NM Shah (2017) Solutions for Class 11 Science Economics Chapter 8 Measures Of Correlation are provided here with simple step-by-step explanations. These solutions for Measures Of Correlation are extremely popular among class 11 Science students for Economics Measures Of Correlation Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the NM Shah (2017) Book of class 11 Science Economics Chapter 8 are provided here for you for free. You will also love the ad-free experience on Meritnation’s NM Shah (2017) Solutions. All NM Shah (2017) Solutions for class 11 Science Economics are prepared by experts and are 100% accurate.
Page No 312:
Question 1:
The following pairs give the value of variables of capital employed and profit.
Capital employed (in crores of â¹ ) (X) | : | 2 | 3 | 5 | 6 | 8 | 9 |
Profit (in lacs of â¹ ) (Y) | : | 6 | 5 | 7 | 8 | 12 | 11 |
(b) Do you think that there is any correlation between profit and capital employed? Is it positive or negative ? Is it high or low?
(c) By graphic inspection , draw an estimating line.
Answer:
a) Scatter Diagram
b) The points obtained on the scatter diagram lie close to each other and reflect an upward trend. Thus, there exists a high degree of positive correlation between capital employed and profits earned.
c)
Page No 312:
Question 2:
Plot the following data as a scatter diagram and comment on the result obtained:
X | : | 11 | 10 | 15 | 13 | 10 | 16 | 13 | 8 | 17 | 14 |
Y | : | 6 | 7 | 9 | 9 | 7 | 11 | 9 | 6 | 12 | 11 |
Answer:
Scatter Diagram
Thus, there exists a positive correlation of moderate degree between X and Y.
Page No 312:
Question 3:
Following are the heights and weights of 10 students in a class. Draw a scatter diagram and indicate whether the correlation is positive or negative.
Height (in inches) | : | 72 | 60 | 63 | 66 | 70 | 75 | 58 | 78 | 72 | 62 |
Weight (in kg) | : | 65 | 54 | 55 | 61 | 60 | 54 | 50 | 63 | 65 | 50 |
Answer:
Thus, there exists a very low degree of positive correlation between height and weight of students.
Page No 313:
Question 4:
Draw a scatter diagram for the data given below and interpret it:
X | : | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 |
Y | : | 32 | 20 | 24 | 36 | 40 | 28 | 48 | 44 |
Answer:
Thus, there exists a moderate degree of correlation between X and Y.
Page No 313:
Question 5:
Draw a scatter diagram of the following data:
X | : | 15 | 18 | 30 | 27 | 25 | 23 | 30 |
Y | : | 7 | 10 | 17 | 16 | 12 | 13 | 9 |
Answer:
Thus, there exists a moderate degree of positive correlation between X and Y.
Page No 313:
Question 6:
From the following data compute the product moment correlation between X and Y.
X series | Y series | |
Arithmetic Mean | 25 | 18 |
Sum of Square of deviations from Arithmetic Mean | 136 | 138 |
Number of points of values = 15
Answer:
Thus, the product moment correlation between X and Y is 0.89.
Page No 313:
Question 7:
Calculate Karl Pearson's Coefficient of Correlation on the following data:
X | : | 15 | 18 | 21 | 24 | 27 | 30 | 36 | 39 | 42 | 48 |
Y | : | 25 | 25 | 27 | 27 | 31 | 33 | 35 | 41 | 41 | 45 |
Answer:
X | Y | (x) |
x2 | (y) |
y2 | xy |
15 | 25 | −15 | 225 | −8 | 64 | 120 |
18 | 25 | −12 | 144 | −8 | 64 | 96 |
21 | 27 | −9 | 81 | −6 | 36 | 54 |
24 | 27 | −6 | 36 | −6 | 36 | 36 |
27 | 31 | −3 | 9 | −2 | 4 | 6 |
30 | 33 | 0 | 0 | 0 | 0 | 0 |
36 | 35 | 6 | 36 | 2 | 4 | 12 |
39 | 41 | 9 | 81 | 8 | 64 | 72 |
42 | 41 | 12 | 144 | 8 | 64 | 96 |
48 | 45 | 18 | 324 | 12 | 144 | 216 |
Æ©X = 300 | Æ©Y =330 | Æ©x2 =1080 | Æ©y2 =480 | Æ©xy =708 |
N = 10
Thus, the value of correlation coefficient is 0.983.
