Statistics (Objective)
Maximum Marks:-17
Time Allowed:- 20 minutes
Note:-You have four choices for each objective type question as A, B, C and D. The choice which you think is correct; fill that circle in front of that question number. Use marker or pen to fill the circles. Cutting or filling two or more circles will result in zero mark in that question. Attempt as many questions as given in objective type question paper and leave others blank. Write the letter A, B, C or D in the column (write correct option) against each question. If there is a contradiction in the bubble and hand written answer, bubble option will be considered correct.

Question#1

• Non-numerical descriptors are:
  
  (A) Qualitative variable
  (B) Quantitative variable
  (C) Discrete variable
  (D) Continuous variable
  
  
• The graph of cumulative frequency distribution is called:
  
  (A) Histogram
  (B) Frequency Polygon
  (C) Ogive
  (D) Pie Chart
  
  
• Column captions of a table are also called:
  
  (A) Body
  (B) Box-head
  (C) Stub
  (D) Title
  
  
• Which average of the following has least value?
  
  (A) A .M.
  (B) G.M.
  (C) H.M.
  (D) Both (a) & (b)
  
  
• The mean of the first n ' natural numbers 1, 2, 3,4, ..... , n is:
  
  (A)  
  (B)
  (C)    
  (D)
  
  
• If X & Y are two independent random variables and given that S.D.(X) = 6 & S.D.(Y)=8, then S.D.(X- Y) =
  
  (A) 14
  (B) - 2
  (C) 10
  (D) 100
  
  
• The second and fourth moments about mean are 4 & 48 respectively, and then the distribution is:
  
  (A) leptokurtic
  (B) Mesokurtic
  (C) Platy Kurtic
  (D) Skewed
  
  
• Half of the difference between upper and lower quartiles is called:
  
  (A) Mean deviation  
  (B) Standard deviation
  (C) Quartile deviation
  (D) Inter Quartile Range
  
  
• Current period quantities are used as weight in:
  
  (A) Laspeyre's 'Nos:
  (B) Paasche's.I.Nos:
  C) Fisher's I. Nos: 
  (D) Chain I. Nos:
  
  
• Retail price index numbers are:
  
  (A) Simple
  (B) Un weighted
  (C) Base year weighted
  (D) Current year weighted
  
  
• The Probability of an event. cannot be:
  
  (A)  = 0
  (B)  <0
  (C)  >0
  (D)  =1
  
  
• The probability of drawing Black Queen from 52 cards is:
  
  (A)  
  (B)  
  (C)
  (D)
  
   (Sum of parallel sides) xBase=Area of the:
  
  (A) Triangle
  (B) Rectangle
  (C) Square
  (D) Trapezoid
  
  
• E(X - μ) =
  
  (A) Zero
  (B) Mean
  (C) Mean deviation
  (D) Standard deviation
  
• Fora Binomial distribution  then S.D. =
  
  (A) 2
  (B) 4
  (C) 6
  (D) 12
  
  
• If in a Binomial distribution, p=0.5, then the distribution is:
  
  (A) Non-symmetrical
  (B) Symmetrical
  (C) Positively skewed
  (D) Negatively skewed
  
  
• The variance of the hyper geometric distribution is
  
  (A)
  (B)    
  (C)
  (D)    
  

Statistics
(Subjective)
Time Allowed: 2.40 hours
Maximum Marks: 68

2. Answer briefly any Eight parts from the followings:-

• What is descriptive statistics?
  
• Write any two sources of primary data?
  
• What are deciles?
  
• Give two demerits of A.M?
  
• For 1,2,3,4,5 prove that  =
  
• Calculate median for 87,87,88,89,89,90.
  
• When is a distribution symmetrical?
  
• What s consumer price index number?
  
• What is family budget method?
  
• What are the methods for selecting base period?
  
• Write formula for Paasche's index number
  
• How do we calculate index number?

3. Answer briefly any Eight parts from the followings:

• Define Tabulation.
  
• What is a component Bar diagram?
  
• Differentiate Absolute and Relative measurements of dispersion.
  
• What is semi-Inter Quartile Range?
  
• If Co-efficient of variation and standard deviation of a distribution are respectively 15% and 11 Find out the value of A.M.
  
• What is meant by negative skewness?
  
• Define the term Co-efficient of Skewness.
  
• If β1=10 and β2 =10 Discuss shape of the curve.
  
• What is the difference between an outcome and an event?
  
• Define mutually Exclusive Events.
  
• What is the subjective approach to probability?
  
• If A and B are independent events with P(A)=4 and P (B)=.3. Find P (AU B).

4.    Answer briefly any Six parts from the followings:-6 x 2 = 12

• Define continuous random variable giving examples.
  
• Define random numbers.
  
• If E(X) = 5 and E(Y)= - 23 then E(X-Y)=?
  
• What are the uses of random numbers?
  
• How random numbers are generated?
  
• Define Bernoulli trial
  
• In a binomial distribution mean = 5 and SD = 3. Calculate the value of P and comments it.
  
• Define hyper geometric experiment along with its properties.
  
• Calculate the probability of all aces in a sample of 4 out of 52 playing cards. When cards are drawn without replacement.

SECTION-----ll

Note: Attempt any three questions. (8 x 3 = 24)       
Question#5
(a) With the help of the following data. show that A.M. > G.M.

(b) The following frequency distribution has been obtained from a continuous variable X after making the substitution U=

Calculate the Median

Question#6
(a) The following scores are made by two batsmen A&B in a series of innings:

(i)   Who is better as a run getter?
(ii)  Who is a more consistent player?
(b) The S.D. of a symmetrical distribution is 5. What must be the value of m4 so that the distribution is?
(i) Platy Kurtic
(ii) Lepto Kurds

Question#7
(a) From the following data given below. Compute the index numbers of prices taking 2007 as a base
(i) Aggregative method
(ii) simple average of pricerelatives method.

(b)(i) A card is drawn from an ordinary deck of 52 playing cards. Find the probability of A is the event     of getting King card.
(ii) A coin is tossed twice, each sample point with probability of 1/4 . If A and B are events that head at first coin and tail on second coin respectively. Then find P(AUB)

Question#8
(a) For the distribution given below Find
(i) E(x)
(ii) E(x)²

(b) A continuous random variable x having values between 0 and 4 has a density function by: f(x)=- ax, where 'a' is a constant find (i) a  (ii) P(1 ≤ x ≤ 2)

Question#9
9.(a) If 10% of the parts produced by machine are defective, determine the probability that of 4 parts chosen at random with replacement.
 (i) one is defective
(ii) no is defective
(b) A committee of size 5 is to be selected at random from 3 women and 5 men. Find the probability distribution for the number of women on the committee and also find expected women on the committee.