\\ { b }_{ yx }=0.8\\ r=\sqrt { { b }_{ xy }\times { b }_{ yx } } \\ r=\sqrt { 0.36 } \\ r=0.6$

Where r is coefficient of correlation.

The defects of rank correlation is/are_______________.

0%
the original values are taken
0%
the original values are not taken
0%
it becomes tedious to calculate if number exceeds 30
0%
both (B) and (C)

Karl Pearson's method is popularly known as ______________.

0%
concurrent deviation method
0%
correlation co-efficient
0%
technical co-efficient
0%
rank correlation

Correlation is said to be simple when_____________.

0%
more than two variables are studied
0%
only two variables are studied
0%
only one variable is studied
0%
the value of two variables move in the opposite direction

Coefficient of Correlation is:

0%
Always positive
0%
Always negative
0%
Positive as well as negative
0%
Always Zero

If the letter of the word

$SCHOOL$ are arranged as per dictionary then rank of the word

$SCHOOL$ is

0%
$303$
0%
$301$
0%
$302$
0%
$304$

Explanation

Find rank of the world 'SCHOOL'

5 S $\frac{5}{2!}$ $\times$ 5!	1 C $\frac{0}{2!}$ $\times$ 4!	2 H $\frac{0}{2!}$ $\times$ 3!	4 O $\frac{1}{2!}$ $\times$ 2!	4 O $\frac{1}{2!}$ $\times$ 1!	3 L $\frac{0}{2!}$ $\times$ 0!
300	0	0	1	1	0

300+0+0+1+1+0=302

302+1=303

i.e, Rank of the world 'SCHOOL' = 303

1227371_1307664_ans_108bf07bad29444fa919ca59b97536d6.png

$Which\,of\,the\,following\,is\,always\,true\,?$

0%
$1)\,\left( {p \to q} \right) \cong \left( { \sim q \to \sim p} \right)$
0%
$2) \sim \left( {p \vee q} \right) \cong \left( { \sim p \vee \sim q} \right)$
0%
$3) \sim \left( {p \to q} \right) \cong \left( {p \vee \sim q} \right)$
0%
$4) \sim \left( {p \wedge q} \right) \cong \left( { \sim p \wedge q} \right)$

The average age of

$12$ children is

$20$ years. If the age of one more child is added, the average is decreased by

$1$ . What is the age of the child added later ?

0%
$9$ years
0%
$8$ years
0%
$7$ years
0%
$6$ years

Explanation

Let the age of child added later be

$x$ years.

average age of

$12$ children

$= 20 \text{ years}$

$\therefore$ Total age of

$12$ children

$= 20 \times 12 = 240 \text{ years}$

After one more child is added-

Average of

$13$ children

$= 20 - 1 = 19 \text{ years}$

Average age of

$13$ children

$= \cfrac{\text{sum of 12 children} + x}{13}$

$19 = \cfrac{240 + x}{13}$

$\Rightarrow 240 + x = 247$

$\Rightarrow x = 247 - 240 = 7 \text{ years}$

Hence the age of child added later is

$7$ years.

Which of the following is NOT true with respect to Correlation?

0%

Correlation can be expressed graphically
0%

Correlation cannot be obtained using all type of series
0%

Correlation can be obtained through ranks
0%

Correlation can be positive, negative and zero, but never be less than one

Calculate the coefficient of correlation from following data:
Summation of products of deviation from their respective means of X and Y = 4880, SDX = 28.70, SDy = 18.02, N = 10.

0%
0.74
0%
0.84
0%
0.94
0%
None of the above

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

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

Interpret the result.

0%
This indicates a moderate positive relationship between marks in Physics and Mathematics.
0%
This indicates a high positive relationship between marks in Physics and Mathematics.
0%
This indicates a negative relationship between marks in Physics and Mathematics.
0%
None of the above

Explanation

Descending order arranged data will be as follows:

Physics:

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

Mathematics:

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

Thus data will be

Physics $(P)$

Mathematics $(M)$

Rank $(P)$

$|d|$

$d^2$

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

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

Since $r>0$ we can say that this indicate a moderate positive relationship between marks of physics and mathematics.

The given data shows test scores and sales by nine salesman during last year in a firm. Find regression of Y on X.

