Correlation Test

Result

Correlation Test - 13

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1

1 / -0

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

0.76

0.66

0.56

0.48 Solution

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

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

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

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

Question 2

1 / -0

Directions For Questions

Study the following table and answer the questions based on it.
Expenditure of a Company (in Lakh Rupees) per Annum Over the given years.

Year	Salary	Fuel and Transport	Bonus	Interest on Loans	Taxes
$$1998$$	$$288$$	$$98$$	$$3.00$$	$$23.4$$	$$83$$
$$1999$$	$$342$$	$$112$$	$$2.52$$	$$32.5$$	$$108$$
$$2000$$	$$324$$	$$101$$	$$3.84$$	$$41.6$$	$$74$$
$$2001$$	$$336$$	$$133$$	$$3.68$$	$$36.4$$	$$88$$
$$2002$$	$$420$$	$$142$$	$$3.96$$	$$49.4$$	$$98$$

...view full instructions

Total expenditure on all these items in $$1998$$ was approximately what percent of the total expenditure in $$2002$$?

$$62$$%

$$66$$%

$$69$$%

$$71$$%

Solution

Required percentage $$= \left [\dfrac {(288 + 98 + 3.00 + 23.4 + 83)}{(420 + 142 + 3.96 + 49.4 + 98)} \times 100\right ]$$%
$$= \left [\dfrac {485.4}{713.36}\times 100\right ]$$%
$$\approx 69.45$$%.

Question 3
1 / -0

If increase in value of one variable is accompnied by the proportional decrease in second variable, then corrrelation between two variables is

A
perfect positive

B
perfect negative

C
imperfect positive

D
imperfect negative

Solution

If increase in value of one variable is accompnied by the proportional decrease in second variable, then corrrelation between two variables is perfect negative.
Question 4
1 / -0

The correlation between number of hours and efficiency of work is

A
perfect positive

B
perfect negative

C
imperfect positive

D
imperfect negative

Solution

relationship between their output and their working hours
$$\therefore$$ The correlation between number of hours and efficiency of work is imperfect negative
Option D is correct
Question 5
1 / -0

Find Karl pearson's correlation coefficient.
Marks in english 10 25 13 25 22 11 12 25 21 20
Marks in hindi 12 22 16 15 18 18 17 23 24 17

A
$$0.99$$

B
$$0.6$$

C
$$.235$$

D
$$0.462$$

Solution

$$\bar { x } =\cfrac { \sum { x } }{ n }=\cfrac{184}{10}=18.4 $$
$$\bar { y } =\cfrac { \sum {y } }{ n }=\cfrac{182}{10}=18.2 $$
$$r=\cfrac { \sum { (x-\bar { x } )(y-\bar { y } ) } }{ \sqrt { \sum { { (x-\bar { x } ) }^{ 2 } } \sum { { (y-\bar { y } ) }^{ 2 } } } } =\cfrac { 97.44 }{ \sqrt { 348.4\times 127.50 } } =0.462$$

Question 6

1 / -0

	Height	Long Jump	High Jump
A	158	324	175
B	165	365	185
C	162	380	180
D	170	400	184
E	175	350	199
F	163	350	172
G	178	425	189

Find rank correlation between height & long jump and height & high jump.

$$0.9 \ and \ 0.25$$

$$0.86 \ and\ 0.52$$

$$0.52 \ and \ 0.86$$

$$0.89 and \ 0.63$$

Solution

$$Height$$	$$Rank(Height)$$	$$Long\,Jump$$	$$Rank(Long\,jump)$$	$$d$$	$$d^2$$
$$158$$	$$7$$	$$324$$	$$6$$	$$1$$	$$1$$
$$165$$	$$4$$	$$365$$	$$4$$	$$0$$	$$0$$
$$162$$	$$6$$	$$380$$	$$3$$	$$3$$	$$9$$
$$170$$	$$3$$	$$400$$	$$2$$	$$1$$	$$1$$
$$175$$	$$2$$	$$350$$	$$6$$	$$4$$	$$16$$
$$163$$	$$5$$	$$350$$	$$5$$	$$0$$	$$0$$
$$178$$	$$1$$	$$425$$	$$1$$	$$0$$	$$0$$
					$$\sum d^2=26$$

