University Of Pune Question Paper
B. C. A. ( Semester - II ) Examination - 2013
ELEMENTS OF STATISTICS
(New 2008 Pattern)
Time : 3 Hours] [Max. Marks : 80
Instructions :
(1) All questions are compulsory.
(2) All questions carry equal marks.
(3) Figures to the right indicate full marks.
(4) Use of statistical tables and calculator is allowed.
(5) Symbols and abbreviations have their usual meanings.
Q.1) Attempt any four of the following : [4x4=16]
(a) Define the following terms :
(i) Raw Data
(ii) Attribute
(iii) Classification
(iv) Frequency of a Class
(b) Explain Absolute and Relative Measures of Dispersion.
(c) Explain the causes of variation in SQC.
(d) Define the following terms :
(i) Deterministic Experiment
(ii) Sample Space
(iii) Conditional Probability
(iv) Independent Events
[4373]-202 1 P.T.O.
Seat
No.
(e) The Intelligence Quotients (I.Q.s.) of 10 boys in a class are given
below :
70, 120, 110, 101, 88, 83, 95, 98, 101, 100
Obtain Mean, Median and Modal I.Q. of boys.
(f) A candidate obtained the following percentages of marks in an
examination :
English - 60, Hindi - 75, Mathematics - 63, Physics - 59 and
Chemistry - 55.
Find the Candidate’s Weighted Arithmetic Mean if weights 1,
2, 1, 3, 3 respectively are alloted to the subjects.
Q.2) Attempt any four of the following : [4x4=16]
(a) State merits and demerits of Mode.
(b) In how many ways can the letters of the word ‘STRANGE’ be
arranged so that the vowels are always together ?
(c) Find Median of Wages from the following frequency distribution
of Wages in Rs. per week :
Wages Less 35-38 38-41 41-44 Above 44
(in Rs. than 35
per week)
No. of
Wage
Earners 14 62 99 18 7
(d) Number of permutations of n objects taken 4 at a time is twice
the number of permutations of 5 objects taken 3 at a time. Find
value of ‘n’.
(e) Following is the frequency distribution of number of students
according to the marks scored in certain examination :
Marks 0-19 20-39 40-59 60-79 80-99
No. of
Students 18 26 34 12 8
[4373]-202 2 Contd.
Obtain :
(i) Class limits of second class.
(ii) Class boundaries of third class.
(iii) Class width of second class.
(iv) Number of students scoring marks more than 60.
(f) Calculate Standard Deviation and Coefficient of Variation from
the following data :
Class 1-3 3-5 5-7 7-9 9-11
Frequency 2 3 53 2
Q.3) Attempt any four of the following : [4x4=16]
(a) There are four 10 km segments to an automobile trip. If the
car is driven as follows :
100 km/hr for the first 10 km,
90 km/hr for the second 10 km,
80 km/hr for the third 10 km and
110 km/ha for the fourth 10 km.
Find average speed of the car.
(b) Compute the Standard Deviation of the two groups combined
together from the information given as below :
Group No. of Items Average S.D.
A 450 60 10
B 550 40 8
(c) Calculate Geometric Mean of the following data :
1, 7, 18, 65, 91, 103.
[4373]-202 3 P.T.O.
(d) Let A and B be the two events defined on sample space Ω. If
P(A) = 0.8, P(B) = 0.5, P(A∩B) = 0.2, then find the probability
of occurrence of :
(i) atleast one of the events
(ii) none of the events
(iii) only event A
(iv) not event B
(e) What is the Probability that a leap year will contain 53 Thursdays
or Fridays ?
(f) Explain the Methods of Classification.
Q.4) Attempt any four of the following : [4x4=16]
(a) The Mean Value of the following frequency distribution related
with the number of accidents was found to be 1.46 :
Number of
Accidents 0 1 2 3 4 5 Total
Number of
Days 46 ? ? 25 10 5 200
Calculate missing frequencies.
(b) The Standard Deviation of a distribution of 100 values was
Rs. 2. If the sum of squares of actual values was Rs. 3,600,
what was the mean of this distribution ?
(c) Four cards are drawn atrandom from a pack of well-shuffled
52 cards. Find the probability that :
(i) there is one card of each suit.
