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Syllabus

solutions of statistics for economics by T.R.Jain

V.K.ohri

From the following information determine coefficient of correlation between X and Y series.

X SERIES :

No. of items = 15

Mean = 25

S.D. = 3.01

Sum of squares of deviation from Mean = 136

Sum of product of deviations of X and Y from their respective means = 122

Y SERIES :

No. of items = 15

Mean = 18

S.D. = 3.03

Sum of squares of deviation from mean = 138

Sum of product of deviations of X and Y from their respective means = 122

how can we derive the formula of karl pearson's cefficient of correlation in shortcut method?

1. a straight line parallel to x axis

2. a straight line parallel to y axis

3. a straight line sloping upward

4 a straight sloping downward

prove that coefficient of correlation always lies between -1 to +1

From the following data relating to playing habits in various age groups of 900 students. Calculate coefficient of correlation between age group and playing habits.

Age group = 15-16, 16-17, 17-18, 18-19, 19-20, 20-21

No.of students = 250, 200, 150, 120, 100, 80

Regular Players = 200, 150, 90, 48, 30, 12

From the following data determine Karl Pearson's coefficient of correlation between X and Y series for 15 pairs.

X SERIES :

Mean = 80

Sum of squares of deviation from A.M. = 56

Sum of product of deviations of X and Y from their respective Means = 92

Y SERIES :

Mean = 120

Sum of squares of deviation from A.M. = 156

Sum of product of deviations of X and Y from their respective Means = 92

and Y?

plse solv Q. 13 , Q 14 , Q 15 of saraswati statistics book on pg 190

_{k}a). Coefficient of correlation is between -1 and +1 . How would you express it arithmetically?

b). define Karl pearson's method of calculating coefficient of correlation and spearman's rank difference method.

c). What are limits of correlation coefficient r ?

d). If r = +1 in one situation and r = -1 in the other, what kind of relationship exist between the variables X and Y ?

e). What are the limits of coefficient of rank correlation ?

f). If thje values of X and Y have been ranked and we compute correaltion between ranks of Xand Y, will this correlation be equal to the value of coefficient of rank correlation ?

how to calculate the step deviation

X 42 44 58 55 89 98

Y 56 49 53 58 65 76

find out rank difference correlation of x and y

x-80,78,75,75,58;67;60;59y-12,13,14,14,14,16,15,17q. calculate corelation coefficient

x ; 65 66 57 67 68 69 70 72

y ; 67 56 65 68 72 72 69 71

from dis formula ;

r= ∑xy ∕ Nsd(x) sd(y)

can we use assumed mean method to calculate karl pearson's correlation coefficient

experts please give the answers with same numbers which is provided in question don’t change the numbers and don’t provide any link.)Calculate the correlation coefficient between X and Y and comment on their relationship

X1

3

4

5

7

8

Y2

6

8

10

14

16

Following data relates to density of population, number of deaths and population of various cities. Calculate death rate and Karl pearson coefficient between density of population and death rate.

Cities = P, Q, R, S, T, U

Density of population = 200, 500, 700, 500, 600, 900

No. of deaths = 840, 300, 312, 560, 1440, 1224

Population = 42000, 30000, 24000, 40000, 90000, 72000

correlation, given the following data:

X 78 89 97 69 59 79 68 61

Y 125 137 156 112 107 106 123 138

what is assumed mean method for karl pearson's coefficient?

a). Coefficient of correlation is between -1 and +1 . How would you express it arithmetically?

b). define Karl pearson's method of calculating coefficient of correlation and spearman's rank difference method.

c). What are limits of correlation coefficient r ?

d). If r = +1 in one situation and r = -1 in the other, what kind of relationship exist between the variables X and Y ?

e). What are the limits of coefficient of rank correlation ?

f). If thje values of X and Y have been ranked and we compute correaltion between ranks of Xand Y, will this correlation be equal to the value of coefficient of rank correlation ?

by using karl pearson actual mean method

Age (year); 1 2 3 4 5

weight(kg);3 4 6 7 10

experts please give the answers with same numbers which is provided in question don’t change the numbers and don’t provide any link.)b. Calculate coefficient of correlation from the following data.X- 1, 2, 3, 4, 5, 6 ,7, 8, 9

Y- 9, 8 ,10, 12 ,11 ,13, 14, 16, 15

Calculate the correlation coefficient between the heights of fathers in inches (X) and their sons (Y)

X65

66

57

67

68

69

70

72

Y67

56

65

68

72

72

69

71

of children.