Test Score	14	19	24	21	26	22	15	20	19
Sales (in 000'Rs )	31	36	48	37	50	45	33	41	39

0%
$0.66x-y=96$
0%
$1.61x-y+7.83=$
0%
$.25x+2y=5$
0%
$x-0.5y=45$

The coefficient of rank correlation of marks obtained by 10 students in English and Economics was to be fount 0.It was later discovered that the difference in ranks in the two subjects obtained by one of the students was wrongly taken as 3 instead ofFind correct coefficient of rank correlation.

0%
122.5
0%
132.7
0%
142.3
0%
145.6

The marks obtained by the students in physics and in mathematics are as follows.

Marks in Physics	35	23	47	17	10	43	9	6	28
Marks in Mathematics	30	33	45	23	8	49	12	4	31

Compute of correlation of ranks.

0%
0.2
0%
0.3
0%
0.7
0%
0.9

Explanation

Marks of Physics $(X)$

Marks in Maths $(Y)$

$XY$

$X^2$

$Y^2$

1050

759

2115

391

2107

108

868

1225

529

2209

289

100

1849

784

900

1089

2025

529

2401

144

961

$\sum X=218,\quad \sum Y=235,\quad \sum XY=7502,\quad \sum X^2=7102,\quad \sum Y^2=8129$

$N=09$

Cov $(x,y)=\cfrac{\sum XY}{N}-\cfrac{\sum X}{N}.\cfrac{\sum Y}{N}=\cfrac{7502}{09}-\cfrac{218}{9}.\cfrac{235}{9}=201.08$

$\sigma_x=\sqrt{\cfrac{\sum X^2}{N}-\left(\cfrac{\sum X^2}{N}\right)^2}=\sqrt{\cfrac{7102}{09}-\left(\cfrac{218}{09}\right)^2}=14.22$

$\sigma_y=\sqrt{\cfrac{\sum Y^2}{N}-\left(\cfrac{\sum Y^2}{N}\right)^2}=\sqrt{\cfrac{8129}{09}-\left(\cfrac{235}{9}\right)^2}=14.88$

$r=\cfrac{Cov(x,y)}{\sigma_x.\sigma_y}=\cfrac{201.08}{14.22\times 14.88}=0..95$

Calculate the coefficient of correlation between

$x$ and

$y$ for the data

x	1	2	3	4	5	6	7	8	9	10
y	3	10	5	1	2	9	4	8	7	6

0%
$0.12$
0%
$0.19$
0%
$0.22$
0%
$0.62$

Explanation

$x\\ 1\\ 2\\ 3\\ 4\\ 5\\ 6\\ 7\\ 8\\ 9\\ 10\\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \sum { x=55 }$

$y\\ 3\\ 10\\ 5\\ 1\\ 2\\ 9\\ 4\\ 8\\ 7\\ 6\\ \_ \_ \_ \_ \_ \_ \_ \\ \sum { y=55 }$

$X=x-\overline { x } \\ -4.5\\ -3.5\\ -2.5\\ -1.5\\ -0.5\\ \quad 0.5\\ \quad 1.5\\ \quad 2.5\\ \quad 3.5\\ \quad 4.5\\ \_ \_ \_ \_ \_ \_ \_ \\ \quad 0$

$XY\\ \quad 11.25\\ -15.75\\ \quad 1.25\\ \quad 6.75\\ \quad 1.75\\ \quad 1.75\\ -1.25\\ \quad 6.25\\ \quad 1.75\\ \quad 2.25\\ \_ \_ \_ \_ \_ \_ \_ \\ \quad 16\\$

${ \quad X }^{ 2 }\\ 20.25\\ 12.25\\ 06.25\\ 02.25\\ 00.25\\ 00.25\\ 02.25\\ 06.25\\ 12.25\\ 20.25\\ \_ \_ \_ \_ \_ \_ \_ \\ 82.50$

${ \quad Y }^{ 2 }\\ 06.25\\ 20.25\\ 00.25\\ 12.25\\ 12.25\\ 02.25\\ 06.25\\ 02.25\\ 00.25\\ \_ \_ \_ \_ \_ \_ \_ \\ \quad 82.50$

Therefore,

$\overline { x } =\cfrac { 55 }{ 10 } \\ \quad =5.5$

$\cfrac { \sum { y } }{ 10 } =5.5$

Therefore,

$r=\cfrac { \sum { XY } }{ \sqrt { \sum { { X }^{ 2 }\sum { { Y }^{ 2 } } } } } \\ =\cfrac { 16 }{ 82.5 } \\ =0.19$

In a skating competition the judges gave the five competitors the following marks. Calculate a coefficient of rank correlation.

