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## Questions:-

Assignment A
Q.1 Q1.) Find the Bowley’s coefficient of skewness form the following data.
X: 1-10 11-20 21-30 31-40 41-50 51-60 61-70
F: 5 15 25 10 6 5 4
Q.2 Q2.) For a distribution, Bowley’s Coefficient of skewness is (-) 0.36,
Q1= 8.6 and Median = 12.3. what is its quartile coefficient of dispersion?
Q3.) A sample of size 50 has mean 20 and deviation 5. The value at highest concentration point is 16. it was later discovered that an item 12 was misread 30, find the value of coefficient of skewness.
Q4.) Obtain two regression equation from the following data:
X: 25 28 35 32 31 36 29 38 34 32
Y: 43 46 49 41 36 32 31 30 33 39
Q5.) The following table gives the ages of husbands and wives for 50 newly married couples. Find the two regression equations. Estimate the age of husband when the age of wife is 20 and the age of wife when the age of husband is 30.
Age of Wives
Age of Husbands Total

20-25 25-30 30-35

16 – 20 9 14 -- 23
20 – 24 6 11 3 20
24 – 28 -- -- 7 7
Total 15 25 10 50
Assignment B
1. The rank correlation coefficient between marks obtained by some students in ‘Statistics’ and ‘Accountancy’ is 0.8. If the total of squares of rank differences is 33, find the number of students.
2. Find 4-yearly moving averages from the following time series data
Year: 1968 1969 1970 1971 1972 1973 1974
Production: 30 45 39 41 42 46 49
(’000 units)
3. An urn contains 8 red, 3 white and 9 blue balls. If 3 balls are drawn at random, determine the probability that (a) all 3 are red, (b) all 3 are white, (c) 2 are red and 1 blue ball, (d) one of each colour is drawn, and (e) balls are drawn in the order red, white and blue.

Assignment  B

Case Study:
The ranks of the same 16 students tests in Mathematics and Statistics were as follows, the two numbers within brackets denoting the ranks of the of the same student in Mathematics and Statistics respectively.

(1,1) (2,10)
(3,3) (4,4)
(5,5) (6,7)
(7,2) (8,6)
(9,8) (10,11)
(11,15) (12,9)
(13,14) (14,12)
(15,16) (16,13)

Student R_1 R_2 D D^2 Dx Dy ã€–DXã€—^2 ã€–DYã€—^2 DxDy
1 1 1 0 0 1 1 1 1 1
2 2 10 -8 64 2 10 4 100 20
3 3 3 0 0 3 3 9 9 9
4 4 4 0 0 4 4 16 16 16
5 5 5 0 0 5 5 25 25 25
6 6 7 -1 1 6 7 36 49 42
7 7 2 5 25 7 2 49 4 14
8 8 6 2 4 8 6 64 36 48
9 9 8 1 1 9 8 81 64 72
10 10 11 -1 1 10 11 100 121 110
11 11 15 -4 16 11 15 121 225 165
12 12 9 3 9 12 9 144 81 108
13 13 14 -1 1 13 14 169 196 182
14 14 12 2 4 14 12 196 144 168
15 15 16 -1 1 15 16 225 256 240
16 16 13 3 9 16 13 226 169 208
1496 1496 1428

R = ∑â–’dxdy
√(∑â–’ã€–ã€–dxã€—^(2 ) Xã€–dyã€—^(2 ) ã€—)

= 1428
√1496X1496

= 0.95

(A) Calculate the rank correlation coefficient for proficiencies of this group in Mathematics and Statistics.

(B) What does the value of the coefficient obtained indicate?
(C) If you had found out Karl Pearson’s simple coefficient of correlation between the ranks of these 16 students, would your result have been the same as obtained in (A) or different?

Assignment C (Multiple choice Objective Questions)

1. Who stated that statistics is a branch of applied mathematics which specializes in data?
Horace Secrist
R. A. Fisher
Ya-lun-chou
L. R. Connor

2. If the quartile deviation of a series is 60, the mean deviation of this series
72
48
50
75

3. Which measure of dispersion is least affected by extreme values?
range
mean deviation
standard deviation
quartile deviation

4. If the minimum value in a set is 9 and its range is 57, the maximum value of the set is
33
66
48
none of the above

5. The range of values for the frequency distribution given in the following frequency distribution is:-
Classes Frequency
2– 4 2
4– 6 5
6– 8 4
8– 10 1
02
10
08
06