(ii) two cards are red and two cards are black.
(d) Let A and B be the two events defined on sample space Ω and
suppose P(A) = 0.4, P(A∪B) = 0.7 and P(B) = ‘P’. Then,
(i) for what choice of ‘P’ are A and B mutually exclusive ?
(ii) for what choice of ‘P’ are A and B independent ?
(e) Explain Population and Sample with an illustration.
[4373]-202 4 Contd.
(f) Let A and B be the two events defined on sample space Ω such
that, P(A) = 0.8, P(B) = 0.5 and P(A∩B) = 0.45. Obtain
(i) P(B/A)
(ii) P(A’/B’)
Q.5) Attempt any two of the following : [16]
(a) (i) The number of defects observed on 10 carpets manufactured
are as follows :
3, 4, 5, 6, 3, 3, 5, 3, 6, 2.
Construct the suitable control chart and comment on it. [06]
(ii) State the control limits of np-chart. [02]
(b) (i) In the manufacturing process of an article, X and R charts
are drawn for certain measurement of the articles. For 20
samples each of size 4, X = 41.20 and
R
= 0.34.
Compute the control limits of
X
and R Charts. [06]
(For given n, A2
= 0.729, D3
= 0, D4
= 2.282)
(ii) State the addition theorem of probability for three events. [02]
(c) (i) Two workers on the same job show the following results
over a long period of time :
Worker ‘A’ Worker ‘B’
Mean time of completing
the job (in minutes) 30 35
Standard Deviation (in minutes) 6 4
(1) Which worker appears to be faster in completing the
job ? Justify.
(2) Which worker appears to be more consistent in the
time he requires to complete the job ? Justify. [04]
[4373]-202 5 P.T.O.
(ii) Write down the sample space for each of the following
experiments :
(1) A coin is tossed until head occurs.
(2) Ten seeds are planted and total number of seeds
germinated are recorded after a week.
(3) A point is randomly selected in the circle with radius
5 cm. and its distance from the centre is noted.
(4) A two digit number is formed from the digits 4, 5,
6 using each digit only once.
B. C. A. ( Semester - II ) Examination - 2013
ELEMENTS OF STATISTICS
(New 2008 Pattern)
Time : 3 Hours] [Max. Marks : 80
Instructions :
(1) All questions are compulsory.
(2) All questions carry equal marks.
(3) Figures to the right indicate full marks.
(4) Use of statistical tables and calculator is allowed.
(5) Symbols and abbreviations have their usual meanings.
Q.1) Attempt any four of the following : [4x4=16]
(a) Define the following terms :
(i) Raw Data
(ii) Attribute
(iii) Classification
(iv) Frequency of a Class
(b) Explain Absolute and Relative Measures of Dispersion.
(c) Explain the causes of variation in SQC.
(d) Define the following terms :
(i) Deterministic Experiment
(ii) Sample Space
(iii) Conditional Probability
(iv) Independent Events
[4373]-202 1 P.T.O.
Seat
No.
(e) The Intelligence Quotients (I.Q.s.) of 10 boys in a class are given
below :
70, 120, 110, 101, 88, 83, 95, 98, 101, 100
Obtain Mean, Median and Modal I.Q. of boys.
(f) A candidate obtained the following percentages of marks in an
examination :
English - 60, Hindi - 75, Mathematics - 63, Physics - 59 and
Chemistry - 55.
Find the Candidate’s Weighted Arithmetic Mean if weights 1,
2, 1, 3, 3 respectively are alloted to the subjects.
Q.2) Attempt any four of the following : [4x4=16]
(a) State merits and demerits of Mode.
(b) In how many ways can the letters of the word ‘STRANGE’ be
arranged so that the vowels are always together ?
(c) Find Median of Wages from the following frequency distribution
of Wages in Rs. per week :
Wages Less 35-38 38-41 41-44 Above 44
(in Rs. than 35
per week)
No. of
Wage
Earners 14 62 99 18 7
(d) Number of permutations of n objects taken 4 at a time is twice
the number of permutations of 5 objects taken 3 at a time. Find
value of ‘n’.