Page No 313:
Question 9:
Calculate Karl Pearson's Coefficient of Correlation between the sales and expenses of the following 10 firms:
Firms | : | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
Sales(in â¹ '000) | : | 50 | 50 | 55 | 60 | 65 | 65 | 65 | 60 | 60 | 50 |
Expenses (in â¹ '000) | : | 11 | 13 | 14 | 16 | 16 | 15 | 15 | 14 | 13 | 13 |
Answer:
Sales (X) |
Expenses (Y) |
x |
x2 | y |
y2 | xy |
50 | 11 | −8 | 64 | −3 | 9 | 24 |
50 | 13 | −8 | 64 | −1 | 1 | 8 |
55 | 14 | −3 | 9 | 0 | 0 | 0 |
60 | 16 | 2 | 4 | 2 | 4 | 4 |
65 | 16 | 7 | 49 | 2 | 4 | 14 |
65 | 15 | 7 | 49 | 1 | 1 | 7 |
65 | 15 | 7 | 49 | 1 | 1 | 7 |
60 | 14 | 2 | 4 | 0 | 0 | 0 |
60 | 13 | 2 | 4 | −1 | 1 | −2 |
50 | 13 | −8 | 64 | −1 | 1 | 8 |
580 | 140 | 360 | 22 | 70 |
N = 10
Note: As per the textbook, coefficient of correlation is 0.67. However, as per the above solution coefficient of correlation should be 0.786.
Page No 313:
Question 10:
Calculate correlation coefficient between X, the number of rainy days per month and Y, the number of rain coats sold in that month in a certain shop for 12 months. 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 |
Answer:
X | Y | (x) |
x2 | (y) |
y2 | xy |
14 | 15 | 3 | 9 | 3 | 9 | 9 |
8 | 11 | −3 | 9 | −1 | 1 | 3 |
18 | 20 | 7 | 49 | 8 | 64 | 56 |
10 | 12 | −1 | 1 | 0 | 0 | 0 |
22 | 15 | 11 | 121 | 3 | 9 | 33 |
9 | 7 | −2 | 4 | −5 | 25 | 10 |
3 | 3 | −8 | 64 | −9 | 81 | 72 |
5 | 4 | −6 | 36 | −8 | 64 | 48 |
6 | 7 | −5 | 25 | −5 | 25 | 25 |
11 | 10 | 0 | 0 | −2 | 4 | 0 |
13 | 11 | 2 | 4 | −1 | 1 | −2 |
13 | 29 | 2 | 4 | 17 | 289 | 34 |
Æ©X =132 | Æ©Y =144 | Æ©x2 =326 | Æ©y2 =572 | Æ©xy =288 |
N = 12
There is a moderate degree of (+) correlation between the number of rainy days and the number of rain coats sold. In other words, as the number of rainy days increases in a month, the number of rain coats sold in that month increases moderately.
Note: As per the textbook, coefficient of correlation is 0.67. However, as per the above solution coefficient of correlation should be +0.67.
Page No 313:
Question 11:
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 |
Calculate the Karl Pearson's coefficient of correlation and interpret the result .
Answer:
x | y | x2 | y2 | xy |
−4 | 3 | 16 | 9 | −12 |
−3 | −3 | 9 | 9 | 9 |
−2 | −4 | 4 | 16 | 8 |
−1 | 0 | 1 | 0 | 0 |
0 | 4 | 0 | 16 | 0 |
1 | 1 | 1 | 1 | 1 |
2 | 2 | 4 | 4 | 4 |
3 | −2 | 9 | 4 | −6 |
4 | −1 | 16 | 1 | −4 |
Æ©x2 =60 | Æ©y2 =60 | Æ©xy =0 |
Thus, there is no correlation between series X and series Y.
Page No 313:
Question 12:
Find the product moment correlation of the following data:
X | : | 1 | 2 | 3 | 4 | 5 |
Y | : | 9 | 8 | 10 | 12 | 11 |
Answer:
X | Y | x |
y |
x2 | y2 | xy |
1 | 9 | −2 | −1 | 4 | 1 | 2 |
2 | 8 | −1 | −2 | 1 | 4 | 2 |
3 | 10 | 0 | 0 | 0 | 0 | 0 |
4 | 12 | 1 | 2 | 1 | 4 | 2 |
5 | 11 | 2 | 1 | 4 | 1 | 2 |
Æ©X =15 | Æ©Y =50 | Æ©x2 = 10 | Æ©y2 = 10 | Æ©xy = 8 |
N = 5
Thus, the product moment correlation is 0.80.
