Assignment Pre Ph.d

8/6/2019 Assignment Pre Ph.d.

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INTEGRAL UNIVERSITY

First Assignment-2011Pre Ph.D. Course

Research Methodology (Unit II&III)

Q1. Find the Mean , Median and Mode of the following data :

x 21 25 28 31 33 36 41

f 3 18 22 17 15 21 11

Q2. Calculate Mean , Median and Mode to the following frequency distribution:

C.I. 0-10 10-20 20-30 30-40 40-50 50-60

Frequency

10 15 30 25 20 12

Q3.The arithmetic mean of the following distribution is 33. Find the missing frequency

Class 0-10 10-20 20-30 30-40 40-50 50-60

Frequenc

y

10 15 - 25 25 20

Q4.. The median of the following frequency distribution is 33. Find the missing

frequency.

C.I. 0-10 10-20 20-30 30-40 40-50 50-60

Frequenc

y

10 15 30 ----- 25 20

Q5. The expenditure of 100 families is given as

Expenditure. 0-20 20-40 40-60 60-80 80-100

No. of families 14 23 ------ 21 ----

Given that Mode is 48. Determine the missing frequencies

Q6. Calculate mean deviation about mean to the following frequency distribution:

C.I. 0-10 10-20 20-30 30-40 40-50 50-60

Frequenc

y

10 15 30 25 25 20

Q7. Calculate 556,1 & PDQ from the following data:

C.I. 0-10 10-20 20-30 30-40 40-50 50-60

Frequenc

y

8 12 32 20 18 10

Q8. Calculate Quartiles deviation of the following data


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Marks Less than

10

Less than

20

Less than

30

Less than

40

Less than

50

Less than

60

Less than

70

Less than

80

No. of

Students

12 16 40 78 98 112 120 141

Q9. Find the Mode of the following frequency distribution.

C.I. 0-10 10-20 20-30 30-40 40-50 50-60

Frequenc

y

12 18 33 23 20 7

Q10. Calculate coefficient of quartiles deviation of the following data:

C.I. 0-10 10-20 20-30 30-40 40-50 50-60

Frequenc

y

6 10 30 18 14 12

Q11. Find coefficient of variance of the following frequency distribution.

C.I. 0-50 50-100 100-150 150-200 200-250 250-300Frequenc

y

15 22 32 20 16 7

.Q12. Two sample of size 40 and 50 have the same mean53 but different standard

deviations 19 and 8 respectively. Find the standard deviation of the combined sample of

size 90.

Q13. Calculate the combined mean and variance if the following set of observations.

X 75 35 97 24 72 81 90 62 62

Y 83 52 88 56 66 63 83 54 50

Q14. The scores of two batsmen X and Y, in the series of 9 matches are given below;

determine which batsman is more reliable.

X 79 37 99 26 76 83 91 63 66

Y 83 50 90 59 67 61 85 57 52

Q15. Calculate the Karl Pearsons coefficient of correlation from the following data:

Height of father 64 65 66 67 68 69 70

Height of son 66 63 65 61 70 68 67

Q16. Find the Correlation Coefficient between X and Y

X 70 37 85 26 76 83 91 63 64Y 83 52 90 59 67 61 85 57 55

Q17. Find the Rank Correlation Coefficient between X andY :x 4 2 1 3 5

y 1 4 5 3 2

Q18. Find the Rank Correlation Coefficient between X andY


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X 73 34 96 23 73 80 88 60 63

Y 92 49 89 58 66 49 84 56 49

Q19. Find the two, regression lines of the following data :

x 6 2 10 4 8

y 9 11 5 8 7

Q20. If 03354 =YX and 0721840 =YX are two lines of regression. Find the(i). Mean value of X and Y.

(ii). Regression coefficient X on Y and Y on X.(iii). Correlation coefficient between X and Y.

(iv). Standard deviation of Y, if variance of X is 9.

Q21. If two regression lines are 734 YX and 0843 =YX find(i). Mean value of X and Y.

(ii). Regression coefficient X on Y and Y on X.

(iii). Correlation coefficient between X and Y.(iv). Standard deviation of Y, if variance of X is 4.

(v) Estimate the value of x for y=6

Q22. From the following information on values of two variable X and Y. find the two

regression lines, regression coefficients and the correlation coefficient between X and Y.

= 200410240402010 22 xyyxyxn ,,,,,Q23. Find the regression coefficients xyyx bandb for the following data:

= 1579737412247 22 xyyxyxn ,,,,,Q24. For 100 students of a class, the regression equation of marks in Statistics (x) on themarks in Mathematics (y) is .018053 =xy the mean marks in Mathematics is 50 andvariance of marks in Statistics is 4/9th of the variance of marks in Mathematics. Find the

mean marks in Statistics and the coefficient of correlation between marks in the twosubjects.

Q25. If 5 per cent of the item produced turn out to be defective, then find out theprobability that out of 20 items selected at random there are:

(i) exactly three defective

(ii) at least two defective

(iii) at most one defective

(iv) find the mean and the variance

Q26. A small scale unit operates an automatic machine which produces Screws. It isknown from the past records that the machine produces 5 per cent defective on an

average. Certain unassembled equipment need 95 such screws for assembly and is

supplied with a box of 100 screws produced by the unit. What is the probability that apurchase of such box of Screws:

(i) will get exactly five defective in the box


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(ii) will not have enough good screws to complete the assembly.

Q27. Consider a project that yields an average flow of Rs. 500 lakhs with a standard

deviation of Rs. 60 lakhs. Calculate the following probabilities:

(i). Cash flow will be more than Rs. 560 lakhs(ii). Cash flow will be less than Rs. 420 lakhs

(iii). Cash flow will lie between Rs. 460 and Rs. 540 lakhs

Q28. The Nicotine content (in mg) of two samples of tobacco were found to be as follows

Sample A 24 27 26 21 25

Sample B 27 30 28 31 22 36

Can it be said that the two samples come from the same normal population at 5% level of

significant? (Given 26.2)9(05.0=t

)

Q29. The time taken by workers in performing a job by two different methods is as

follows

Method I 20 16 26 27 23 22

Method II 27 33 42 35 33 34 38

Do the data show that the variances of time distribution of population from which these

samples are drawn do not differ significantly?

(Given 95.4)6,5(05.0 =F ; 39.4)5,6(05.0 =F )Q30. A die is thrown 276 times and the results of these throws are given as

No. appeared on the die 1 2 3 4 5 6Sample B 40 32 29 59 57 59

Test whether the die is biased or not. (Given 07.11)5(05.02 = )

Q31. In a locality 100 persons were randomly selected and asked about their educational

achievements. The results are given below:

Sex Education

Middle High school College

Male 10 15 25

Female 25 10 15

Based on this information can you say that education depends on sex?(Given 99.5)2(05.0

2 = )


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Dr. Quazzafi Rabbani

(Department of Mathematics)

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Assignment Pre Ph.d