NCERT Solutions for Class 11 Economics (Statistics for Economics) Chapter 6 Correlation
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Page 1
NCERT
SOLUTIONS
CLASS - 11th
aglase .co
SOLUTIONS
CLASS - 11th
aglase .co
Page 2
Book : Statistics for Economics Ncert Solutions | Chapter - 7 Statistics
Class : 11th
Subject : Statistics
Chapter : 7
Chapter Name : Correlation
Q1 The unit of correlation coefficient between height in feet and weight in
kgs is
(i) kg/feet
(ii) percentage
(iii) non-existent
Answer. Option (iii) is correct. There is no relation between the two quantities.
Page : 105 , Block Name : Exercises
Q2 The range of simple correlation coefficient is
(i) 0 to infinity
(ii) minus one to plus one
(iii) minus infinity to infinity
Answer. Option (ii) is correct. The range of simple correlation coefficient is -1 to 1.
Page : 105 , Block Name : Exercises
Q3 If rxy 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
Answer. Option (i) is correct. If rxy is positive, then it indicates positive correlation and
the two quantities move in same direction.
Page : 105 , Block Name : Exercises
Q4 If rxy = 0 the variable X and Y are
(i) linearly related
(ii) not linearly related
(iii) independent
Page 1 of 8
Class : 11th
Subject : Statistics
Chapter : 7
Chapter Name : Correlation
Q1 The unit of correlation coefficient between height in feet and weight in
kgs is
(i) kg/feet
(ii) percentage
(iii) non-existent
Answer. Option (iii) is correct. There is no relation between the two quantities.
Page : 105 , Block Name : Exercises
Q2 The range of simple correlation coefficient is
(i) 0 to infinity
(ii) minus one to plus one
(iii) minus infinity to infinity
Answer. Option (ii) is correct. The range of simple correlation coefficient is -1 to 1.
Page : 105 , Block Name : Exercises
Q3 If rxy 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
Answer. Option (i) is correct. If rxy is positive, then it indicates positive correlation and
the two quantities move in same direction.
Page : 105 , Block Name : Exercises
Q4 If rxy = 0 the variable X and Y are
(i) linearly related
(ii) not linearly related
(iii) independent
Page 1 of 8
Page 3
Book : Statistics for Economics Ncert Solutions | Chapter - 7 Statistics
Answer. Option (ii) is correct. There is no linear relation between the two quantities if
is zero.
Page : 105 , Block Name : Exercises
Q5 Of the following three measures which can measure any type of relationship
(i) Karl Pearson’s coefficient of correlation
(ii) Spearman’s rank correlation
(iii) Scatter diagram
Answer. Option (iii) is correct. The scatter diagram can be used to measure any type of
relationship as it is the simplest form of representation which does not involve any
values.
Page : 105 , Block Name : Exercises
Q6 If precisely measured data are available the simple correlation coefficient is
(i) more accurate than rank correlation coefficient
(ii) less accurate than rank correlation coefficient
(iii) as accurate as the rank correlation coefficient
Answer. Option (i) is correct. In case of simple correlation coefficient, it is the most
accurate if precisely measured data is available.
Page : 105 , Block Name : Exercises
Q7 Why is preferred to covariance as a measure of association?
Answer. It is due to the following reasons,
1. It is a ratio, and has no unit.
2. It lies between 0 and 1.
3. It is unaffected by change of origin and selection of scale.
Page : 105 , Block Name : Exercises
Q8 Can r lie outside the –1 and 1 range depending on the type of data?
Answer. No, The value of r must lie between -1 and 1. If it goes beyond this range, it
implies some error in the calculation.
Page 2 of 8
Answer. Option (ii) is correct. There is no linear relation between the two quantities if
is zero.
Page : 105 , Block Name : Exercises
Q5 Of the following three measures which can measure any type of relationship
(i) Karl Pearson’s coefficient of correlation
(ii) Spearman’s rank correlation
(iii) Scatter diagram
Answer. Option (iii) is correct. The scatter diagram can be used to measure any type of
relationship as it is the simplest form of representation which does not involve any
values.
Page : 105 , Block Name : Exercises
Q6 If precisely measured data are available the simple correlation coefficient is
(i) more accurate than rank correlation coefficient
(ii) less accurate than rank correlation coefficient
(iii) as accurate as the rank correlation coefficient
Answer. Option (i) is correct. In case of simple correlation coefficient, it is the most
accurate if precisely measured data is available.
Page : 105 , Block Name : Exercises
Q7 Why is preferred to covariance as a measure of association?
Answer. It is due to the following reasons,
1. It is a ratio, and has no unit.
2. It lies between 0 and 1.
3. It is unaffected by change of origin and selection of scale.
Page : 105 , Block Name : Exercises
Q8 Can r lie outside the –1 and 1 range depending on the type of data?
Answer. No, The value of r must lie between -1 and 1. If it goes beyond this range, it
implies some error in the calculation.
