STATISTICS
TIME ALLOWED : 20 Minutes
OBJECTIVE
MAXIMUM MARKS: 17
Note: You have four choices for each objective type question as A, B, C and D. The choice which you think b correct, fill that circle in front of that question number. Use manner 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. No credit will be awarded in ease BUBBLES are not filed. Do not solve question en this sheet of OBJECTIVE PAPER.

Question#1

• Laspeyre's formula is used in the construction of consumer price index:-
  
  (A) Aggregative expend tuna method
  (B) Family budget method
  (C) Both A and B  
  (D) None of these
  
  
• The probability of selecting a vowel 'letter at random from the word ''STATISTICS" is:-
  
  (A)  
  (B)  
  (C)  
  (D)
  
  
• A pair of dice is rolled, the total number of outcomes can be:-
  
  (A) 6
  (B) 12
  (C) 24
  (D) 36
  
  
• A discrete probability distribution may be is-presented by:-
  
  (A) A table
  (B) A graph
  (C) A mathematical equation
  (D) All of these
  
  
• If X is a random variable, then E (5x + 2) is:-
  
  (A) 5 E ( X )
  (B) 5E (X ) + 2         
  (C) 5+ E(X)
  (D) 2 E(X ) + 5
  
  
• The binomial random variable can assume values:-
  
  (A) From 0 to π  
  (B) From -∞ to ∞ 
  (C) From - I  to + I
  (D) From 0 to 1
  
  
• The mean of the binomial distribution is:-
  
  (A) n p q
  (B)    
  (C)  n q
  (B) n P
  
  
• Ina hypergeometric random experiment, the successive trials are:-
  
  (A) Independent    
  (B) Dependent
  (C) Some times independent
  (D) Some times dependent
  
  
• The life of a television tube is a:-
  
  (A) Continuous variable   
  (B) Discrete variable
  (C) Qualitative variable
  (D) Categorical variable
  
  
• The number of observations falling in a class is called:-
  
  (A) Class-mark
  (B) Class-frequency
  (C) Cumulative frequency
  (D) Class-interval
  
  
• The mean is affected by the change of:-
  
  (A) Origin 
  (B) Scale
  (C) Origin and Scale 
  (D) None of these
  
  
• The median of the data - 2, 0, 2, 5, -1, 4, is-  
  
  (A) 4
  (B) 1
  (C) 3.5
  (D) 5
  
  
• The harmonic mean of the numbers a and b is.-
  
  (A) 
  (b) 
  (c) (ab)1/2
  (D)  
  
• ______is a relative measure of dispersion.
  
  (A) Standard deviation
  (B) Variance         
  (C) Coefficient of variation
  (D) Mean deviation
  
  
• The variance of 5 numbers is 10. If each number is divided by 2, the variance of the new numbers
  
  (A) 20 
  (B) 5
  (C) 2.5
  (D) 10
  
  
• If a data is measured in inches the coefficient of mean deviation is expressed in:
  
  (A) Inches 
  (B) Square of inch
  (C) Without units
  (D) Percent
  
  
• ______formula is called current year weighing.
    
  (A) Laspeyre's Index Number
  (B) Paasche's Index Number
  (C) Fisher's Index Number
  (D) None of these

INTERMEDIATE PART-I
STATISTICS
TIME ALLOWED: 3.10 Hours
MAXIMUM MARKS: 83
SUBJECTIVE
NOTE: - Write same question number and its part number on answer book, as given in the question paper.
SECTION-I

2. Attempt any eight parts.(8 x 2 = 16)

• Differentiate between a Variable and a Random Variable.
  
• Expand the following summation (a)   (b) 
  
• Define Arithmetic Mean.
  
• Compute the Median for the data - 2 , 5, 0, - I. 4, 2                          
  
• The Stan of deviations of 15 values from 20 is 45. Find A
  
• In a single peaked symmetrical distribution mean = 5, median= 5. then what will be the Value of mode?
  
