Quantitative Techniques
Worksheet
Datta Meghe Institute of Management Studies
Atrey Layout, Nagpur-440022
2014
UNIT 1- CENTRAL TENDENCY AND DISPERSION
Arithmetic MEAN
1.
2.
Calculate Arithmetic mean of the following data.
S. N
1
2
3
4
5
6
X
110
100
105
125
162
148
Calculate Arithmetic mean of the following data.
S.N
A
B
C
D
E
X
0.82
0.96
1.01
1.80
1.90
7
119
8
110
F
2.09
9
111
G
2.11
10
114
11
12
164
120
Soln:- 124
H
2.98
I
J
3.05
3.99
Soln:- 2.072
3.
Following are the heights of 100 students in a class. Calculate arithmetic mean of the data.
Roll N.
1
2
3
4
5
6
7
8
9
10
11
12
Heights in
60
61
63
64
66
67
68
69
70
71
72
73
Inches
No. of
2
3
4
9
18
20
17
14
5
3
3
2
Students
Soln:- 67.06
4.
Calculate arithmetic mean for the following frequency distribution.
Class
0-2
2-4
4-6
6-8
8-10
10-12
Interval
Frequency
3
7
12
18
20
14
5.
6.
7.
8.
9.
DMIMS
12-14
13
Calculate arithmetic mean for the following frequency distribution.
Class
0-5
5-10
10-15 15-20 20-25 25-30 30-35
Interval
Frequency
15
24
28
40
50
30
25
Calculate arithmetic mean by using the following data.
Class
35-39
30-34
25-29
20-24
Interval
Frequency
6
10
14
20
Calculate the missing frequencies.
No. of Accidents
0
1
Frequency
46
?
2
?
5
26
3
25
6
34
35-40
40-45
20
24
30
5-9
24
Soln:- 21.05
70-78
78-85
10
5
8
9
45-50
10
8
Soln:- 22.34
10-14
7
40
16-18
10
3
Soln:- 9.14
15-19
Calculate arithmetic mean for the following frequency distribution.
Class
0-10
10-25
25-35
35-50
50-59
Interval
Frequency
5
10
16
30
19
Calculate the mean from the following data.
Value
1
2
3
4
Frequency
21
30
28
40
14-16
85-100
5
Soln:- 46.95
9
10
15
27
Soln:- 5.72
4
5
10
5
Soln:- f1=76, f2=38
Page 2
10. By using the following information find out the missing values.
Savings(Rs.)
95
100
112
115
118
Depositors
5
10
18
22
16
?
14
122
125
6
5
Soln:- 114.66
130
4
11. Following information is about the working hours of 200 machines in a factory. Calculate average
working hours of the factory by using arithmetic mean.
Working Hours
No. of Machines
Less than 100
10
Less than 200
30
Less than 300
55
Less than 400
86
Less than 500
126
Less than 600
150
Less than 700
169
Less than 800
185
Less than 900
195
Less than 1000
200
Soln:- 447
12. From the following information pertaining to 150 workers. Calculate average wage paid to workers.
Wages Rs.
No. of Workers
More than 75
150
More than 85
140
More than 95
115
More than 105
95
More than 115
70
More than 125
60
More than 135
40
More than 145
25
Soln:- 116.33
13. Calculate weighted average for the following data. It is not the same as simple arithmetic mean.
Comment on the result.
Income (Rs.)
5000
3400
1500
800
750
500
Weights
5
8
10
15
25
47
Soln:- 1104.1
14. An expedition team traveled for one week and covered a distance in the following way. What is the
average speed of the team?
Days
Mon
Tue
Wed
Thu
Fri
Sat
Sun
Speed KM
50
61
58
55
65
60
62
No. of Hrs
8
9
9
10
7
8
7
Soln:- 58.45
15. From the following find out the mean profits.
Profits per shop
No. of Shops
Rs.
100-200
10
200-300
18
300-400
20
400-500
26
500-600
30
600-700
28
700-800
18
Soln:- 486
DMIMS
Page 3
MEDIAN
16. The following are the details of production of 12 units. Calculate median.
S.No
1
2
3
4
5
6
7
8
Production
25
16
30
18
19
35
22
34
9
23
10
17
17. The following are the daily wages of 187 workers in a factory. Calculate median.
Wages
38
45
50
56
58
60
65
70
78
(Rs.)