Page 2 of 8
Page 4
Book : Statistics for Economics Ncert Solutions | Chapter - 7 Statistics
Page : 105 , Block Name : Exercises
Q9 Does correlation imply causation?
Answer. No, correlation only defines the level of relationship two quantities have
between them.
Page : 105 , Block Name : Exercises
Q10 When is rank correlation more precise than simple correlation coefficient?
Answer. The Rank correlation is more precise when the measurement of variables is
not qualitative. Also, it is more precise when extreme values are present in the
observations.
Page : 105 , Block Name : Exercises
Q11 Does zero correlation mean independence?
Answer. No, zero correlation only means that there is no linear relationship between the
two quantities involved. There can be a non linear relationship between them.
Page : 105 , Block Name : Exercises
Q12 Can simple correlation coefficient measure any type of relationship?
Answer. No, simple correlation coefficient cannot measure any type of relationship. It
can only measure linear relationship between the quantities.
Page : 105 , Block Name : Exercises
Q13 Collect the price of five vegetables from your local market every day for
a week. Calculate their correlation coefficients. Interpret the result.
Answer. This question involves multivariate results, and is out of the scope of syllabus
of CBSE.
Page : 105 , Block Name : Exercises
Page 3 of 8
Page : 105 , Block Name : Exercises
Q9 Does correlation imply causation?
Answer. No, correlation only defines the level of relationship two quantities have
between them.
Page : 105 , Block Name : Exercises
Q10 When is rank correlation more precise than simple correlation coefficient?
Answer. The Rank correlation is more precise when the measurement of variables is
not qualitative. Also, it is more precise when extreme values are present in the
observations.
Page : 105 , Block Name : Exercises
Q11 Does zero correlation mean independence?
Answer. No, zero correlation only means that there is no linear relationship between the
two quantities involved. There can be a non linear relationship between them.
Page : 105 , Block Name : Exercises
Q12 Can simple correlation coefficient measure any type of relationship?
Answer. No, simple correlation coefficient cannot measure any type of relationship. It
can only measure linear relationship between the quantities.
Page : 105 , Block Name : Exercises
Q13 Collect the price of five vegetables from your local market every day for
a week. Calculate their correlation coefficients. Interpret the result.
Answer. This question involves multivariate results, and is out of the scope of syllabus
of CBSE.
Page : 105 , Block Name : Exercises
Page 3 of 8
Page 5
Book : Statistics for Economics Ncert Solutions | Chapter - 7 Statistics
Q14 Measure the height of your classmates. Ask them the height of their benchmate.
Calculate the correlation coefficient of these two variables. Interpret the result.
Answer. The values in the observation are:
X Y XY
67 65 4355 4489 4225
56 66 3696 3136 4356
65 57 3705 4225 3249
68 67 4556 4624 4489
72 68 4896 5184 4624
72 69 4968 5184 4761
69 70 4830 4761 4900
71 72 5112 5041 5184
= 540 = 534 = = =
36118 36644 35788
Here, X is the height of the classmate and Y is the height of his benchmate.
r=
r=
r=
r = 0.44
Therefore, there is a medium correlation between the heights.
Page : 105 , Block Name : Exercises
Page 4 of 8
Q14 Measure the height of your classmates. Ask them the height of their benchmate.
Calculate the correlation coefficient of these two variables. Interpret the result.
Answer. The values in the observation are:
X Y XY
67 65 4355 4489 4225
56 66 3696 3136 4356
65 57 3705 4225 3249
68 67 4556 4624 4489
72 68 4896 5184 4624
72 69 4968 5184 4761
69 70 4830 4761 4900
71 72 5112 5041 5184
= 540 = 534 = = =
36118 36644 35788
Here, X is the height of the classmate and Y is the height of his benchmate.
r=
r=
r=
r = 0.44
Therefore, there is a medium correlation between the heights.
Page : 105 , Block Name : Exercises
Page 4 of 8
Page 6
Book : Statistics for Economics Ncert Solutions | Chapter - 7 Statistics
Q15 List some variables where accurate measurement is difficult.
Answer. Some of such variables are:
1. Temperature and number of frost bites
2. Rainfall and Yield of Crops
3. Honesty and Industrialisation
4. Overpopulation and Poverty
Page : 106 , Block Name : Exercises
Q16 Interpret the values of r as 1, –1 and 0.
Answer. If r is positive, it indicates a positive correlation between the variables. If r is
negative, it indicates a negative correlation between variables. If r is zero, it means
there is no linear relationship between the variables.
Page : 106 , Block Name : Exercises
Q17 Why does rank correlation coefficient differ from Pearsonian correlation
Coefficient?
Answer. The following points will highlight the difference between the coefficients:
1. Pearson’s method measures quantitative data whereas rank correlation
coefficient measures qualitative data.
2. Pearsonian method calculates deviation from mean whereas rank correlation
coefficient measures differences in rank.
3. Pearson’s method gives high weightage to extreme values but rank correlation
method gives no weightage to extreme values.