Page No 313:
Question 13:
Calculate the correlation coefficient of the marks obtained by 12 students in Mathematics and Statistics and interpret it.
Students | : | A | B | C | D | E | F | G | H | I | J | K | L |
Marks (in Maths) | : | 50 | 54 | 56 | 59 | 60 | 62 | 61 | 65 | 67 | 71 | 71 | 74 |
Marks ( in Statis.) | : | 22 | 25 | 34 | 28 | 26 | 30 | 32 | 30 | 28 | 34 | 36 | 40 |
Answer:
Maths (X) |
Statis. (Y) |
x |
x2 | (y) |
y2 | xy |
50 | 22 | −12.5 | 156.25 | −8.41 | 70.72 | 105.12 |
54 | 25 | −8.5 | 72.25 | −5.41 | 29.26 | 45.98 |
56 | 34 | −6.5 | 42.25 | 3.59 | 12.88 | −23.33 |
59 | 28 | −3.5 | 12.25 | −2.41 | 5.80 | 8.43 |
60 | 26 | −2.5 | 6.25 | −4.41 | 19.44 | 11.02 |
62 | 30 | −0.5 | 0.25 | −0.41 | 0.168 | 0.205 |
61 | 32 | −1.5 | 2.25 | 1.59 | 2.52 | −2.38 |
65 | 30 | 2.5 | 6.25 | −.41 | 0.168 | −1.02 |
67 | 28 | 4.5 | 20.25 | −2.41 | 5.80 | −10.84 |
71 | 34 | 8.5 | 72.25 | 3.59 | 12.88 | 30.51 |
71 | 36 | 8.5 | 72.25 | 5.59 | 31.24 | 47.51 |
74 | 40 | 11.5 | 132.25 | 9.59 | 91.96 | 110.28 |
Æ©X = 750 | Æ©Y= 365 | Æ©x2 = 595 | Æ©y2 = 282.836 | Æ©xy = 321.485 |
N = 12
Thus, there exists sufficiently high degree of positive correlation marks in Mathematics and marks in Statistics.
Page No 314:
Question 14:
The height of fathers and sons are given below:
Height of fathers (in inches) | : | 65 | 66 | 67 | 67 | 68 | 69 | 71 | 73 |
Height of sons (in inches) | : | 67 | 68 | 64 | 68 | 72 | 70 | 69 | 70 |
Answer:
Father's Height (X) |
Son's Height (Y) |
x |
x2 | y |
y2 | xy |
65 | 67 | −3.25 | 10.56 | −1.5 | 2.25 | 4.875 |
66 | 68 | −2.25 | 5.06 | −0.5 | 0.25 | 1.125 |
67 | 64 | −1.25 | 1.56 | −4.5 | 20.25 | 5.625 |
67 | 68 | −1.25 | 1.56 | −0.5 | 0.25 | 0.625 |
68 | 72 | −0.25 | 0.06 | 3.5 | 12.25 | −0.875 |
69 | 70 | 0 .75 | 0.56 | 1.5 | 2.25 | 1.125 |
74 | 69 | 2.75 | 7.56 | 0.5 | 0.25 | 1.375 |
73 | 70 | 4.75 | 22.56 | 1.5 | 2.25 | 7.125 |
Æ©X = 546 | Æ©Y = 548 | Æ©x2 = 49.48 | Æ©y2 = 40 | Æ©xy = 21 |
N = 8
Page No 314:
Question 15:
Find Karl Pearson's coefficient of correlation from the following index numbers and interpret it.