Workers
5
8
15
28
30
32
25
22
12
18.
19.
20.
21.
22.
DMIMS
11
12
33
20
Soln:- 22.5
80
90
6
4
Soln:- 60
Following are the defects found in different operations in 260 units in a year in a company. Calculate
median.
Defects
No. of Units
2.5-4.5
20
4.5-6.5
25
6.5-8.5
30
8.5-10.5
42
10.5-12.5
55
12.5-14.5
38
14.5-16.5
21
16.5-18.5
19
18.5-20.5
10
Soln:- 10.97
Calculate the median for information given below.
Class
5-9 10-14 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59
Frequency
11
15
19
21
35
30
12
10
8
4
3
Soln:- 27.07
Calculate the median for the following frequency distribution.
Expenditure Rs, 00
No. of Units
Less than 15
5
Less than 25
12
Less than 35
21
Less than 45
40
Less than 55
68
Less than 65
82
Less than 75
92
Less than 85
100
Less than 95
105
Soln:- 49.46
Following is the distribution of marks obtained by 50 students in marketing. Calculate median.
No. of
Marks More than
students
0
50
10
46
20
40
30
20
40
10
50
3
Soln:- 153.79
By using the median found out the missing frequencies. It is given that median is 43.6 and total of
frequency is 132.
Class
0-10
10-20
20-30
30-40
40-50
50-60
60-7o
70-80
80-90
Intervals
Frequency
10
12
15
?
25
?
12
11
9
Soln:- 43.6
Page 4
23. Calculate the value of the median quartile one and quartile three from the following.
Values
Frequency
Values
Frequency
4-6
2
18-20
10
6-8
5
20-22
7
8-10
4
22-24
6
10-12
11
24-26
4
12-14
11
26-28
3
14-16
11
28-30
1
16-18
13
Soln:- Q1=12, Q3=19.8
MODE
24. Locate mode of the data by grouping method.
X
0.5
1.5
2.5
3.5
4.5
5.5
F
6
11
12
19
22
18
25. Calculate mode of following data.
Marks
0-9
10-19
20-29
Student
2
10
18
30-39
20
40-49
38
6.5
10
50-59
25
7.5
22
8.5
3
9.5
2
10.5
11.5
1
1
Soln:- 4.5
60-69
16
70-79
10
80-89
90-99
8
3
Soln:- 45.31
250300
19
300350400350
400
450
10
3
3
Soln:- 204.84
26. Calculate the mode from the following series.
Size of item
Frequency
0-5
20
5-10
24
10-15
32
15-20
28
20-25
20
25-30
16
30-35
34
35-40
10
40-45
8
Soln:- 13.33
27. Calculate Mode of the following information.
Class
1001500-50
50-100
Interval
150
200
Frequency
2
2
18
22
200250
21
28. Calculate the modal value from the following.
Income Rs.
No. of Persons
Less than 100
8
Less than 200
22
Less than 300
35
Less than 400
50
Less than 500
57
Less than 600
60
Soln:- 257.96
29. Find out the mode from the following table with which profits are made
Profits Rs.
3-4
4-5
5-6
6-7
7-8
Frequency
83
27
25
50
75
DMIMS
8-9
38
9-10
18
Soln:- 7.40
Page 5
Range
30. Find the range of weight of 10 students from the following.
41
11
14
65
73
64
53
31. Calculate the range and semi-inter quartile range for wages.
Wages Rs. 30-32
32-34
34-36
36-38
Labourers
12
18
16
14
32. Compute range and its Co-efficient for the following data.
Classes
10-20
20-30
30-40
40-50
50-60
Frequency
12
15
16
16
25
35
71
55
Soln:- Range=62, Coeff of range=0.738
38-40
12
40-42
8
60-70
30
70-80
25
42-44
6
Soln:- Rs.14
80-90
90-100
10
8
Soln:- 0.82
QUARTILE DEVIATION
33. Compute quartile deviation and its co-efficient for the following data.
X
110
111
112
113
114
115
116
117
118
119
120
121
Soln:- 0.028
34. Compute quartile deviation and co-efficient of quartile deviation for the given information.
X
10
12
14
16
18
20
22
24
28
30
34
36
38
F
3
6
10
15
20
24
30
22
18
14
10
6
6
Soln:- 0.22
35. The following are the marks of 115 students. Calculate co-efficient of quartile deviation.
Marks
Below Below Below Below Below Below Below Below Below
10
20
30
40
50
60
70
80
90
Students
2
10
12
42
67
88
102
108
112
Soln:36. Compute Mean Deviation and Co-efficient of mean deviation for A series & B series.
