MODEL PAPER-I (2011) Statistical Method BCA-I . Q.1
Q.2
Q.3
Q.4
Mention the correct answer from the answers provided. (a) A single figure
(b) A group of homogeneous facts and figures.
(c) An isolated fact
(d) None of the above
Which of the following would you regard as discrete variables. (a) Height & weight
(b) Time
(c) Wages paid to workers
(d) Number of persons in a family.
Prof. M.A. sturges, rule for determining determining the number of classes is (a) K = 1+3.322 log N
(b) 1-3.3 Log N
(c) K = 1+3.22 log N
(d) None of these.
The positional measure of central tendency is (a) geometric mean
Q.5
(b) Median
(c) harmonic mean
(d) Arithmetic's Arithmeti c's mean
The algebraic sum of the deviation of 20 observations measured from 30 is 2. Find the mean of these observations. observations. (a) 30.2
Q6.
(b) 30.1 (c) 29.8
(d) none of these
The mean of 20 observations is 15. on checking it was found that two observations were wrongly copied as 3 and 6. If wrong observations are replaced by correct values 8 and 4, then find the correct mean: (a) 15.14
Q.7
(b) 15
(c) 16
(d) 15.15
10 is the mean of a set of 7 observations and 5 is the mean of a set of 3 observations. Find the mean of a combined set. (a) 8.6
Q.8
(d) none of these
(b) the median
(c) the geometric mean (d) none of these
(b) The median (c) The mode
(d) none of these
(b) Continuous (c) Both (a) and (b)
(d) none of these
The average of the 7 numbers 7,9,12 x, 5,4, 11 is 9. The missing number ‘x’ is:(a) 13
Q.13
(c) 12
A frequency distribution distributio n can be: (a) Discrete
Q.12
(b) 16
The most stable measure of central tendency is : (a) The mean
Q.11
(d) none of these
The point of intersection intersecti on of the ‘less then’ and ‘greater then’ ogive corresponds to: (a) the mean
Q.10
(c) 8.5
The geometric mean of 2,4,16, and 32. (a) 8
Q.9
(b) 7
(b) 14
(c) 15
(d) 8
For a group of 100 candidates, the mean was found to be 40. Later on it was discovered that a value 45 was misread as 54. The correct mean is : (a) 40.50
(b) 39.85
(c) 39.80
(d) 39.91
Q.14
The average of five numbers is 40 and th e average of another four numbers is 50. the average of all numbers taken together is : (a) 44.44
Q.15
(b) 45.00
(c) 45.55
(d) 90.00
(c) 6
(d) 8
The median of the following set of data: 0, 1, -1, -2, 6, 4, 5, 8, 12, 10, 11 (a) 4
Q.16
(b) 5
The algebraic sum of deviations of all observations from th eir arithmetic mean is always: (a) A positive value
Q.17
(c) Equals to zero
(d) All above
(c) 12
(d) none of these
The mean of the observations 11,15,19,17,3,7 11,15,19,17,3, 7 is (a) 19
Q.18
(b) A negative value
(b) 3
If a constant 35 is subtracted from each observation s of a given set of observations, the mean of the set is – (a) Increased by 25
Q.19
(b) 7
(c) 2
(d) 9
……………… is not affected by extreme observations. observations . (a) Average
Q.1
(c) Not affected (d) None of these
The median of the series 5,7,8,9,6,8,7,5,7,9,2,7 is (a) 5
Q.20
(b) Decreased by 25
(b) Mean
(c) Median
(d) None of these
(a) What do you mean by measure of central tendency. Explain the essentials requisites of a good measure of central tendency. (b) Wh What is the limitation of central tendency ?
Q.2
(a) Calculate Arithmetic Mean, Median and Mode from the following data-
No. of wages earners
14
62
99
18
7
(b) Explain the merits and demerits of Arithmetic Mean. Q.3
Write shot notes on(i)
Difference between inclu clusiv sive serie eries s and excl xclusive sive ser series. ies.
(ii)
Cumulative frequency frequency distribution.
(iii) Ogives curves (iv) Relative frequency distribution. distribution. (v) Q.4 Q.4
Frequency polygon An anal analys ysis is of mont monthl hly y wage wages s paid paid to work worke ers in two firm firms s A & B belongin nging g to the the same same industry gives the following results:
No. of workers
586
648
Average of Monthly Monthly wages wages
52.5
47.5
Variance of distribution distributi on of wages
100
121
(i)
Which firm A or B pays out the largest amount as monthly wages?
(ii)
Which firm A or B has greater variability in individual wages?
(iii) Find the average monthly wages and standard deviation of the wages of all workers in two firms, taken together.
