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#### Question 1:

Make a scatter diagram from the following data and interpret the result.

 X 4 5 6 7 8 9 10 11 12 Y 78 72 66 60 54 48 42 36 30

Thus, there is perfect negative correlation between X and Y.

#### Question 2:

Represent correlation between the following figures through scatter diagram.

 X 8 16 24 31 42 50 Y 70 58 50 32 26 12

Thus, there is very high degree of negative correlation between X and Y series.

#### Question 3:

Given the following pairs of values of the variables X and Y:

 X 1 2 3 4 5 6 7 8 Y 11 12 15 20 24 18 26 29
Make a scatter diagram. Comment on the nature of relationship between variables X and Y.

Thus, there is a high degree of positive correlation between X and Y.

#### Question 4:

Given the following pair of values of the variables X and Y:

 X 8 10 12 11 9 7 13 14 15 Y 5 7 9 8 6 4 10 11 12
Also describe relationship between X and Y.

Thus, there is a perfect positive correlation between X and Y.

#### Question 5:

Find the coefficient of correlation between X and Y series from the data:

 X 10 12 8 15 20 25 40 Y 15 10 6 25 16 12 8

 X Y X2 Y2 XY 10 12 8 15 20 25 40 15 10 6 25 16 12 8 100 144 64 225 400 625 1600 225 100 36 625 256 144 64 150 120 48 375 320 300 320 $\mathbit{\Sigma }\mathbit{X}$=130 $\mathbit{\Sigma }\mathbit{Y}$=92 $\mathbit{\Sigma }{\mathbit{X}}^{\mathbf{2}}$=3158 $\mathbit{\Sigma }{\mathbit{Y}}^{\mathbf{2}}$=1450 $\mathbit{\Sigma }\mathbit{X}\mathbit{Y}$=1633

N = 7

Thus, coefficient of correlation is 0.178.

#### Question 6:

The data on price and quantity purchased relating to a commodity for 10 months are given below:Calculate coefficient of correlation between price and quantity.

 Price (₹) 10 14 12 11 9 7 15 16 18 20 Quantity (kg.) 25 20 30 32 35 40 19 16 12 10

 Price (X) Quantity (Y) X2 Y2 XY 10 14 12 11 9 7 15 16 18 20 25 20 30 32 35 40 19 16 12 10 100 196 144 121 81 49 225 256 324 400 625 400 900 1024 1225 1600 361 256 144 100 250 280 360 352 315 280 285 256 216 200 $\mathbit{\Sigma }\mathbit{X}$=132 $\mathbit{\Sigma }\mathbit{Y}$=239 $\mathbit{\Sigma }{\mathbit{X}}^{\mathbf{2}}$=1896 $\mathbit{\Sigma }{\mathbit{Y}}^{\mathbf{2}}$=6635 $\mathbit{\Sigma }\mathbit{X}\mathbit{Y}$=2794

N = 10

Thus, the coefficient of correlation between price and quantity is -0.958.

#### Question 7:

From the following data, calculate coefficient correlation between the variables X and Y using Karl Pearson's method:

 X 10 6 9 10 12 13 11 9 Y 9 4 6 9 11 13 8 4

 X Y X2 Y2 XY 10 6 9 10 12 13 11 9 9 4 6 9 11 13 8 4 100 36 81 100 144 169 121 81 81 16 36 81 121 169 64 16 90 24 54 90 132 169 88 36 $\sum X=80$ $\sum Y=64$ $\sum {X}^{2}=832$ $\sum {Y}^{2}=584$ $\sum XY=683$

N = 8

Thus, the coefficient of correlation between the variables X and Y is 0.895.

#### Question 8:

Calculate coefficient of correlation for the ages of husband and wife.

 Age of husband 24 25 22 30 34 37 Age of wife 20 21 18 26 28 30

 Age of Husband (X) Age of Wife (Y) X2 Y2 XY 24 25 22 30 34 37 20 21 18 26 28 30 576 625 484 900 1156 1369 400 441 324 676 784 900 480 525 396 780 952 1110 $\mathbit{\Sigma }\mathbit{X}$=172 $\mathbit{\Sigma }\mathbit{Y}$=143 $\mathbit{\Sigma }{\mathbit{X}}^{\mathbf{2}}$=5110 $\mathbit{\Sigma }{\mathbit{Y}}^{\mathbf{2}}$=3525 $\mathbit{\Sigma }\mathbit{X}\mathbit{Y}$=4243

N = 6

Thus, the coefficient of correlation for the ages of husband and wife is 0.992.

