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 |
Calculate the correlation between Age and Pay for the above bivariate data.
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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 |
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.
For the following frequency distribution of scores in Statistics of 50 students selected at random from among those appearing in a certain examination, compute the first four moments about mean:
| Score: | 50-60 | 60-70 | 70-80 | 80-90 | 90-100 | 100-110 | 110-120 | 120-130 | 130-140 |
| Frequency: | 1 | 0 | 0 | 1 | 1 | 2 | 1 | 0 | 4 |
| Score | 140-150 | 150-160 | 160-170 | 170-180 | 180-190 | 190-200 | 200-210 | 210-220 | 220-230 |
| Frequency: | 4 | 2 | 5 | 10 | 11 | 4 | 1 | 1 | 2 |
The following table gives the IQ values of 1000 students at a college according to the economic conditions of their parents:
| Economic Condition | IQ Level | Total | |
| High | Low | ||
| Rich | 460 | 140 | 600 |
| Poor | 240 | 160 | 400 |
| Total | 700 | 300 | 1000 |
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 |
State whether the following statements are true or false and also give the reason in support of your answer:
a) The SD of 10 values of a data is 50. If each value is divided by 5, then the New SD will be 10.
b) The values of regression on coefficient bxy and bxy are and 20, respectively.
c) , then neither x nor yexceeds
, if the data is consistent.
d) If Y is proportional to X, then r(X, Y) = 1.
e) The mean weight of 150 students in a class is 60 kg. The mean weight of boys in the class is 70 kg and that of girls is 55 kg. Then the ratio of boys and girls in the class is 3:2.