Wages (â¹) | : | 100 | 101 | 103 | 102 | 100 | 99 | 97 | 98 | 96 | 95 |
Cost of living | : | 98 | 99 | 99 | 97 | 95 | 92 | 95 | 94 | 90 | 91 |
Answer:
Wages (X) |
Cost of Living (Y) |
x |
x2 | y |
y2 | xy |
100 | 98 | 0.9 | 0.81 | 3 | 9 | 27 |
101 | 99 | 1.9 | 3.61 | 4 | 16 | 7.6 |
103 | 99 | 3.9 | 15.21 | 4 | 16 | 5.6 |
102 | 97 | 2.9 | 8.41 | 2 | 4 | 5.8 |
100 | 95 | 0.9 | 0.81 | 0 | 0 | 0 |
99 | 92 | −0.1 | 0.01 | −3 | 9 | 0.3 |
97 | 95 | −2.1 | 4.41 | 0 | 0 | 0 |
98 | 94 | −1.1 | 1.21 | −1 | 1 | 1.1 |
96 | 90 | −3.1 | 9.61 | −5 | 25 | 15.5 |
95 | 91 | −4.1 | 16.81 | −4 | 16 | 16.6 |
Æ©X = 991 | Æ©Y = 950 | Æ©x2 = 60.9 | Æ©y2 = 96 | Æ©xy = 65.2 |
N = 10
Wages and cost of living has high positive correlation. If wages increase by 1 unit, the cost of living increases by 0.85 units.
Page No 314:
Question 16:
Find the product moment correlation between sales and expenses of the following 10 firms.
Firms | : | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
Sales | : | 50 | 50 | 55 | 60 | 65 | 65 | 65 | 60 | 60 | 50 |
Expenses | : | 11 | 13 | 14 | 16 | 16 | 15 | 15 | 14 | 13 | 13 |
Answer:
Sales (X) |
Expenses (Y) |
x |
x2 | y |
y2 | xy |
50 | 11 | −8 | 64 | −3 | 9 | 24 |
50 | 13 | −8 | 64 | −1 | 1 | 8 |
55 | 14 | −3 | 9 | 0 | 0 | 0 |
60 | 16 | 2 | 4 | 2 | 4 | 4 |
65 | 16 | 7 | 49 | 2 | 4 | 14 |
65 | 15 | 7 | 49 | 1 | 1 | 7 |
65 | 15 | 7 | 49 | 1 | 1 | 7 |
60 | 14 | 2 | 4 | 0 | 0 | 0 |
60 | 13 | 2 | 4 | −1 | 1 | −2 |
50 | 13 | −8 | 64 | −1 | 1 | 8 |
Æ©X = 580 | Æ©X = 140 | Æ©x2 = 360 | Æ©y2 = 22 | Æ©xy = 70 |
N = 10
Thus, there exists high positive correlation between sales of firm and expenses.
Page No 314:
Question 17:
Calculate the coefficient of correlation for the following ages of husbands and wives in years at the time of their marriage.
Age of Husbands | : | 23 | 27 | 28 | 28 | 29 | 30 | 31 | 33 | 35 | 36 |
Age of Wives | : | 18 | 20 | 22 | 27 | 21 | 29 | 27 | 29 | 28 | 29 |
Answer:
Husband (X) |
Wife (Y) |
x |
x2 | y |
y2 | xy |
23 | 18 | −7 | 49 | −7 | 49 | 49 |
27 | 20 | −3 | 9 | −5 | 25 | 15 |
28 | 22 | −2 | 4 | −3 | 9 | 6 |
28 | 27 | −2 | 4 | 2 | 4 | −4 |
29 | 21 | −1 | 1 | −4 | 16 | 4 |
30 | 29 | 0 | 0 | 4 | 16 | 0 |
31 | 27 | 1 | 1 | 2 | 4 | 2 |
33 | 29 | 3 | 9 | 4 | 16 | 12 |
35 | 28 | 5 | 25 | 3 | 9 | 15 |
36 | 29 | 6 | 36 | 4 | 16 | 24 |
Æ©X = 300 | Æ©Y = 250 | Æ©x2 =138 | Æ©y2 =164 | Æ©xy =123 |
N = 10
Thus, there exists high positive correlation between age of husband and age of wife.
Page No 314:
Question 18:
Find Karl Pearson's coefficient of correlation for the following data:
Fertilizers used ( in tons ) | : | 15 | 18 | 20 | 24 | 30 | 35 | 40 | 50 |
Productivity ( in tons) | : | 85 | 90 | 95 | 105 | 120 | 130 | 150 | 160 |
Answer:
Fertilizers (X) |
Productivity (Y) |
x |
x2 | y |
y2 | xy |
15 | 85 | −14 | 196 | −32.25 | 1040.06 | 451.5 |
18 | 93 | −11 | 121 | −24.25 | 588.06 | 266.75 |
20 | 95 | −9 | 81 | −22.25 | 495.06 | 200.25 |
24 | 105 | −5 | 25 | −12.25 | 150.06 | 61.25 |
30 | 120 | 1 | 1 | 2.75 | 7.56 | 2.75 |
35 | 130 | 6 | 36 | 12.75 | 162.56 | 76.5 |
40 | 150 | 11 | 121 | 32.75 | 1072.56 | 360.25 |
50 | 160 | 21 | 441 | 42.75 | 1827.56 | 897.75 |
Æ©X =232 | Æ©Y = 938 | Æ©x2 =1022 | Æ©y2 =5343.48 | Æ©xy =2317 |
N = 8
Thus, there exists high positive correlation between the amount of fertilizers used and the productivity.