#### Question 9:

Find out the correlation between the marks in Statistics and marks in Accountancy:

 No. of Students 1 2 3 4 5 6 7 8 9 10 Marks in Statistics 20 35 15 40 10 35 30 25 45 30 marks in Accountancy 25 30 20 35 20 25 25 35 35 30

 Marks in Statistics (X) Marks in Accountancy (Y) X2 Y2 XY 20 35 15 40 10 35 30 25 45 30 25 30 20 35 20 25 25 35 35 30 400 1225 225 1600 100 1225 900 625 2025 900 625 900 400 1225 400 625 625 1225 1225 900 500 1050 300 1400 200 875 750 875 1575 900 $\mathbit{\Sigma }\mathbit{X}$=285 $\mathbit{\Sigma }\mathbit{Y}$=280 $\mathbit{\Sigma }{\mathbit{X}}^{\mathbf{2}}$=9225 $\mathbit{\Sigma }{\mathbit{Y}}^{\mathbf{2}}$=8150 $\mathbit{\Sigma }\mathbit{X}\mathbit{Y}$=8425

N = 10

Thus, there exists a high degree of positive correlation between the marks in Statistics and marks in Accountancy.

#### Question 10:

Find Karl Pearson's coefficient of correlation between the values of X and Y given data:

 X 128 129 130 140 132 135 125 130 132 135 Y 80 89 90 95 96 94 80 100 96 100

 X Y X2 Y2 XY 128 129 130 140 132 135 125 130 132 135 80 89 90 95 96 94 80 100 96 100 16384 16641 16900 19600 17424 18225 15625 16900 17424 18225 6400 7921 8100 9025 9261 8836 6400 10000 9216 10000 10240 11481 11700 13300 12672 12690 10000 13000 12672 13500 $\mathbit{\Sigma }\mathbit{X}$=1316 $\mathbit{\Sigma }\mathbit{Y}$=920 $\mathbit{\Sigma }{\mathbit{X}}^{\mathbf{2}}$=173348 $\mathbit{\Sigma }{\mathbit{Y}}^{\mathbf{2}}$=85159 $\mathbit{\Sigma }\mathbit{X}\mathbit{Y}$=121255

N = 10

Thus, the correlation coefficient between the values  of X and Y is 0.63.

#### Question 11:

Calculate coefficient of correlation from the following data:

 Height of fathers (inches) 66 68 69 72 65 59 62 67 61 71 Height of Sons (inches) 65 64 67 69 64 60 59 68 60 64

 Height of Fathers (X) Height of Sons (Y) X2 Y2 XY 66 68 69 72 65 59 62 67 61 71 65 64 67 69 64 60 59 68 60 64 4356 4624 4761 5184 4225 3481 3844 4489 3721 5041 4225 4096 4489 4761 4096 3600 3481 4624 3600 4096 4290 4352 4623 4968 4160 3540 3658 4556 3660 4544 $\mathbit{\Sigma }\mathbit{X}$=660 $\mathbit{\Sigma }\mathbit{Y}$=640 $\mathbit{\Sigma }{\mathbit{X}}^{\mathbf{2}}$=43726 $\mathbit{\Sigma }{\mathbit{Y}}^{\mathbf{2}}$=41068 $\mathbit{\Sigma }\mathbit{X}\mathbit{Y}$=42351

N = 10

Therefore, coefficient of correlation= 0.829YNΣX2(ΣX)2NΣY2(ΣY)2r =10×1212551316×92010×173348(1316)210×85114(920)2r=183040.29×68.84r =0.

#### Question 12:

Making use of the data given below, calculate the coefficient of correlation.

 X 10 6 9 10 12 13 11 9 Y 9 4 6 9 11 13 8 4

 X Y X2 Y2 XY 10 6 9 10 12 13 11 9 9 4 6 9 11 13 8 4 100 36 81 100 144 169 121 81 81 16 36 81 121 169 64 16 90 24 54 90 132 169 88 36 $\mathbit{\Sigma }\mathbit{X}$=80 $\mathbit{\Sigma }\mathbit{Y}$=64 $\mathbit{\Sigma }{\mathbit{X}}^{\mathbf{2}}$=832 $\mathbit{\Sigma }{\mathbit{Y}}^{\mathbf{2}}$=584 $\mathbit{\Sigma }\mathbit{X}\mathbit{Y}$=683

N = 8

Therefore, coefficient of correlation= 0.895.