A
105
112
110
125
138
149
161
175
185
B
22
24
26
28
30
32
34
40
44
37. Calculate Mean Deviation of the following data.
X
12
14
16
F
2
2
3
18
2
22
1
Below
100
115
0.28
190
50
Soln:- 0.128
24
1
Soln:- 0.16
MEAN DEVIATION
38. Calculate mean deviation from the following data
X
2
4
F
1
4
6
6
8
4
10
1
Soln:- 1.5
39. Calculate mean deviation from median of mark obtained from the following data.
8,20,15,17,2,10,30,38,28,39,4,8,6,12,18,18,29,37,23,18,16,15,24,14,28,27,35,49,9,13,6,18,22,25,30
Soln:- 9.114
40. Calculate mean deviation for the following frequency distribution.
No. of colds
experienced
0
1
2
3
4
5
6
7
8
9
in 12 months
f
25
46
91
162
110
95
82
26
13
2
Soln:- 1.5
DMIMS
Page 6
41. With median as the base calculate the mean deviation of the two series A and B
Series A
Series B
3484
487
4572
508
4124
620
3682
382
5624
408
4388
266
3680
186
4308
218
Soln:- A=490.25, B=121.38
42. Calculate mean deviation from median from the following
Marks Less than
No. of Students
80
100
70
90
60
80
50
60
40
32
30
20
20
13
10
5
Soln:- 14.28
43. Calculate mean deviation and coefficient of mean deviation from the following data.
Class Interval
f
20-25
6
25-30
12
30-40
17
40-45
30
45-50
10
20-25
6
50-55
10
55-60
8
60-70
5
70-80
2
Soln:- M.D=8.75, Co. M.D=0.206
44. Calculate mean deviation from mean from the following
Size of item
Frequency
3-4
3
4-5
7
5-6
22
6-7
60
7-8
85
8-9
32
9-10
8
Soln:- 0.915
DMIMS
Page 7
STANDARD DEVIATION
45. Calculate the Standard Deviation and its Co-efficient for the following data.
S.N
1
2
3
4
5
6
7
8
9
X
30
50
60
70
90
100
105
120
125
46. Calculate standard deviation of the following data.
S.N.
1
2
3
4
5
X
40
42
38
56
15
6
71
7
82
10
11
12
130
150
170
Soln:- 40.16%
8
9
65
37
Soln:- 23.74
10
80
47. Calculate Standard Deviation and its Co-efficient for the sales in a year by 100 salesmen.
Sales
50
100
150
200
250
300
350
(Rs. 000)
Salesmen
4
14
22
30
20
8
2
Soln:- 35.3%
48. The following data is about the expenditure of 100 units in a firm. Compute standard deviation and Coefficient.
Expenses 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90100110100
110
120
Units
4
10
11
12
18
15
10
8
8
4
Soln:- 23.6
49. The following are the share prices of five industries in ten months. Compute standard deviation and
find out the industry whose prices are more consistent and which company is more variable.
Months
Share Prices (Rs.)
A
B
C
D
E
Jan
26
75
150
150
200
Feb
28
77
120
155
210
Mar
29
80
110
160
220
Apr
35
82
125
165
230
May
30
84
145
170
240
Jun
29
82
172
175
250
July
36
80
175
180
260
Aug
48
85
182
185
270
Sept
53
88
195
190
280
Oct
76
97
196
200
290
Soln:- A
50. By using the following data calculate co-efficient of X & Y.
Particulars
X
Y
Variance
25
16
Average
150
85
Soln:- 4.71
DMIMS
Page 8
UNIT II - REGRESSION ANALYSIS
Regression Equation
1.
By using the following information obtain two regression equations.
X
2
4
8
6
7
9
Y
5
4
9
8
9
7
Soln: x= -0.37+0.191y, y= -59+11x
2.
From the data given below calculate the regression equation by taking deviations from the mean of X
& Y series and estimate Y when X is 12 and estimate X when Y is 14.
X
2
3
4
5
6
7
8
Y
4
6
8
9
12
15
16
Soln: X= 0.3+0.47Y, Y=0.35+2.07X
3.