Page No 314:
Question 19:
Calculate product moment correlation between age of cars and annual maintenance cost and comment.
Age of cars (years) | : | 2 | 4 | 6 | 7 | 8 | 10 | 12 |
Annual maintenance âCost (in â¹) |
: | 1600 | 1500 | 1800 | 1900 | 1700 | 2100 | 2000 |
Answer:
Age of Cars (X) |
Maintenance (Y) |
x |
y |
x2 | y2 | xy |
2 | 1600 | −5 | −200 | 25 | 40000 | 1000 |
4 | 1500 | −3 | −30 | 9 | 90000 | 900 |
6 | 1800 | −1 | 0 | 1 | 0 | 0 |
7 | 1900 | 0 | 100 | 0 | 10000 | 0 |
8 | 1700 | 1 | −100 | 1 | 10000 | −100 |
10 | 2100 | 3 | 300 | 9 | 90000 | 900 |
12 | 2000 | 5 | 200 | 25 | 40000 | 1000 |
Æ©X = 49 | Æ©Y =12600 | Æ©x2 =70 | Æ©y2 =280000 | Æ©xy =3700 |
N = 7
Thus, there exists high positive correlation between age of car and maintenance cost.
Page No 314:
Question 20:
Calculate coefficient of correlation by Pearson's method between the density of population and death rate.
Cities | : | A | B | C | D | E | F |
Density | : | 200 | 500 | 400 | 700 | 600 | 300 |
Death rate | : | 10 | 16 | 14 | 20 | 17 | 13 |
Answer:
Density (X) |
Death rate (Y) |
x |
x2 | y |
y2 | xy |
200 | 10 | −250 | 62500 | −5 | 25 | 1250 |
500 | 16 | 50 | 2500 | 1 | 1 | 50 |
400 | 14 | −50 | 2500 | −1 | 1 | 50 |
700 | 20 | 250 | 62500 | 5 | 25 | 1250 |
600 | 17 | 150 | 22500 | 2 | 4 | 300 |
300 | 13 | −150 | 22500 | −2 | 4 | 300 |
Æ©X = 2700 | Æ©Y =90 | Æ©x2 =175000 | Æ©y2 =60 | Æ©xy =3200 |
N = 6
Thus, there exists high positive correlation between density of population and death rate.
Page No 314:
Question 21:
The total of the multiplication deviation of X and Y = 3044
Number of pairs of observations = 10
Total of the deviation of X = −20
Total of the deviation Y = −170
Total of squares of deviation of X = 2264
Total of the squares of deviation of Y = 8288
Find out Karl Pearson' s coefficient of correlation when assumed mean of X and Y are 82 and 68 respectively.
Answer:
Given:
n = 10
Σdxdy = 3044
Σdx = −17 assumed (instead of −170 see note below)
Σdy = −20
Σdx2 = 2264
Σdy2 = 8288
Hence, Karl Pearson's coefficient of correlation is 0.7.
Note:
1. If we take Σdx equal to −170, then the calculation of Karl Pearson's coefficient of correlation is as follows:
Since, the square root of a negative number is not defined among the set of real numbers, thus we have assumed Σdx as −17.
2. The answer as per the book is 0.78 and the answer as per our calculation is 0.70. The difference in the answer may be due to the assumption (i.e. Σdx = −17) made by us.
Page No 315:
Question 22:
Number of pairs of observations of X and Y series = 10 .
X series : Arithmetic Average = 65
: Standard Deviation = 23.33
Y series : Arithmetic Average = 66
Standard deviation = 14.9
Summation of products of corresponding deviations of X and Y series from their respective means = 2704.
Calculate product moment correlation of X and Y series.
