An analysis of monthly wages paid to the workers of two firms A and B belonging to the same industry gives the following results:
Firm A Firm B
Number of Workers 500 600
Average daily wage Rs. 186 Rs. 175
Variance of Distribution of wages 81 100
i) Which firm A or B has a larger wage bill?
ii) In which firm, A or B, is there greater variability in individual wages?
iii) Calculate (a) the average daily wage, and (b) the variance of the distribution of wages of all the workers in the firms A and B taken together.
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The following table gives frequency distribution of 45 clerks in a business office according to age and pay:
| Pay
Age | 600-700 | 700-800 | 800-900 | 900-1000 | 1000-1100 | Total |
| 20-30
30-40
40-50
50-60
60-70 | 4
2
1
–
– | 3
5
2
1
– | 1
2
3
3
1 | –
1
2
5
1 | –
–
1
2
5 | 8
10
9
11
7 |
| Total | 7 | 11 | 10 | 9 | 8 | 45 |
In a statistical study related to the price (in of two shares X and Y, the following two regression lines were found:
Y = 4X – 35 and 9X = Y + 135
The standard deviation of the price of Share Y is Rs12. You are required to calculate:
i) Average Price of shares X and Y
ii) Standard deviation of the price of Share X and
iii) Coefficient of correlation between the price of Shares X and Y.
Calculate the coefficient of rank correlation for the following data:
| X: | 48 | 33 | 40 | 09 | 16 | 16 | 65 | 24 | 16 | 57 |
| Y: | 13 | 13 | 24 | 06 | 15 | 04 | 20 | 09 | 06 | 19 |
800 candidates of both sexes appeared at an examination. The boys outnumbered the girls by 15% of the total. The number of candidates who passed exceeds the number failed by 480. Equal number of boys and girls failed in examination. Prepare a 2 x 2 table and find the coefficient of association. Also comment.
A number of particular articles has been classified according to their weights. After drying for two weeks the same articles have again been weighted and similarly classified. It is known that median weight in the First Weighing was 20.83 gm, while in the Second Weighing it was 17.35 gm. Some frequencies a and b in the First Weighing and x and y in the Second Weighing are missing. It is known that . and
Find out the values of the missing frequencies.
Class: 0-5 5-10 10-15 15-20 20-25 25-30
Ist Weighing: a b 11 52 75 22
IInd Weighing: x y 40 50 30 28
In a trivariate distribution:
1 = 2,
2 =
3 = 3, r12 = 0.7, r23 = r31 = 0.5
Find (i) r23.1 , (ii) R1.23 , (iii) b12.3 , b13.2 and (iv) 1.23
Among the adult population of a certain town 50 percent are males, 60 percent are wage earners and 50 percent are 45 years of age or over, 10 percent of the males are not wageearners, and 40 per cent of the males are under 45 years. Make the best possible inference about the limits within which the percentage of persons (male or female) of 45 years or over are wage earners.