#### Question 13:

The data on price and demand for a commodity is given below:

 Price (₹) 14 16 17 18 19 20 21 22 23 Demand (kg.) 84 78 70 75 66 67 62 58 60
Calculate the coefficient of correlation between price and demand and comment on its sign and magnitude.

 Price (X) demand (Y) X2 Y2 XY 14 16 17 18 19 20 21 22 23 84 78 70 75 66 67 62 58 60 196 256 289 324 361 400 441 484 529 7056 6084 4900 5625 4356 4489 3844 3364 3600 1176 1248 1190 1350 1254 1340 1302 1276 1380 $\mathbit{\Sigma }\mathbit{X}$=170 $\mathbit{\Sigma }\mathbit{Y}$=620 $\mathbit{\Sigma }{\mathbit{X}}^{\mathbf{2}}$=3280 $\mathbit{\Sigma }{\mathbit{Y}}^{\mathbf{2}}$=43318 $\mathbit{\Sigma }\mathbit{X}\mathbit{Y}$=11516

N = 9

Hence, there is a high degree of negative correlation between price and demand.

#### Question 14:

Find coefficient of correlation from the following figures:

 X 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Y 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000

 X Y X2 Y2 XY 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 1000 2000 3000 4000 5000 6000 7000 8000 9000 0.25 1.00 2.25 4.00 6.25 9.0 12.25 16.0 20.5 1000000 4000000 9000000 16000000 25000000 36000000 49000000 64000000 81000000 500 2000 4500 8000 12500 18000 24500 32000 40500 $\mathbit{\Sigma }\mathbit{X}$=22.5 $\mathbit{\Sigma }\mathbit{Y}$=45000 $\mathbit{\Sigma }{\mathbit{X}}^{\mathbf{2}}$=71.25 $\mathbit{\Sigma }{\mathbit{Y}}^{\mathbf{2}}$=285000000 $\mathbit{\Sigma }\mathbit{X}\mathbit{Y}$=142500

N = 9

Thus, the coefficient of correlation is 1.

#### Question 15:

Calculate product moment correlation between the values of X and Y.

 X 2 3 1 5 6 4 Y 4 5 3 4 6 2

 X Y X2 Y2 XY 2 3 1 5 6 4 4 5 3 4 6 2 4 9 1 25 36 16 16 25 9 16 36 4 8 15 3 20 36 8 $\mathbit{\Sigma }\mathbit{X}$=21 $\mathbit{\Sigma }\mathbit{Y}$=24 $\mathbit{\Sigma }{\mathbit{X}}^{\mathbf{2}}$=91 $\mathbit{\Sigma }{\mathbit{Y}}^{\mathbf{2}}$=106 $\mathbit{\Sigma }\mathbit{X}\mathbit{Y}$=90

N = 6

Hence, product moment correlation = 0.454

#### Question 16:

Following are the heights and weights of 10 students of a class:

 Height (inches) 60 64 68 62 67 69 70 72 65 61 Weight (kg) 50 48 56 65 49 52 57 60 59 47

Calculate the coefficient of correlation by Karl Pearson's method:

 Height (X) Weight (Y) X2 Y2 XY 60 64 68 62 67 69 70 72 65 61 50 48 56 65 49 52 57 60 59 47 3600 4096 4624 3844 4489 4761 4900 5184 4225 3721 2500 2304 3136 4225 2401 2704 3249 3600 3481 2209 3000 3072 3808 4030 3283 3588 3990 4320 3835 2867 $\mathbit{\Sigma }\mathbit{X}$=658 $\mathbit{\Sigma }\mathbit{Y}$=543 $\mathbit{\Sigma }{\mathbit{X}}^{\mathbf{2}}$=43444 $\mathbit{\Sigma }{\mathbit{Y}}^{\mathbf{2}}$=29809 $\mathbit{\Sigma }\mathbit{X}\mathbit{Y}$=35793

N = 10

Hence, coefficient of correlation is 0.29.