Competitors	A	B	C	D	E
1st judge	5.7	5.8	5.9	5.6	5.5
2nd judge	5.6	5.7	6.0	5.5	5.8

0%
$0.4$
0%
$0.56$
0%
$0.67$
0%
$0.89$

Explanation

Competition

$1st$ Judge

Rank

$2nd$ Judge

Rank

$|d|$

$d^2$

5.7

5.8

5.9

5.6

5.5

5.6

5.7

6.0

5.5

5.8

$n=5,\quad \sum d^2=12$

$r=1-\cfrac{6\sum d^2}{n(n^2-1)}=1-\cfrac{6\times 12}{5(5^2-1)}=1-\cfrac{72}{240}=0.44$

If the dependent variable increases as the independent variable increases in an estimating equation, the coefficient of correlation will be in the range of _________.

0%
0 to (-) 1
0%
0 to (-) 0
0%
0 to (-) 0.05
0%
0 to 1

Match the following items in List - I with most suitable options in List - II:

List-I	List-II
(a) Fisher	Inverse probability
(b) Karl Pearson	Normal Distribution
(c) Thomas Baye's	Correlation Coefficient
(d) Karl Gauss	Index Numbers

0%
$(a) - 4, (b) - 3, (c) - 2, (d) - 1$
0%
$(a) - 4, (b) - 3, (c) - 1, (d) - 2$
0%
$(a) - 4, (b) - 2, (c) - 3, (d) - 1$
0%
$(a) - 4, (b) - 2, (c) - 1, (d) - 3$

Karl Pearson's co-efficient of correlation between two variables is _____________.

0%
the product of their standard deviations
0%
the square root of the product of their regression co-efficient
0%
the co-variance between the variables
0%
none of the above

Following are the ranks of

$10$ students in Maths and Biology projects given by

$2$ professors. Find the rank correlation coefficient.

Maths	4	8	5	3	1	2	10	7	6	9
Biology	1	4	5	6	2	3	8	9	7	10

0%
$0.2787$
0%
$0.7213$
0%
$0.8232$
0%
$0.9031$

Explanation

Let the ranks of students obtained in Maths be

$x$ and the ranks of students obtained in Biology be

$y$ .

$x$	$4$	$8$	$5$	$3$	$1$	$2$	$10$	$7$	$6$	$9$
$y$	$1$	$4$	$5$	$6$	$2$	$3$	$8$	$9$	$7$	$10$
$d=x-y$	$3$	$4$	$0$	$-3$	$-1$	$-1$	$2$	$-2$	$-1$	$-1$
$d^2$	$9$	$16$	$0$	$9$	$1$	$1$	$4$	$4$	$1$	$1$
					$\sum d^2$ $=46$

The rank correlation coefficient is given by

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

$=1-\dfrac{6 \times 46}{10(100-1)}$

$=1-\dfrac{276}{10 \times 99}$

$=1-\dfrac{276}{990}$

$=1-0.2787$

$=0.7213$

Therefore, the rank correlation coefficient is

$0.7213$ .

If bxy

$=0.25$ and byx

$=0.64$ , correlation coefficient is _________.

0%
$0.16$
0%
$0.40$
0%
$0.89$
0%
$0.30$

Which one of the following is false statement ?

0%
The sign of the regression coefficients are always the same.
0%
Correlation coefficient is the geometric mean of the regression coefficients.
0%
The co-variance between two variables divided by the product of their standard deviations produces the value of coefficient of correlation.
0%
Coefficient of correlation is independent of origin but not of sale.

Karl Pearsons Coefficient of Correlation is also known as ______.

0%
simple correlation coefficient
0%
product moment correlation
0%
both A and B
0%
none of the above

Estimate the value of coefficient of correlation between x and y if the two coefficient of regression are 0.64 and 1 :___

0%
0.9
0%
0.7
0%
0.8
0%
1.0

CBSE Questions for Class 11 Commerce Economics Correlation Quiz 4 - MCQExams.com

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Practice Class 11 Commerce Economics Quiz Questions and Answers

CBSE Questions for Class 11 Commerce Economics Correlation Quiz 4 - MCQExams.com

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Practice Class 11 Commerce Economics Quiz Questions and Answers

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