**Questions:-**

** Business Statistics**

**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 〖DX〗^2 〖DY〗^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 = ∑▒dxdy

√(∑▒〖〖dx〗^(2 ) X〖dy〗^(2 ) 〗)

= 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

3**1. 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