Find the two regression lines by using the following data and estimate Y when X is, 9, 10 &12.
X
15
18
26
28
31
25
19
35
Y
10
11
16
19
17
14
11
24
Soln: Y= 6.94, 7.6, 8.92
4.
Calculate two regression equations by using Karl Pearson’s coefficient of correlation and standard
deviations for the given information.
X
2
4
6
7
8
10
12
Y
16
15
18
19
17
21
20
Soln: X= -16.94+1.33Y, Y=14.29+0.53X
5.
Calculate two regression equations by using Karl Pearson’s coefficient of correlation and standard
deviations for sales and profits as given below. Estimate profits when sales increase to Rs.42 Lakhs and
Rs.45 Lakhs.
Sales in Rs.
5
10
15
20
25
30
35
Lakhs X
Profits in
6
8
12
14
16
18
20
Rs.”000” Y
Soln: X=0.32+1.64Y, Y=6.8+0.26X
6.
Determine the regression of Y on X and X on Y for the following data by using normal equation
method.
X
5
8
7
6
4
Y
3
4
5
2
1
Soln: Y= -1.8+0.8x, X=3.6+0.8y
7.
From the following data obtain two regression equations by using normal equations.
X
6
2
10
4
8
Y
9
11
5
8
7
Soln: Y=11.9-0.65x, X=16.4-1.3y
8.
Obtain two regression equations X on Y and Y on X for the following data.
X
7
8
11
5
3
1
15
Y
18
20
35
20
15
12
45
Soln: Y=6.6+2.4x, X=1.8+0.38y
9.
Determine regression equation Y on X for the information given below and estimate Y when
X=100, 105, 110 and 115.
DMIMS
Page 9
X
Y
50
3.5
80
7.0
60
5.0
70
6.0
90
5.0
60
4.0
80
6.0
50
70
90
4.0
5.5
4.0
Soln: Y=2.55+0.03x
10. By using the following information obtain regression equation Y on X on Y.
X
Y
A.M
22.5
18.8
Standard Deviation
2.87
1.4
Co-efficient of Correlation
0.97
Soln: X=1.99y-14.9, Y=8.2+0.47x
11. By using the following information obtain regression equation Y on X. and X on Y.
X
Y
A.M
5
12
Standard Deviation
2.6
2.6
Co-efficient of Correlation
0.95
Soln: X= -6.4+0.95y, Y= 7.25+0.95x
12. Construct regress equation for the information given below.
X
23
43
53
63
73
83
Y
5
6
7
8
9
10
Soln: Y=26.73+0.56x, X= -29.38+11.43y
13. From the data given below find the regression equations
X
1
5
3
2
1
1
7
3
y
6
1
0
0
1
2
1
5
(i)
Estimate y, when x= 10
(ii)
Estimate x, when y=13
Soln:- Y= -0.304x+2.874, X=0.278y+3.431, Y= -0.13, X= 2.62
14. Calculate the two regression equations from the data given below,
Price (Rs.)
10
12
13
12
16
15
Demand(Units) 40
38
43
45
37
43
Soln:- Y= -0.25x+44.25, X=-0.12y+17.92
15. The following table shows number of motor registrations in a certain territory for a term of 5
years and the sale of motor tyres by a firm in that territory for same period.
Year Motor registrations No.pf tyres sold
1
600
1250
2
630
1100
3
720
1300
4
750
1350
5
800
1500
Find the regression equation to estimate the sale of tyres when motor registration is known.
Estimate sales of tyres when registration is 850.
Soln:- Y=1.493X++254.9; Y=15.24
16. The heights of a group of fathers and sons are given below.
Height of 158
160
163
165
167
170
father
Height of 163
158
167
170
160
180
Son
DMIMS
172
175
177
181
170
175
172
175
Page 10
Find the lines of regression and estimate the height of the son when the height of the father
is 164 cm.
Soln:- X=0.76Y-40.36; Y=0.71X+49.15; Y=165.59
17. The following data give the monthly income and expenditure on food of 10 families.
Income
120
90
80
150
130
140
110
95
70
105
Expenditure 40
36
40
45
40
44
45
38
50
35
Calculate regression of food on income
Soln:- Y=0.011X+40.101
18. By using karl pearsons find out;
(a) Regression equation of Y on X
(b) Regression equation of X on Y
(c) Most probable value of Y, when X is 10
X
1
2
3
4
5
Y
2
5
3
8
7
Soln:- (a) Y=1.1+1.3X; (b) X=0.5+0.5Y; (c) Y=14.1
19. You are given the data of purchase and sales. Obtain two regression equations by least
square and estimate the likely sales when purchase equal to 100.
