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solutions of statistics for economics by T.R.Jain
V.K.ohri
how can we derive the formula of karl pearson's cefficient of correlation in shortcut method?
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
plse solv Q. 13 , Q 14 , Q 15 of saraswati statistics book on pg 190
find out rank difference correlation of x and y
x- 80,78,75,75,58;67;60;59
y-12,13,14,14,14,16,15,17
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
how to calculate the step deviation
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 ?
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 ?
can we use assumed mean method to calculate karl pearson's correlation coefficient
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
Calculate the correlation coefficient between X and Y and comment on their relationship
X
1
3
4
5
7
8
Y
2
6
10
14
16
what is assumed mean method for karl pearson's coefficient?
Explain the relation between price and quantity supplied through a scattered diagram
Price 10 20 30 40 50 60
Quantity 25 50 75 100 125 150
by using karl pearson actual mean method
Age (year); 1 2 3 4 5
weight(kg);3 4 6 7 10
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)
65
66
57
67
68
69
70
72
56
71
q. 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)
Why is r preferred to covariance as a measure of association?
If rxy = 0 the variable X and Y are
(i) linearly related
(ii) not linearly related
(iii) independent
how to draw a scatter diagram when r= -0.9 and r= o.3
Please make me understand about karl pearsons cofficient of correlation..
I have to learn how to construct correlation from all methods...???
From the following information determine coefficient of correlation between X and Y 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
Mean = 18
S.D. = 3.03
Sum of squares of deviation from mean = 138
Why does rank correlation coefficient differ from Pearsonian correlation coefficient?
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 ?
The unit of correlation coefficient between height in feet and weight in kgs is
(i) kg/feet
(ii) percentage
(iii) non-existent
Calculate the correlation coefficient between X and Y and comment on their relationship:
–3
–2
–1
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
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
Differentiate between Karl pearson's coefficient of correlation and spearman's rank correlation.
Can simple correlation coefficient measure any type of relationship?
calculate coefficient of correlation of the age of husband and wife using karl pearson's method
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
When is rank correlation more precise than simple correlation coefficient?
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
Does zero correlation mean independence?
Name the methods used to measure correlation and also define them briefly.
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Syllabus
solutions of statistics for economics by T.R.Jain
V.K.ohri
how can we derive the formula of karl pearson's cefficient of correlation in shortcut method?
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
plse solv Q. 13 , Q 14 , Q 15 of saraswati statistics book on pg 190
find out rank difference correlation of x and y
x- 80,78,75,75,58;67;60;59
y-12,13,14,14,14,16,15,17
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
how to calculate the step deviation
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 ?
can we use assumed mean method to calculate karl pearson's correlation coefficient
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
Calculate the correlation coefficient between X and Y and comment on their relationship
X
1
3
4
5
7
8
Y
2
6
8
10
14
16
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 ?
Explain the relation between price and quantity supplied through a scattered diagram
Price 10 20 30 40 50 60
Quantity 25 50 75 100 125 150
by using karl pearson actual mean method
Age (year); 1 2 3 4 5
weight(kg);3 4 6 7 10
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)
X
65
66
57
67
68
69
70
72
Y
67
56
65
68
72
72
69
71
q. 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)
called ____________ (fill in the blank) (1)
2. Every element of population is included in investigation (choose cor-
rect option) (1)
(a) Sample survey (b) Survey for all
(c) secondary survey (d) census survey
3. Choose the correct match (1)
(a) Bar diagram height and weight of bars are not equal
(b) Ogive represent median diagrammatically
(c) Histogram width of rectangles are always equal
(d) Pie diagram represent two discrete variables on a pie diagram
4. Which of the following is not a positional value? (1)
(a) Median (b) Quartile
(c) Deciles (d) Mode
5. The sum of deviation of items from mean is always zero, (true/false)
(1)
6. Coefficient of range for the following data is Age: 18, 14, 20, 30, 26,
10, 19, 23, 22, 12 (1)
(a) 0.2 (b) 6
(c) 0.3 (d) 0.5
7. Absolute measure of dispersion cannot be used when comparison of
two or more variable is involved, (true/false) (1)
8. Consumer Price Index (CPI) is not used in (1)
(a) Wages decision (b) Production policy
(c) Price policy (d) Taxation
Why is r preferred to covariance as a measure of association?
If rxy = 0 the variable X and Y are
(i) linearly related
(ii) not linearly related
(iii) independent
how to draw a scatter diagram when r= -0.9 and r= o.3
Please make me understand about karl pearsons cofficient of correlation..
I have to learn how to construct correlation from all methods...???
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
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
Why does rank correlation coefficient differ from Pearsonian correlation coefficient?
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 ?
The unit of correlation coefficient between height in feet and weight in kgs is
(i) kg/feet
(ii) percentage
(iii) non-existent
Calculate the correlation coefficient 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
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
Differentiate between Karl pearson's coefficient of correlation and spearman's rank correlation.
Q.2. Calculate Karl Pearson's coefficient of correlation, between the age and weight of children.
(Ans. r = + 0.98)
Can simple correlation coefficient measure any type of relationship?
calculate coefficient of correlation of the age of husband and wife using karl pearson's method
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
When is rank correlation more precise than simple correlation coefficient?
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
Does zero correlation mean independence?
Name the methods used to measure correlation and also define them briefly.