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 |
Find also the corrected values of the moments after Sheppard’s corrections are applied. Also obtain moment coefficients of skewness and kurtosis and comment on the nature of the distribution.
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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
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
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.
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 Karl Pearson’s coefficient of correlation between X and Y for the following data:
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 |