#### Question 17:

Calculate coefficient of correlation from the following data:

 X 30 36 42 48 54 60 72 82 Y 50 50 54 54 62 66 70 82

 X Y X2 Y2 XY 30 36 42 48 54 60 72 82 50 50 54 54 62 66 70 82 900 1296 1764 2304 2916 3600 5184 6724 2500 2500 2916 2916 3844 4356 4900 6724 1500 1800 2268 2592 3348 3960 5040 6724 $\mathbit{\Sigma }\mathbit{X}$=424 $\mathbit{\Sigma }\mathbit{Y}$=488 $\mathbit{\Sigma }{\mathbit{X}}^{\mathbf{2}}$=24688 $\mathbit{\Sigma }{\mathbit{Y}}^{\mathbf{2}}$=30656 $\mathbit{\Sigma }\mathbit{X}\mathbit{Y}$=27232

N = 8

Hence, coefficient of correlation= 0.9753

#### Question 18:

Calculate Karl Pearson's coefficient of correlation between income and expenditure of 10 families from the following data:

 Income (in '000) 59 55 58 60 65 63 54 56 66 64 Expenditure (in '000) 52 53 55 58 57 66 59 54 52 54

 Income (X) Expenditure (Y) X2 Y2 XY 59 55 58 60 65 63 54 56 66 64 52 53 55 58 57 66 59 54 52 54 3481 3025 3364 3600 4225 3969 2916 3136 4356 4096 2704 2809 3025 3364 3249 4356 3481 2916 2704 2916 3068 2915 3190 3480 3705 4158 3186 3024 3432 3456 $\mathbit{\Sigma }\mathbit{X}$=600 $\mathbit{\Sigma }\mathbit{Y}$=560 $\mathbit{\Sigma }{\mathbit{X}}^{\mathbf{2}}$=36168 $\mathbit{\Sigma }{\mathbit{Y}}^{\mathbf{2}}$=31524 $\mathbit{\Sigma }\mathbit{X}\mathbit{Y}$=33614

N = 10

Thus, coefficient of correlation = 0.0843

#### Question 19:

Calculate Karl Pearson's coefficient between the marks (out of 30) in English and Hindi obtained by 10 students.

 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

 Marks in English (X) Marks in Hindi (Y) X2 Y2 XY 10 25 13 25 22 11 12 25 21 20 12 22 16 15 18 18 17 23 24 17 100 625 169 625 484 121 144 625 441 400 144 484 256 225 324 324 289 529 576 289 120 550 208 375 396 198 204 575 504 340 $\mathbit{\Sigma }\mathbit{X}$=184 $\mathbit{\Sigma }\mathbit{Y}$=182 $\mathbit{\Sigma }{\mathbit{X}}^{\mathbf{2}}$=3734 $\mathbit{\Sigma }{\mathbit{Y}}^{\mathbf{2}}$=3440 $\mathbit{\Sigma }\mathbit{X}\mathbit{Y}$=3470

N = 10

Thus, coefficient of correlation = 0.574

#### Question 20:

Calculate coefficient of correlation from the following data:
(i) Sum of deviation of X values = −6
(ii) Sum of deviation of Y values = 1
(iii) Sum of squares of deviations of X values = 196
(iv) Sum of squares of deviation of Y values = 87
(v) Sum of the product of deviations of X and Y values =124
(vi) No of pairs of observations = 6

Given:

Hence, coefficient of correlation=0.974

#### Question 21:

Two judges in a beauty competition rank the 12 entries as follows:

 X 1 2 3 4 5 6 7 8 9 10 11 12 Y 12 9 6 10 3 5 4 7 8 2 11 1

Calculate the Spearman's rank coefficient of correlation.

 X Y R1 R2 D=R1−R2 D2 1 2 3 4 5 6 7 8 9 10 11 12 12 9 6 10 3 5 4 7 8 2 11 1 1 2 3 4 5 6 7 8 9 10 11 12 12 9 6 10 3 5 4 7 8 2 11 1 −11 −7 −3 −6 2 1 3 1 1 8 0 11 121 49 9 36 4 1 9 1 1 64 0 121 N = 12 $\Sigma {D}^{2}$=416

Here, m = 0

Hence, spearmen's rank coefficient of correlation = -0.454

#### Question 22:

A group of ten workers of a factory is ranked according to their efficiency by two different judges as follows:

 Name of Worker A B C D E F G H I J Rank by Judge A 4 8 6 7 1 3 2 5 10 9 Rank by Judge B 3 9 6 5 1 2 4 7 8 10

Calculate the coefficient of rank correlation.