Page : 106 , Block Name : Exercises
Q18 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
Page 5 of 8
Q15 List some variables where accurate measurement is difficult.
Answer. Some of such variables are:
1. Temperature and number of frost bites
2. Rainfall and Yield of Crops
3. Honesty and Industrialisation
4. Overpopulation and Poverty
Page : 106 , Block Name : Exercises
Q16 Interpret the values of r as 1, –1 and 0.
Answer. If r is positive, it indicates a positive correlation between the variables. If r is
negative, it indicates a negative correlation between variables. If r is zero, it means
there is no linear relationship between the variables.
Page : 106 , Block Name : Exercises
Q17 Why does rank correlation coefficient differ from Pearsonian correlation
Coefficient?
Answer. The following points will highlight the difference between the coefficients:
1. Pearson’s method measures quantitative data whereas rank correlation
coefficient measures qualitative data.
2. Pearsonian method calculates deviation from mean whereas rank correlation
coefficient measures differences in rank.
3. Pearson’s method gives high weightage to extreme values but rank correlation
method gives no weightage to extreme values.
Page : 106 , Block Name : Exercises
Q18 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
Page 5 of 8
Page 7
Book : Statistics for Economics Ncert Solutions | Chapter - 7 Statistics
Answer. The calculation of parameters can be done as:
X-Series Y-Series
XY
X Y
65 4225 67 4489 4355
66 4356 56 3136 3696
57 3249 65 4225 3705
67 4489 68 4624 4556
68 4624 72 5184 4896
69 4761 72 5184 4968
70 4900 69 4761 4830
72 5184 71 5041 5112
= 534 = = =
= 540
35788 36644 36118
Now,
r=
r=
r=
r = 0.44
Page : 106 , Block Name : Exercises
Q19 Calculate the correlation coefficient between X and Y and comment on their
relationship :
Page 6 of 8
Answer. The calculation of parameters can be done as:
X-Series Y-Series
XY
X Y
65 4225 67 4489 4355
66 4356 56 3136 3696
57 3249 65 4225 3705
67 4489 68 4624 4556
68 4624 72 5184 4896
69 4761 72 5184 4968
70 4900 69 4761 4830
72 5184 71 5041 5112
= 534 = = =
= 540
35788 36644 36118
Now,
r=
r=
r=
r = 0.44
Page : 106 , Block Name : Exercises
Q19 Calculate the correlation coefficient between X and Y and comment on their
relationship :
Page 6 of 8
Page 8
Book : Statistics for Economics Ncert Solutions | Chapter - 7 Statistics
X -3 -2 -1 1 2 3
Y 9 4 1 1 4 9
Answer. The tabulation of values:
X-Series Y-Series
XY
X Y
-3 9 9 81 -27
-2 4 4 16 -8
-1 1 1 1 -1
1 1 1 1 1
2 4 4 16 8
3 9 9 81 27
=0 = 28 = 28 = 196 =0
Now,
r=
r=
r=
r=0
Page : 106 , Block Name : Exercises
Q20 Calculate the correlation coefficient between X and Y and comment on their
relationship
Page 7 of 8
X -3 -2 -1 1 2 3
Y 9 4 1 1 4 9
Answer. The tabulation of values:
X-Series Y-Series
XY
X Y
-3 9 9 81 -27
-2 4 4 16 -8
-1 1 1 1 -1
1 1 1 1 1
2 4 4 16 8
3 9 9 81 27
=0 = 28 = 28 = 196 =0
Now,
r=
r=
r=
r=0
Page : 106 , Block Name : Exercises
Q20 Calculate the correlation coefficient between X and Y and comment on their
relationship
Page 7 of 8
Page 9
Book : Statistics for Economics Ncert Solutions | Chapter - 7 Statistics
X 1 3 4 5 7 8
Y 2 6 8 10 14 16
Answer. The tabulation of values is as under:
X-Series Y-Series
XY
X Y
1 1 2 4 2
3 9 6 36 18
4 16 8 64 32
5 25 10 100 50
7 49 14 196 98
8 64 16 256 128
=
28 = 164 = 56 = 656 = 328
Now,
r=
r=
r=
r = 1.00
Since the coefficient of correlation 1, it implies a perfect positive correlation.
Page : 106 , Block Name : Exercises
Page 8 of 8
X 1 3 4 5 7 8
Y 2 6 8 10 14 16
Answer. The tabulation of values is as under:
X-Series Y-Series
XY
X Y
1 1 2 4 2
3 9 6 36 18
4 16 8 64 32
5 25 10 100 50
7 49 14 196 98
8 64 16 256 128
=
28 = 164 = 56 = 656 = 328
Now,
r=
r=
r=
r = 1.00
Since the coefficient of correlation 1, it implies a perfect positive correlation.
Page : 106 , Block Name : Exercises
Page 8 of 8
Document Details
| Board / Org | NCERT |
| Exam | Class 11 |
| Type | Solution |
| Pages | 9 |
| Updated | 30 Apr 2026 |