• A distribution consists of 3 components with respective size 45, 40 and 65, along with their Means 2, 2.5 and 2.Compete the combined mean.
  
• What is the Market Basket?
  
• Write the two methods of calculating the Un-weighted Index Numbers.
  
• Given Ʃp„q„ = 3600, Ʃp1q„  Aq„ = 4300, Ʃp„q1 = 4100 and Ʃp1q„  = 4890 Calculate Fisher's Index Number.
  
• How many methods are used for selection of base period? Name the methods.
  
• Given Ʃp„q„ = 10 and Ʃpnqo = 2040.Calculate CPI using aggregate expenditure method.

3. Attempt any eight parts. (8 x 2 = 16)

• Explain the term “Open End" Classes.
  
• What is Tabulation?
  
• Find Variance of given data 5.5,5,5.5.5 and 5.
  
• If Var (X )= 8, find Var ( X+ 3 )
  
• What is Kurtosis?
  
• Give my two properties of Variance.
  
• IFQ1 =136.62, Q2 = 146 and Q3 = 153.13 find Bowles Coefficient of Skewness.
  
• If Var (x)= 8, find var ( 2x)
  
• Write the sample space when 3 coins are tossed.
  
• Define Probability.
  
• A card is drawn from a deck of 52 playing cards. What is probability of pictured card?
  
• If P (A) = 0.2 and P(B) = 0.15 then find p(A ∩ B) where A & B are independent events

4. Attempt any six parts. (6 x 2 =12)

• Define a discrete random variable.
  
• Write down the properties of a continuous random variable.
  
• What is meant by mathematical expectation of a random variable?
  
• What is meant by Probability Distribution?
  
• Given (x)=,  x= I, 2, 3. Find k.
  
• What are properties of binomial experiment? (Any two)
  
• Write down parameters, mean and variance of hypergeometricc distribution.
  
• A random variable X has a binomial distribution with n = 5 and p = 0.2. Find mean and variance of X.
  
• Given N= 40, n = 5 and k 8 Find mean and variance of X.

SECTION-II

NOTE: - Attempt any three questions.
Question#5
(a) The weight of 100 students are recorded to the nearest kg. 4

Find Arithmetic Mean.
(b) Calculate Mode for the given data:- 4

Question#6
(a) First four moments about Mean of a distribution are 0.3, 74, 45 and 121.Find out whether the distribution is leptokurtic or platykurtc. 4
(b) Given the following data:-4
n1 = 25,     X1 = 25.2,   = 4.90
n2 = 30,   X2 = 21.5,         = 6.25
Find the Combined Mean and Variance

Question#7
(a) Compute Fisher's Index Number for the following data:- 4

(b) A bag is containing 5 white 7 black balls. If 3 balls are drawn from the bag what is the probability that:-4
(i) two white and one black
(ii) all are of same colour 

Question#8
(a) Find E( X ) and Var ( X ) from the following probability distribution:- 4 

(b) Given (x)=cx 0 ≤ x≤ 2 Find the value of c and also find p (0 < x < I ). 4

Question#9
(a) An event has the probability, p=3/8 ,Find complete binomial distribution, for n = 5. 4
(b) A committee of size 3 is selected from 4 men and 2 women. Find the probability distribution by the Hypergeometric experiment for the number of Men in the committee. 4

SECTION-lll
(PRACTICAL)

10. Attempt any three parts.(3 x 5 = 15)

Where u =   Find the value of Median.
(B)

Find Coefficient of Variation.
(C) Find the chain indices from the following price relatives of 3 commodities wing the median.

(D)   A committee of size 3 is selected from 3 men and 4 women. Find the probability distribution'by hypergeometric experiment for the number of women in the committee. Also find its mean.
(E) Four dice are tossed 96 times. Find the expected frequencies when throwing of a 4, 5 or 6 is regarded as a success.