Answer:
Now,
Thus, product moment correlation of X and Y series is 0.78.
Page No 315:
Question 23:
Calculate Spearman's rank correlation from the following data:
X | : | 10 | 12 | 8 | 15 | 20 | 25 | 40 |
Y | : | 15 | 10 | 6 | 25 | 16 | 12 | 8 |
Answer:
X | R1 | Y | R2 | (R1 − R2) D |
D2 |
10 | 2 | 15 | 5 | −3 | 9 |
12 | 3 | 10 | 3 | 0 | 0 |
8 | 1 | 6 | 1 | 0 | 0 |
15 | 4 | 25 | 7 | −3 | 9 |
20 | 5 | 16 | 6 | −1 | 1 |
25 | 6 | 12 | 4 | 2 | 4 |
40 | 7 | 8 | 2 | 5 | 25 |
Given:
N = 7
Now,
Thus, the rank coefficient of correlation is 0.143.
Page No 315:
Question 24:
The following are the marks obtained (out of 100) by a group of candidates in an employment interview held by two independent judges separately. Calculate the rank coefficient of correlation.
Candidates | : | A | B | C | D | E | F | G | H | I | J |
Judge X | : | 20 | 25 | 18 | 15 | 12 | 16 | 11 | 13 | 14 | 10 |
Judge Y | : | 22 | 20 | 15 | 14 | 10 | 8 | 11 | 12 | 13 | 9 |
Answer:
Candidate | Judge X |
R1 | Judge Y |
R2 | (R1 − R2) D |
D2 |
A | 20 | 9 | 22 | 10 | −1 | 1 |
B | 25 | 10 | 20 | 9 | 1 | 1 |
C | 18 | 8 | 15 | 8 | 0 | 0 |
D | 15 | 6 | 14 | 7 | −1 | 1 |
E | 12 | 3 | 10 | 3 | 0 | 0 |
F | 16 | 7 | 8 | 1 | 6 | 36 |
G | 11 | 2 | 11 | 4 | −2 | 4 |
H | 13 | 4 | 12 | 5 | −1 | 1 |
I | 14 | 5 | 13 | 6 | −1 | 1 |
J | 10 | 1 | 9 | 2 | −1 | 1 |
Given:
N = 10
Now,
Thus, the rank coefficient of correlation is 0.721.
Page No 315:
Question 25:
Two judges in a beautry 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 |
Answer:
X (R1) |
Y (R2) |
(R1 − R2) D |
D2 |
1 | 12 | −11 | 121 |
2 | 9 | −7 | 49 |
3 | 6 | −3 | 9 |
4 | 10 | −6 | 36 |
5 | 3 | 2 | 4 |
6 | 5 | 1 | 1 |
7 | 4 | 3 | 9 |
8 | 7 | 1 | 1 |
9 | 8 | 1 | 1 |
10 | 2 | 8 | 64 |
11 | 11 | 0 | 0 |
12 | 1 | 11 | 121 |
Given,
N = 12
Now,
Thus, the rank coefficient of correlation is 0.454.
Page No 315:
Question 26:
Calculate rank coefficient of correlation of the following data.
X | : | 80 | 78 | 75 | 75 | 68 | 67 | 60 | 59 |
Y | : | 12 | 13 | 14 | 14 | 14 | 16 | 15 | 17 |
Answer:
X | R1 | Y | R2 | (R1 − R2) D |
D2 |
80 78 75 75 68 67 60 59 |
8 7 5.5 5.5 4 3 2 1 |
12 13 14 14 14 16 15 17 |
1 2 4 4 4 7 6 8 |
7 5 1.5 1.5 0 4 4 7 |
49 25 2.25 2.25 0 16 16 49 |
Given:
N = 8
Now, in the given case, where a rank is repeated more than once, the following formula will be used,
Thus, the rank coefficient of correlation is 0.93.