Purchase
62
72
98
76
81
56
76
92
88
49
Sales
112
124
131
117
132
96
120
136
97
85
Soln:- X=0.65Y+0.25; Y=0.78X+56.5; Expected sales=134.5
20. Use the following data;
X
1
5
3
2
1
1
7
Y
6
1
0
0
1
2
1
(a) Fit a regression line of Y on X and hence predict X if Y=25
(b) Fit a regression line of X on Y and hence predict Y if X=5
(c) Calculate Karl Pearson’s correlation coefficient
Soln:- (a) Y= -0.304X+2.874; Y=1.354
(b) X= -0.287Y+3.431; X=2.736
(c) y= 0.291
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
DMIMS
3
5
Define the term Regression and explain its features and objectives.
What is regression analysis? How does it differ from correlation analysis?
What is regression? Explain different types of regression with examples.
Explain the concept of regression. How do you measure regression?
What is regression Line? Explain its uses.
State any two merits of the method of the Least Square.
What is the utility of regression?
What do you mean by Regression Coefficient?
What are the properties of Regression Coefficient?
“Y=a+bx” where it is used?
Page 11
UNIT III - CORRELATION ANALYSIS
1. Calculate the coefficient of correlation between x & y from the following data;
X
1
2
3
4
5
6
Y
2
4
5
3
8
6
7
7
Soln:-ᵞ =0.79
2. Calculate Karl Pearson’s coefficient of correlation.
X
2
4
6
Y
12
14
16
8
18
10
20
Soln:-ᵞ=1
3. Calculate Karl Pearson’s coefficient of correlation.
X
2
4
6
Y
20
18
16
8
14
10
12
Soln:-ᵞ=-1
4. From the following table calculate the coefficient of correlation by Karl Pearson’s.
X
6
2
10
4
8
Y
9
11
?
8
7
Arithmetic mean of X & Y are 6 & 8 respectively.
Soln:- r=-0.92
5. Find the coefficient of correlation between the sales and expenses of the following 10
firms;
Firm
1
2
3
4
5
6
7
8
9
10
Sales
50
50
55
60
65
65
65
60
60
50
Expense 11
13
14
16
16
15
15
14
13
13
Soln:- ᵞ= 0.7866
6. Calculate pearson’s coefficient f correlation from the following taking 100 and 50 as
the assumed averages of X & Y respectively
X 104 111 104 104 118 117 105 108
106
100
104
105
Y 57
55 47
45
45
50
64
63
66
62
69
61
Soln:- ᵞ=-0.674
7. The index numbers of prices of all commodities in Bombay and in Calcutta were as;
Month Price in Calcutta Price in Bombay
Jan
169
204
Feb
182
222
Mar
182
225
Pr
192
228
May
198
229
Jun
209
233
Jul
227
249
Aug
238
266
Sept
250
255
Oct
253
255
Calculate the coefficient of correlation between prices in Calcutta & Bombay.
Soln:- ᵞ= 0.943
DMIMS
Page 12
8. Calculate the coefficient of correlation between age of cars and annual maintenance
cost and comment;
Age of car
Maintenance cost
2
16
4
15
6
18
7
19
8
17
10
21
12
20
Soln:- ᵞ= 0.8357
9. The following are the result of an examination;
Age of
Candidates
Successful
candidates
appeared
candidates
13-14
200
124
14-15
300
180
15-16
100
65
16-17
50
34
17-18
150
99
18-19
400
252
19-20
250
145
20-21
150
81
21-22
25
12
22-23
75
33
Calculate coefficient of correlation between age and successful candidates.
Soln:- ᵞ=-0.77
10. The following table gives the distribution of the total population and those who are
totally and partially blind among them. Find is any relation in age & blindness.
Age
0-10
10-20
20-30
30-40
40-50
50-60
60-70
70-80
No of
100
60
40
36
24
11
6
3
person
Blind
55
40
40
40
36
22
18
15
Soln:- ᵞ= 0.898
11. The following table gives the frequency according to age groups of marks obtained by
67 students in an intelligence test;
Test Marks
Age in years
18
19
20
21
Total
200-250
4
4
2
1
11
250-300
3
5
4
2
14
300-350
2
6
8
5
21
350-400
1
4
6
10
21
Is there any relationship between age and intelligence?