Age (years) 1 2 3 4 5

Weight (kg) 3 4 6 7 10

Experts pls give me the solution of this probelm

$\overline{)\begin{array}{ccccccccc}AgeofHusband& 20& 23& 27& 31& 35& 58& 40& 42\\ AgeofWife& 18& 20& 24& 30& 32& 34& 36& 38\end{array}}$

Why is

rpreferred to covariance as a measure of association?X 18 21 22 19 20 17 20 23 18 22

Y 14 15 18 16 12 13 15 15 17 15

how to draw a scatter diagram when r= -0.9 and r= o.3

If

r= 0 the variable X and Y are_{xy }(i) linearly related

(ii) not linearly related

(iii) independent

Please make me understand about karl pearsons cofficient of correlation..

I have to learn how to construct correlation from all methods...???

experts please give the answers with same numbers which is provided in question don’t change the numbers and don’t provide any link.)Why does rank correlation coefficient differ from Pearsonian correlation coefficient?

calculate rank correlation and Karlpear sons method of correlation

x 77,54,27,52,14,35,90,25.56,60

y 35,58,60,46,50,40,35,56,44,42

In the method of karl pearson for the coefficient of correlation can we find the standard deviation by the root of variance if discrete sries is given to us and then proceed further ?

Calculate the correlation coefficient between X and Y and comment on their relationship:

X–3

–2

–1

1

2

3

Y9

4

1

1

4

9

calculate the correlation cofficient between X and Y and comment on their relationship:

X -3 -2 -1 1 2 3

Y 9 4 1 1 4 9

following data relates to age group and percentage of regular players . calculate karl pearson 's cofficient of correlation. age group : 20-25 25-30 30-35 35-40 40-45 45-50 % of regular players : 40 35 28 20 15 5

The unit of correlation coefficient between height in feet and weight in kgs is

(i) kg/feet

(ii) percentage

(iii) non-existent

I.e 1× m3-m

12

But for how long will we keep on adding this correction factor ??

Is it related with the NUMBER OF VARIABLES USED to find correlation ??

Pls tell ... ? AND explain in detail

Differentiate between Karl pearson's coefficient of correlation and spearman's rank correlation.

calculate coefficient of correlation of the age of husband and wife using karl pearson's method

Explain the relation between price and quantity supplied through a scattered diagramPrice 10 20 30 40 50 60

Quantity 25 50 75 100 125 150

Can simple correlation coefficient measure any type of relationship?

According to the spearman's rank correlation in ncert book (page101) what does the line - "It is the product moment correlation between the ranks" mean

Define Scattered Diagram??

actual mean method of karl pearson

Q2 Caclulate correlation using Karl pearson method:

X: 112 114 108 124 145 150 119 125 150

Y: 200 190 214 187 170 170 210 190 180 181

When is rank correlation more precise than simple correlation coefficient?

Does zero correlation mean independence?

Q.2. Calculate Karl Pearson's coefficient of correlation, between the age and weight of children.

(Ans. r = + 0.98)

If

r_{xy }is positive the relation between X and Y is of the type(i) When Y increases X increases

(ii) When Y decreases X increases

(iii) When Y increases X does not change

Q.1. Plot the following data asa a scatter diadram and comment over the result :

X : 1110 15 13 10 16 13 8 17 14

Y : 67 99 7 11 9 6 1211

Q.2. From the following data compute the product moment corralation between x and y .

x series y series

Arithmetic mean 25 18

square of deviations from arithmetic mean136 138

Q.3. Calculate karl pearsons cofficient of corralation on the following data :

x : 1518 21 24 27 3036 39 42 48

y : 25 25 27 27 3133 35 41 4145

Q.4. Calculate correlation cofficient between x, the number of raniy days per month and y , the number of rain coats sold in that month in a certain shop for 12 month . interpret the results .

X : 14 8 18 10 22 9 3 5 6 11 13 13

Y : 15 11 20 12 15 7 3 4 7 10 11 29

Q.5. The deviations from their means of two series (x and y) are given below :

x : -4 -3 -2 -1 0 +1 +2 +3 +4

y : +3 -3 -4 0 +4 +1 +2 -2 -1

Q.6. Find suitable coefficient of correlation for the following data :

Fertilizers used (in tons) : 15 18 20 24 30 35 40 50

Productivity (in tons) : 85 93 95 105 120 130150 160

what is partial correlation?

Name the methods used to measure correlation and also define them briefly.

what are the general guidelines for construction of frequency distribution

Model Test Paper 4 Q31: answer for standard deviation sum is -0.895 and not as given.

If

r_{xy }is positive the relation between X and Y is of the type(i) When Y increases X increases

(ii) When Y decreases X increases

(iii) When Y increases X does not change

List some variables where accurate measurement is difficult.