(e) Following is the frequency distribution of number of students
according to the marks scored in certain examination :
Marks 0-19 20-39 40-59 60-79 80-99
No. of
Students 18 26 34 12 8
[4373]-202 2 Contd.
Obtain :
(i) Class limits of second class.
(ii) Class boundaries of third class.
(iii) Class width of second class.
(iv) Number of students scoring marks more than 60.
(f) Calculate Standard Deviation and Coefficient of Variation from
the following data :
Class 1-3 3-5 5-7 7-9 9-11
Frequency 2 3 53 2
Q.3) Attempt any four of the following : [4x4=16]
(a) There are four 10 km segments to an automobile trip. If the
car is driven as follows :
100 km/hr for the first 10 km,
90 km/hr for the second 10 km,
80 km/hr for the third 10 km and
110 km/ha for the fourth 10 km.
Find average speed of the car.
(b) Compute the Standard Deviation of the two groups combined
together from the information given as below :
Group No. of Items Average S.D.
A 450 60 10
B 550 40 8
(c) Calculate Geometric Mean of the following data :
1, 7, 18, 65, 91, 103.
[4373]-202 3 P.T.O.
(d) Let A and B be the two events defined on sample space Ω. If
P(A) = 0.8, P(B) = 0.5, P(A∩B) = 0.2, then find the probability
of occurrence of :
(i) atleast one of the events
(ii) none of the events
(iii) only event A
(iv) not event B
(e) What is the Probability that a leap year will contain 53 Thursdays
or Fridays ?
(f) Explain the Methods of Classification.
Q.4) Attempt any four of the following : [4x4=16]
(a) The Mean Value of the following frequency distribution related
with the number of accidents was found to be 1.46 :
Number of
Accidents 0 1 2 3 4 5 Total
Number of
Days 46 ? ? 25 10 5 200
Calculate missing frequencies.
(b) The Standard Deviation of a distribution of 100 values was
Rs. 2. If the sum of squares of actual values was Rs. 3,600,
what was the mean of this distribution ?
(c) Four cards are drawn atrandom from a pack of well-shuffled
52 cards. Find the probability that :
(i) there is one card of each suit.
(ii) two cards are red and two cards are black.
(d) Let A and B be the two events defined on sample space Ω and
suppose P(A) = 0.4, P(A∪B) = 0.7 and P(B) = ‘P’. Then,
(i) for what choice of ‘P’ are A and B mutually exclusive ?
(ii) for what choice of ‘P’ are A and B independent ?
(e) Explain Population and Sample with an illustration.
[4373]-202 4 Contd.
(f) Let A and B be the two events defined on sample space Ω such
that, P(A) = 0.8, P(B) = 0.5 and P(A∩B) = 0.45. Obtain
(i) P(B/A)
(ii) P(A’/B’)
Q.5) Attempt any two of the following : [16]
(a) (i) The number of defects observed on 10 carpets manufactured
are as follows :
3, 4, 5, 6, 3, 3, 5, 3, 6, 2.
Construct the suitable control chart and comment on it. [06]
(ii) State the control limits of np-chart. [02]
(b) (i) In the manufacturing process of an article, X and R charts
are drawn for certain measurement of the articles. For 20
samples each of size 4, X = 41.20 and
R
= 0.34.
Compute the control limits of
X
and R Charts. [06]
(For given n, A2
= 0.729, D3
= 0, D4
= 2.282)
(ii) State the addition theorem of probability for three events. [02]
(c) (i) Two workers on the same job show the following results
over a long period of time :
Worker ‘A’ Worker ‘B’
Mean time of completing
the job (in minutes) 30 35
Standard Deviation (in minutes) 6 4
(1) Which worker appears to be faster in completing the
job ? Justify.
(2) Which worker appears to be more consistent in the
time he requires to complete the job ? Justify. [04]
[4373]-202 5 P.T.O.
(ii) Write down the sample space for each of the following
experiments :
(1) A coin is tossed until head occurs.
(2) Ten seeds are planted and total number of seeds
germinated are recorded after a week.
(3) A point is randomly selected in the circle with radius
5 cm. and its distance from the centre is noted.
(4) A two digit number is formed from the digits 4, 5,
6 using each digit only once.
0 comments:
Pen down your valuable important comments below