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MODEL PAPER-II (2011) Statistical Method BCA-I . Q.1
The The expe experi rime ment nt of thro throwi wing ng a dice dice is called‐ (a) a trial (b) a sample space
(c) an outcome
(d) an event
Q.2
The probability of drawing one white ball from a bag containing 6 red, 8 black, 10 yellow and 1 green ball is‐ (a) 1/25 (b) 0 (c) 1 (d) 24/25
Q.3
In the simultaneous tossing of two perfect dice, the probability of obtaining 4 as the sum of the resultant faces is ‐ (a) 4/12 (b) 1/12 (c) 3/12 (d) 2/12
Q.4
A single letter is selected at random from the world 'PROBABILITY'. The probability that it is vowel is‐ (a) 3/11 (b) 2/11 (c) 4/11 (d) 0
Q.5
If A and B are mutually exclusive events, then (a) P (A χ B) = P (A).P ( B) (b) P (A χ B)
= P (A)+ P (B)
(c) P (A χ B)
= P (A)‐P (B)
Q.6
(b) 8
(c) 3
(d) 0
In simultaneous tossing of two perfect coins, the probability of having at least one head is ‐ (a) 1/2
Q.8
(d) P (A χ B)
A coin is tossed tossed three times in success succession ion,, the number number of sample sample points points in sample sample space space is‐ (a) 6
Q.7
=0
(b) 1/4
(c) 3/4
(d) 1
A card is drawn from a well‐shuffled pack of playing cards. The probability that the card is either spade or an ace is‐ (a) 4/52
Q.9
(b) 1/18
Q.12 Q.13 Q.13
Q.14. Q.15
(c) 1
Probability:
(b)
13 C9 52C13
Q.18
Q.19
(c) (c) (13 C9)(39C4) 52C13
‐1
‐2
1
2
1/3
1/6
1/6
1/3
then the expected value of X is : (a) 3/2 (b) 1/6
Q.17
(d) 7/9
(d) 4x(13C 9(39C 4) 52C13
A bag contains 3 red, 6 white and 7 blue balls. The probability that that two two balls balls drawn drawn white white and blue is‐ (a) 13/16 (b) 7/20 (c) 6/13 (d) 7/13 If A and B are two events, the probability of occurrence of A and B simultaneously is given as: (a) P(A)+P(B) (b) P(A χ B) (c) P(A∩B) (d) P(A).P(B) From Fro m a pack pack of 52 cards, cards, two cards cards are drawn at random. The proba probability that one is an ace and the other is a king is:‐ (a) (a) 2/13 2/13 (b) (b) 1/16 1/169 9 (c) (c) 16/1 16/169 (d) (d) 8/66 8/663 3 Given that P(A)=1/3, P(B)=3/4, P(A χB)=11/12, the probability, P(B\A) is :‐ (a) 1/6 (b) 4/9 (c) 1/2 (d) None of the above If a random variable X has the following probability distribution :‐ X:
Q.16
(d) 4/13
The prob probab abil ilit ity y of getting 9 card cardss of the same suit in one one hand hand at a ga g ame of brid bridg ge is ‐ (a) 4x13C4 52C13
Q.11
(c) 1/52
If two two dice dice are are thro thrown wn simu simult lt aneously then the probability that the sum is neither 7 nor 11 is‐ (a) 1/6
Q.1 Q.10
(b) 13/52
(c) 1/2
(d) None of the above
If A and B are mutually disjoint events, then the probability of A∩B is always: (a) Infinite (b) Zero (c) One (d) None of these Two dice are thrown thrown simultaneously. simultaneously. Probability that the the sum of the upper face of two dice is 7, is (a) 1/36 (b) 1/6 (c) 7/36 (d) None of these If the letters of the word 'REGULATIONS' be arr anged at ra ndom, w hat is the chance there will be exactly 4 letters between the R and E (a) 6/35 (b) 4/55 (c) 1/55 (d) None of these There are 5 white and 7 red ball in a bag. (a) 6/35 (b) 4/55 (c) 1/55 (d) None of these
Q.20 Q.20
The median of the the foll follow owin ing g set set of data data:: 0, 1, ‐1, ‐2, 6, 4, 5, 8, 12, 10, 11 (a) (a) 4 (b) (b) 5 (c) (c) 6 (d) (d) 8 Short a t answer type questions. Q.1 (a) What you mean by average. Explain the requisites of a good average. (b) An analysis of monthly wages paid to the workers of two firms A and B belonging to the the same industry give the following results Firm A Firm A
Firm B
Number of workers of workers
500
600
Average daily wages
Rs. 180.00
Rs. 175.00
81
100
Variance of distribution of wages (i) (ii)
Which firm A or B has a large wage bill. In which which firm firm A or B is there there greater greater variab variabili ility ty in indivi individua duall wages? wages?
(iii)
Calculate: (a) The average daily wage of all the workers in the two firms A and B take together (b) The variance of the distribution of wages of all the workers in the firms A and B tak en together
Q.2
(a) (a) Calc alculate quartile deviation and and the the coef coeffi fici cien entt of quar quarti tille devia eviati tion on from from the the follo ollowi wing ng data data.. Wages
Less than 35
35-37
38-40
41-43
Over 43
14
62
99
18
7
No. of wages earners
(b) Explain the merits and demerits of quartile deviation. Q.3
(a) The scorer orerss of t wo batsm an A and and B in then then innings during a cert certai ain n seas season on are: A
32
28
47
63
71 71
39
10
60
96
14
B
19
31
48
53
67 67
90
10
62
40
80
Find which of the two batsmen, A o r B is more consistent in scoring. (b) Calculate the first four moment s about the mean fr om the following dat a. Also calculate the value of β and β 2. Marks No of stud studen ents ts Q.4
0‐10 5
10‐20 12
20‐30 18
30‐40 40
40‐50 15
50‐60 7
60‐70 3
(a) (a) Expl Explai ain n the the fol follow lowing ing correlation. (i) Positive or negative
(b)
Simple, partial and multiple
(c) Linear and non‐linear (b) Calcula Calculate the coefficient of correlation correlation between between X and Y from the following following data and calculate probable and s tandard error (by sh ort cut me thod) X Y
78 125
89 137
99 156
60 112
59 107 107
79 136
68 123
61 108
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