 Name of Worker Rank by Judge A (RA) Rank by Judge B (RB) D= RA−RB D2 A B C D E F G H I J 4 8 6 7 1 3 2 5 10 9 3 9 6 5 1 2 4 7 8 10 1 -1 0 2 0 1 -2 -2 2 -1 1 1 0 4 0 1 4 4 4 1 $\Sigma {D}^{2}$=20

N = 10

Hence, coefficient of rank correlation=0.88

#### Question 23:

Ten competitors in a debate contest are ranked by three judges in the following order.

 Competitors A B C D E F G H I J Ranks By 1st Judge 7 4 10 5 9 8 6 2 1 3 Ranks By 2nd Judge 4 1 9 10 7 3 2 5 6 8 Ranks By 3rd Judge 10 2 8 5 7 6 9 1 4 3

Using the ranking correlation method and state which pair of judges have the nearest approach.

 Competitors R1 R2 R3 D1 = R1 - R2 ${\mathbit{D}}_{\mathbf{1}}^{\mathbf{2}}$ D2 = R1 - R3 ${\mathbit{D}}_{\mathbf{2}}^{\mathbf{2}}$ D3 = R2 - R3 ${\mathbit{D}}_{\mathbf{3}}^{\mathbf{2}}$ A B C D E F G H I J 7 4 10 5 9 8 6 2 1 3 4 1 9 10 7 3 2 5 6 8 10 2 8 5 7 6 9 1 4 3 3 3 1 −5 2 5 4 −3 −5 −5 9 9 1 25 4 25 16 9 25 25 −3 2 2 0 2 2 −3 1 −3 0 9 4 4 0 4 4 9 1 9 0 −6 −1 1 5 0 −3 −7 4 2 5 36 1 1 25 0 9 49 16 4 25 $\Sigma {{D}_{1}}^{2}$=148 $\Sigma {{D}_{2}}^{2}$=44 $\Sigma {{D}_{3}}^{2}$=166

N = 10

Rank Correlation between Judge 1 and Judge 2

Rank Correlation between Judge 1 and Judge 3

Rank Correlation between Judge 2 and Judge 3

As the rank correlation coefficient between Judge 1 and Judge 3 is highest, thus Judge 1 and Judge 3 has the nearest approach.

#### Question 24:

A group of 8 students got the following marks in a test in Maths and Accountancy.

 Marks in Maths 50 60 65 70 75 40 80 85 Marks in Accountancy 80 71 60 75 90 82 70 50
Compute the coefficient of rank correlation.

 Marks in Maths Marks in Accountancy R1 R2 D= R1−R2 D2 50 60 65 70 75 40 80 85 80 71 60 75 90 82 70 50 2 3 4 5 6 1 7 8 6 4 2 5 8 7 3 1 −4 −1 2 0 −2 −6 4 7 16 1 4 0 4 36 16 49 $\Sigma {D}^{2}$=126

N = 8

Hence, coefficient of rank correlation = -0.5

#### Question 25:

Calculate rank correlation between advertisement cost and sales as per the data given below:

 Cost (in '000 ₹) 78 36 98 25 75 82 90 62 65 39 Sales (in lakh ₹) 84 51 91 60 68 62 86 58 53 47

 Advertising Cost (X) Sales (Y) R1 R2 D= R1−R2 D2 78 36 98 25 75 82 90 62 65 39 84 51 91 60 68 62 86 58 53 47 7 2 10 1 6 8 9 4 5 3 8 2 10 5 7 6 9 4 3 1 −1 0 0 −4 −1 2 0 0 2 2 1 0 0 16 1 4 0 0 4 4 $\Sigma {D}^{2}$=30

N= 1

Hence, coefficient of rank correlation = -0.82

#### Question 26:

Calculate the coefficient of rank correlation from the following data:

 X 48 33 40 9 16 16 65 24 16 57 Y 13 13 24 6 15 4 20 9 6 19

 X Y R1 R2 D = R1−R2 D2 48 33 40 9 16 16 65 24 16 57 13 13 24 6 15 4 20 9 6 19 8 6 7 1 3 3 10 5 3 9 5.5 5.5 10 2.5 7 1 9 4 2.5 8 2.5 0.5 −3 −1.5 −4 2 1 1 0.5 1 6.25 0.25 9.0 2.25 16 4 1 1 0.25 1.0 $\Sigma {D}^{2}$=41.00

N = 10

Hence, coefficient of rank correlation = 0.733

#### Question 27:

The coefficient of rank correlation of the marks obtained by 10 students in two particular subjects was found to be 0.5. It was later discovered that the difference in ranks in two subjects obtained by one of the students was wrongly taken as 3 instead of 7. What should be the correct value of coefficient of rank correlation.