Soln:- ᵞ=0.4151
12. The following table gives the distribution of the ages in years of husband and wives in
100 couples
Age of wives
Age of husbands
20-25
25-30
30-35
35-40
15-20
20
10
3
2
20-25
4
28
6
4
25-30
5
11
30-35
2
35-40
5
Calculate coeff of correlation between age of husbands & wives.
DMIMS
Page 13
Soln:- ᵞ=0.61
13. Compute the correlation coefficient and the probable error for the following data;
Sales Revenue Advertising Expenditure (Rs. ‘000)
(Rs. ‘000)
5-15
15-25
25-35
35-45
Total
75-125
4
1
5
125-175
7
6
2
1
16
175-225
1
3
4
2
10
225-275
1
1
3
4
9
Total
13
11
9
7
40
Soln:- ᵞ=0.596
14. Find the ceff. Of correlation between marks obtained by 60 candidates in economics
& statistics from the data given below;
Marks in
Marks in economics
statistics
5-15
15-25
25-35
35-45
0-10
1
1
10-20
3
6
5
1
20-30
1
8
9
2
30-40
3
9
3
40-50
4
4
Soln:- ᵞ=0.533
15. The following are the marks obtained by the students in Statistics and Law
R.No.
Marks
R.No.
Marks
Statistic
Law
Statistic
Law
1
15
13
13
14
11
2
0
1
14
9
3
3
1
2
15
8
5
4
3
7
16
13
4
5
16
8
17
10
10
6
2
9
18
13
11
7
18
12
19
11
14
8
5
9
20
11
7
9
4
17
21
12
18
10
17
16
22
18
15
11
6
6
23
9
15
12
19
18
24
7
3
Prepare a correlation table taking the magnitude of each class interval as 4 marks and
class interval as equal to 0 and less than 4. Calculate Karl Pearson’s coeff. of
correlation between marks in stat and law.
Soln:- ᵞ=0.578
16. A survey of incomes & expenses on food of 100 teachers is shown;
Food Exp.
Family Income (Rs.)
(in %)
200-300
300-400
400-500
500-600
10-15
3
15-20
4
9
4
20-25
7
6
12
5
25-30
3
10
19
8
Calculate coeff. of correlation and interpret its value.
DMIMS
600-700
7
3
-
Page 14
Soln:- ᵞ=-0.4381
Rank Correlation
17. Two judges in a beauty competition rank the 12 entries as follows
X 1
2
3
4
5
6
7
8
9
10
Y 12
9
6
10
3
5
4
7
8
2
11
11
12
1
Soln:- ᵞs=-0.4545
18. Calculate Spearman’s rank correlation between advertisement cost and sales;
Advt. Cost
39
65
62
90
82
75
25
98
36
78
(Rs.’000)
Sales
47
53
58
86
62
68
60
91
51
84
(Rs.’00,000)
Soln:- ᵞs=0.82
19. Following are the scores of 10 students in a class and their I.Q.
Student
Scores
I.Q.
1
35
100
2
40
100
3
25
110
4
55
140
5
85
150
6
90
130
7
65
100
8
55
120
9
45
140
10
50
110
Soln:- ᵞs=0.47
20. Ten competitors in a beauty contest are ranked by three judge in following order
1st Judge 1
5
4
8
9
6
10
7
3
2
2nd Judge 4
8
7
6
5
9
10
3
2
1
rd
3 Judge 6
7
8
1
5
10
9
2
3
4
Use rank correlation coefficient to discuss which pair of judges has nearest approach
to common liking.
Soln:-I & II ᵞs=-0.212; II & III ᵞs=0.297; I & III ᵞs=0.636;
21. What is meant by correlation? What are the properties of coefficient of correlation?
22. Distinguish between coefficient of correlation and coefficient of variation.
23. Define Karl Pearson’s coefficient of correlation. What is intended to measure?
24. Distinguish between
(a) Positive & Negative Correlation
(b)Linear & Non Linear Correlation
(c)Simple, Partial and Multiple Correlation
25. Define coefficient of correlation and mention its important properties.
26. What are the methods of calculating coefficient of correlation?
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