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

$$=1-\dfrac{6\times 26}{7((7)^2-1)}$$

$$=0.52$$

$$Height$$	$$Rank(Height)$$	$$High\,jump$$	$$Rank(High\,jump)$$	$$d$$	$$d^2$$
$$158$$	$$7$$	$$175$$	$$6$$	$$1$$	$$1$$
$$165$$	$$4$$	$$185$$	$$3$$	$$1$$	$$1$$
$$162$$	$$6$$	$$180$$	$$5$$	$$1$$	$$1$$
$$170$$	$$3$$	$$184$$	$$4$$	$$1$$	$$1$$
$$175$$	$$2$$	$$199$$	$$1$$	$$1$$	$$1$$
$$163$$	$$5$$	$$172$$	$$7$$	$$2$$	$$4$$
$$178$$	$$1$$	$$189$$	$$2$$	$$1$$	$$1$$
					$$\sum d^2=10$$

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

$$=1-\dfrac{6\times 10}{7((7)^2-1)}$$

$$=0.86$$

Question 7
1 / -0

Chemistry 28 6 9 43 10 17 47 23 35
Biology 8 49 12 4 31 30 33 45 23
The marks obtained in Chemistry and Biology are as follows;

A
$$0.1$$

B
$$-0.35$$

C
$$-0.86$$

D
$$0.78$$

Solution

$$\rho=1-\cfrac{6\sum{{d}^{2}}}{n({n}^{2}-1)}=\cfrac{6\times{162}^{2}}{9\times 80}=-0.35$$
Question 8
1 / -0

When two regression coefficients bear same algebraic signs, then correlation coefficient is:

A
Positive

B
Negative

C
According to two signs

D
Zero

Solution

The '+' or '-' sign is given to the correlation coefficient based on the signs of the two regression coefficients.

$$r=\pm \sqrt{b_{yx}*b_{xy}}$$

where $$r$$ is the correlation coefficient
$$b_{yx},b_{xy}$$ are the regression coefficients.
Question 9
1 / -0

Calculate Spearman's rank coefficient for the data:
Mathematics 1 2 3 4 5 6 7 8 9 10
Statistics 2 4 1 5 3 9 7 10 6 8

A
$$0.56$$

B
$$0.45$$

C
$$-0.76$$

D
$$0.76$$

Solution

$$\rho=1-\cfrac{6\sum{{d}^{2}}}{n({n}^{2}-1)}=1-\cfrac{6\times 40}{10(100-1)}=1-\cfrac{240}{990}=0.758\approx 0.76$$
Question 10
1 / -0

It is high degree of relation if

A
$$-0.7\gt r\gt -0.99$$

B
$$0.7\lt r\lt 0.99$$

C
$$0.5\lt r \lt0.699$$

D
$$r=1$$

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Marks in english	10	25	13	25	22	11	12	25	21	20
Marks in hindi	12	22	16	15	18	18	17	23	24	17

Chemistry	28	6	9	43	10	17	47	23	35
Biology	8	49	12	4	31	30	33	45	23

Correlation Test - 13

Result

Correlation Test - 13

Score

-

Rank

-

SHARING IS CARING

Question 1

0.76

0.66

0.56

0.48

Solution

Question 2

$$62$$%

$$66$$%

$$69$$%

$$71$$%

Solution

Question 3

perfect positive

perfect negative

imperfect positive

imperfect negative

Solution

Question 4

perfect positive

perfect negative

imperfect positive

imperfect negative

Solution

Question 5

$$0.99$$

$$0.6$$

$$.235$$

$$0.462$$

Solution

Question 6

$$0.9 \ and \ 0.25$$

$$0.86 \ and\ 0.52$$

$$0.52 \ and \ 0.86$$

$$0.89 and \ 0.63$$

Solution

Question 7

$$0.1$$

$$-0.35$$

$$-0.86$$

$$0.78$$

Solution

Question 8

Positive

Negative

According to two signs

Zero

Solution

Question 9

$$0.56$$

$$0.45$$

$$-0.76$$

$$0.76$$

Solution

Question 10

$$-0.7\gt r\gt -0.99$$

$$0.7\lt r\lt 0.99$$

$$0.5\lt r \lt0.699$$

$$r=1$$

User

Question Analysis

My Perfomance

Score

-

Rank

-

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.