Given, rk = 0.5
N = 10

Now,

Hence, correct coefficient of rank correlation is 0.257.

#### Question 28:

Find the standard deviation of X series, if coefficient of correlation between two series X and Y is 0.35 and their covariance in 10.5 and variance of Y series is 56.25.

Given,  r = 0.35
Cov (x,y) = 10.5
${\sigma }_{y}^{2}=56.25\phantom{\rule{0ex}{0ex}}⇒{\sigma }_{y}^{}=7.5$
Substituting the given values in the formula we get,

Hence, standard deviation of X series is 4.

#### Question 29:

The ranking of ten students in two subjects A and B as follows:

 Subject A 3 5 8 4 7 10 2 1 6 9 Subject B 6 4 9 8 1 2 3 10 5 7
What is the coefficient of rank correlation?

 RA RB D = RA − RB D2 3 5 8 4 7 10 2 1 6 9 6 4 9 8 1 2 3 10 5 7 −3 1 −1 −4 6 8 −1 −9 1 2 9 1 1 16 36 64 1 81 1 4 $\Sigma {D}^{2}$=214

N = 10

Hence, coefficient of rank correlation is -0.297.

#### Question 30:

Calculate the number of items, when
(i) Standard deviation of series Y = 10
(ii) Coefficient of correlation = 0.6
(iii) Sum of the product of deviation of X and Y from actual means = 150
(iv) Sum of squares of deviations of X from actual means = 125

Squaring both sides, we get

Hence, number of items = 5

#### Question 31:

Find the coefficient of rank correlation between the marks obtained in Mathematics and those in Statistics by 10 students of a class.

 Marks in Mathematics 12 18 32 18 25 24 25 40 38 22 Marks in Statistics 16 15 28 16 24 22 25 36 34 19

 Marks in Maths Marks in Statistics R1 R2 D = R1−R2 D2 12 18 32 18 25 24 25 40 38 22 16 15 28 16 24 22 25 36 34 19 1 2.5 8 2.5 6.5 5 6.5 10 9 4 2.5 1 8 2.5 6 5 7 10 9 4 -1.5 1.5 0 0 0.5 0 -0.5 0 0 0 2.25 2.25 0 0 0.25 0 0.25 0 0 0 $\Sigma {D}^{2}$=5

Here, N = 10
m1= m2 = m3 = 2

Hence, the value of rank correlation coefficient is 0.960.

#### Question 32:

From the following data, calculate coefficient of correlation.

 X 57 59 62 63 64 65 58 66 70 72 Y 113 117 126 125 130 128 110 132 140 149

 X Y X2 Y2 XY 57 59 62 63 64 65 58 66 70 72 113 117 126 125 130 128 110 132 140 149 3249 3481 3844 3969 4096 4225 3364 4356 4900 5184 12769 13689 15876 15625 16900 16384 12100 17424 19600 22201 6441 6903 7812 7875 8320 8320 6380 8712 9800 10728 $\Sigma X$=636 $\Sigma Y$=1270 $\Sigma {X}^{2}$=40668 $\Sigma {Y}^{2}$=162568 $\Sigma XY$=81291

N = 10

Hence, coefficient of correlation is 0.982.

#### Question 33:

Calculate the coefficient of correlation, if:
(i) Covariance between X and Y = 9.2
(ii) Variance of X = 11.5
(iii) Variance of Y = 14.2

Given, Cov(x,y) = 9.2

Hence, coefficient of correlation is 0.721.

#### Question 34:

Find Karl Pearson's coefficient for the following data:

 Marks in English 45 70 65 30 90 40 50 75 85 60 Marks in Maths 35 90 70 40 95 40 60 80 80 50

 Marks in English (X) Marks in Maths (Y) X2 Y2 XY 45 70 65 30 90 40 50 75 85 60 35 90 70 40 95 40 60 80 80 50 2025 4900 4225 900 8100 1600 2500 5625 7225 3600 1225 8100 4900 1600 9025 1600 3600 6400 6400 2500 1575 6300 4550 1200 8550 1600 3000 6000 6800 3000 $\Sigma X$=610 $\Sigma Y$=640 $\Sigma {X}^{2}$=40700 $\Sigma {Y}^{2}$=45350 $\Sigma XY$=42575