Page No 315:
Question 27:
Twelve entries were submitted in a flower show competition. They were ranked by two judges as under:
Entries | : | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
Judge A | : | 7 | 8 | 2 | 1 | 9 | 3 | 12 | 11 | 4 | 10 | 6 | 5 |
Judge B | : | 6 | 4 | 1 | 3 | 11 | 2 | 12 | 10 | 5 | 9 | 7 | 8 |
Answer:
Entries | Judge A (R1) |
Judge B (R2) |
(R1 − R2) D |
D2 |
1 | 7 | 6 | −1 | 1 |
2 | 8 | 4 | 4 | 16 |
3 | 2 | 1 | 1 | 1 |
4 | 1 | 3 | −2 | 4 |
5 | 9 | 11 | −2 | 4 |
6 | 3 | 2 | 1 | 1 |
7 | 12 | 12 | 0 | 0 |
8 | 11 | 10 | 1 | 1 |
9 | 4 | 5 | −1 | 1 |
10 | 10 | 9 | 1 | 1 |
11 | 6 | 7 | −1 | 1 |
12 | 5 | 8 | −3 | 9 |
Given,
N = 12
To calculate Spearman's Rank correlation, the following formula is used,
Thus, the Spearman's rank correlation is 0.860.
Page No 315:
Question 28:
Calculate the coefficient of rank correlation from the following data.
X | : | 48 | 33 | 40 | 9 | 16 | 16 | 65 | 25 | 15 | 57 |
Y | : | 13 | 13 | 24 | 6 | 15 | 4 | 20 | 9 | 6 | 19 |
Answer:
X | R1 | Y | R2 | (R1 − R2) D |
D2 |
48 | 8 | 13 | 5.5 | 2.5 | 6.25 |
33 | 6 | 13 | 5.5 | 0.5 | 0.25 |
40 | 7 | 24 | 10 | −3 | 9 |
9 | 1 | 6 | 2.5 | −1.5 | 2.25 |
16 | 3.5 | 15 | 7 | −3.5 | 12.25 |
16 | 3.5 | 4 | 1 | 2.5 | 6.25 |
65 | 10 | 20 | 9 | 1 | 1 |
25 | 5 | 9 | 4 | 1 | 1 |
15 | 2 | 6 | 2.5 | −0.5 | 0.25 |
57 | 9 | 19 | 8 | 1 | 1 |
Given:
N = 10
When, ranks are repeated more than once, the following formula is used to calculate coefficient of rank correlation.
Thus, the coefficient of rank correlation is 0.751.
Page No 315:
Question 29:
Calculate rank coefficient of correlation between years of service and efficiency rating.
Persons | : | A | B | C | D | E | F | G | H | I | J |
Years of Service | : | 24 | 30 | 12 | 25 | 29 | 19 | 16 | 10 | 11 | 7 |
Efficiency rating | : | 66 | 51 | 84 | 66 | 45 | 81 | 72 | 97 | 92 | 70 |
Answer:
Persons | Years of Service | R1 | Efficiency Rating | R2 | (R1 − R2) D |
D2 |
A | 24 | 7 | 66 | 3.5 | 3.5 | 12.25 |
B | 30 | 10 | 51 | 2 | 8 | 64 |
C | 12 | 4 | 84 | 8 | −4 | 16 |
D | 25 | 8 | 66 | 3.5 | 4.5 | 20.25 |
E | 29 | 9 | 45 | 1 | 8 | 64 |
F | 19 | 6 | 81 | 7 | −1 | 1 |
G | 16 | 5 | 72 | 6 | −1 | 1 |
H | 10 | 2 | 97 | 10 | −8 | 64 |
I | 11 | 3 | 92 | 9 | −6 | 36 |
J | 7 | 1 | 70 | 5 | −4 | 16 |
Given:
N = 10
When ranks are repeated more than once, the following formula is used to calculate rank coefficient of correlation.
Thus, the rank coefficient of correlation is 0.787.
Page No 315:
Question 30:
From the following data calculate coefficient of correlation by the method of rank differences.
X | : | 75 | 68 | 95 | 70 | 60 | 80 | 81 | 50 |
Y | : | 120 | 134 | 150 | 115 | 110 | 140 | 142 | 100 |
Answer:
X | R1 | Y | R2 | (R1 − R2) D |
D2 |
75 | 5 | 120 | 4 | 1 | 1 |
68 | 3 | 134 | 5 | −2 | 4 |
95 | 8 | 150 | 8 | 0 | 0 |
70 | 4 | 115 | 3 | 1 | 1 |
60 | 2 | 110 | 2 | 0 | 0 |
80 | 6 | 140 | 6 | 0 | 0 |
81 | 7 | 142 | 7 | 0 | 0 |
50 | 1 | 100 | 1 | 0 | 0 |
Given:
N = 8
Now,
Thus, the coefficient of rank correlation is 0.93.
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