6. The range of the set of values, 15, 12, 27, 6, 9, 18, 21, is
21
4.5
0.64
03

7. For the table given as follows, calculate the coefficient of quartile deviation:-

Classes Frequency

2– 4 2
4– 6 5
6– 8 4
8– 1 01
4.385
0.228
2.6
11.4

8. The coefficient of range for the values 15, 12, 27, 6, 9, 18, 21 is:-
1.571
4.500
0.636
0.222

9. If p=1, the angle between the two lines of regression is
zero degree
ninety degree
sixty degree
thirty degree

10. To test the linearity of a regression equation, one needs
Error S. S. other than residual S.S.
Residual S.S.
both (a) and (b)
neither (a) nor (b)

11. Regression coefficient is independent of the change of
scale
origin
both origin and scale
neither origin nor scale

12. Let the coefficient of correlation be 0.7. Then the coefficient of alienation
0.51
0.71
0.49
None of the above

13. The number of categories in which the potential parameters of a model can be specified are
one
two
three
four

14. Cycles in a time series are regular in
periodicity
Amplitude
Both (a) and (b)
Neither (a) nor (b)

15. Moving average method of ascertaining trend is not suitable for
Finding trend values
Projections
Both (a) and (b)
Neither (a) nor (b)

16. Simple average method is used to calculate
Trend values
Cyclic variations
Seasonal indices
None of these

17. In case of multiplicative model, the sum of seasonal indices is
100 times the number of seasons
Zero
100
Any of the above

18. In ratio to trend method the median of the trend free indices for each period represents
The seasonal indices
Cyclic variation
Irregular variation
none of the above

19. Ratio to trend method for seasonal indices provides good results if
The periods are of long duration
The periods are given six monthly
The periods are of short duration
All the above situations

20. The best method for finding out seasonal variation is
Simple average method
Ratio to moving average method
Ratio to trend method
None of the above

21. The moving averages in a time series are
Seasonal and cyclic variations
Seasonal and irregular variations
Trend and cyclical variations
Trend and random variations

22. Link relative in a time series remove the influence of
The trend
Cyclic variations
Irregular variations
All the above

23. Cyclic variations are interwoven with
Trend
Seasonal variations
Irregular variations
All the above

24. Graphically cycles of a time series are identifiable through
troughs and crests
concave and convex
cups and crests
all the above

25. In percentage ratio method of measuring cyclic variations one finds
Actual changes
Relative changes
Per cent ratio changes
All the above

26. A time series is affected by
Economic factors
Non-economic factors
Both (a) and (b)
Neither (a) nor (b)

27. Irregular variations are
regular
Cyclic
Episode
All the above

28. Trend can not be
Linear
Non-linear
S-shaped in a short duration
None of these

29. Method of least squares for determining trend is used when
Trend is known
Trend is curvilinear
The value Y is not a function of time t
None of the above

30. If the slope of the trend line is positive, it shows
Rising trend
Declining trend
Stagnation
Any of the above

31. To which component of the time series, the term recession is attached?
Trend
Seasonal
Cycles
Random variation

32. The probability of all possible outcomes of a random experiment is always equal to
Infinity
Zero
One
None of the above

33. In tossing three coins at a time the probability of getting at most one head is
3/8
7/8
1/2
1/8

34. The probability of two persons being borned on the same day (ignoring date) is
1/49
1/365
1/7
None of the above

35. Three dice are rolled simultaneously. The probability of getting 12 spots
1/8
25/216
1/12
None of the above

36. The probability of throwing an odd sum with two fair dice is
1⁄4
1/16
1
1⁄2

37. The probability that a leap year will have 53 Sunday is
1/7
2/7
2/53
52/53

38. With a pair of dice thrown at a time, the probability of getting a sum more than that of 9 is
5/18
7/36
5/6
None of the above

39. An urn contains four tickets marked with numbers 112, 121, 211, 222 and one ticket is drawn at random. Let Ai (I = 1,2, 3) be the event that ith digit of the number of the ticket drawn is 1. Are the events A1, A2 and A3:-
Dependent
Independent
Mutually exclusive
None of the above

40. A group consists of 4 men, 3 women and 2 boys. Three persons are selected at random. The probability that two men are selected is
3/28
7/28
5/28
5/14

Question No. 40
Fisher’s ideal index is
Options
A.M. of Laspeyre’s and Paasche’s index
Median of Laspeyre’s and Paasche’s index
G.M. of Laspeyre’s and Paasche’s index
H.M.of Laspeyre’s and Paasche’s index

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January 29, 2015