INTERMEDIATE PART-I
(11 CLASS)
STATISTICS PAPER-I (NEW SCHEME)          
TIME ALLOWED: 20 Minutes
OBJECTIVE
MAXIMUM MARKS: 17
Note: You have four choices for each objective type question m A, B, C and D. The choice which you think 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. No credit will be awarded in case BUBBLES are not filled. Do not solve question 6 on this sheet of OBJECTIVE PAPER.

Question#1

• A quantity calculated from a population is called
  
  (A) Frequency
  (B) Statistic
  (C) Parameter
  (D) Sample
  
  
• The grouped date is:-
  
  (A) Primary
  (B) Secondary
  (C) Raw data
  (D) None of these
  
  
• The average of lower and upper class limits is called:-
  
  (A) Class boundary
  (B) Class frequency
  (C) Class mark
  (D) Class limit
  
  
• The mean is based on
  
  (A) All the values
  (B) Small values
  (C) Extreme values
  (D) Large values
  
  
• Geometric mean of X: 2, 4, 8 is:-
  
  (A) Zero
  (B) 4
  (C) 6
  (D) 16
  
  
• Second moment about mean is:-
  
  (A) 0
  (B) i
  (C) Variance
  (D) Stardard deviation
  
  
• If Q3=20 and Q1=10 the co-efficient of quartile deviation is:-
  
  (A) 3
  (B) 1/3
  (C) 2/3
  (D) 1
  
  
• In a symmetrical distribution, the coefficient of skewness will always be,
  
  (A) Negative
  (B) Zero
  (C) 1
  (D)-1
  
  
• Index for base period is always taken as,
  
  (A) 100
  (B) One
  (C) 200
  (D) Zero
  
  
• Base year weighted index numbers are:-
  
  (A) Laspeyre's
  (B) Fisher's
  (C) Paasche's
  (D) CPI
  
  
• The probability of drawing any one spade card is:-
  
  (A) 1/32
  (B) 1/13
  (C) 4/13
  (D) 1/4
• --------------------------- cannot be probability of an event.
  
  (A) 0
  (B) 1
  (C) 0.32
  (D) 1.05
  
  
• If "C" is a constant, then E(C) IS :-
  
  (A) C
  (B) 0
  (C) 1
  (D) X
  
  
• E(X-µ)2 ---------------------------------
  
  (A) Zero
  (B) S.D
  (C) Variance
  (D) Mean deviation
  
  
• If p = q=1/2, then distribution is called,
  
  (A) Symmetrical
  (B) Positively
  (C) Skewed
  (D) Negatively
  
  
• The mean and variance of the binomial distribution is:-
  (A) np and  
  (B) np and npq
  (C) np and nq
  (D) n and p
  
  
• In a binomial experiment with three trials, the variable can take:-
  
• 
  (A) 2 values
  (B) 3 values
  (C) 4 values
  (D) 5 values

INTERMEDIATE
PART-I (11 CLASS)
STATISTICS PAPER-I
TIME ALLOWED: 3.10 Hours 
SUBJECTIVE
MAXIMUM MARKS: 83
SECTION-I

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

• Differentiate between Parameter and Statistics.
  
• Name the sources of secondary data.
  
• Given X, = 2.53, X2 = 1.97, X, = 4.05 each Mean is based on 6 observations. Find Combined Mean.
  
• Given u = x-170/570, Σfu= 100, Σf= 200, find A.M.
  
• Define the term Median and write its formula.
  
• Differentiate between Simple Arithmetic Mean and Weighted Arithmetic Mean.
  
• Write down the empirical relationship between Mean, Median and Mode and find Mode when Mean = 30.5 and Median = 12.3.
  
• Given Fisher's Ideal price Index=104.3 and Paasche's Price Index Number = 103.2 then find Laspeyre's Price Index Number.
• Given P, = 16, 15, 12, 20, 22 and P1 = 20,12,15, 22, 22 , then find I = p1/pox 100
  
• Differentiate between Simple and Composite Index Number.
  
• Explain Consumer's Price Index Number and how is it calculated? (xii) Describe the Chain Base Method.

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

• Define Histogram.
  
• Define Relative Frequency.
  
• If Q1 = 88.03, Q3 =94.50, compute coefficient of Q.D.
  
• A series comprises of hundred values each equal to .15". What will be the average and dispersion of the series?
  
• Describe the properties of variance (any two).
  
• What is Kurtosis?
  
• What is a symmetrical distribution?
  
• Define Combined Variance.
  
• State the Multiplication law of probability?
  
• Define Conditional Probability.
  
• Define Mutually Exclusive Events.
  
• State the Compliment Law of Probability.

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

• Define Random Variable.
  
• What is Discrete Probability Distribution?
  
• Make random variable for tails when three coins are tossed.
  
• Write down two laws of mathematical expectation.
  
• Given E(x)=10 and E(x)2 = 500; find coefficient of variation.
  
• Give any two properties of Hypergeometric experiment which are different from Binomial experiment.
  
• What is Mean and Variance of Binomial Distribution?
  
• If n = 8 and p = 0.4 , then find variance of Binomial Distribution.
  
• If N =10, n = 3, k = 4 , find variance of klypergeometric Distribution.

SECTION-II

NOTE: - Attempt any three questions.

Question#5.
(a) The arithmetic mean and harmonic mean of two observations are 5 and 3.2 respectively. Find the geometric mean. 4
(b) Compute the median from the following data 4

Question#6
(a) Calculate M.D from mean from the following data:- 4

(b) First three moments about x=62 are 1, 4 and 10. Find first three moments about mean.  

Question#7
(a) For the data given (i) Σp1q1=1500, Σp1qo=780, Σp1qo=880, Σpoq1 = 1370 Compute 4
(i) Base year weighted index numbers
(ii) Current year weighted index numbers
(iii) Fisher's index numbers
(b) From a well shuftled pack of 52 playing cards, a card is drawn et random. Find the probability that card drawn is-4
(i) Red card
(ii) Black card
(iii) Diamond card
(iv) Pictured card

Question#8
(a) A random variable x has the probability distribution f(x)= A(5/x), x=0, I, 2, 3. 4
(i) Determine the value of A
(ii) Determine E(X)
(b) A continuous random variable X can assume value between X=1 and X=3 has a density function given by f (x)= (x/2)
(i) show that area under the curve is equal to one
(ii) p ( < 2 )

Question#9
(a) A committee of size 4 is to be selected at random from 3 women and 4 men Find the probability that 4
(i) 2 women
(ii) At least 2 women will be selected in the committee.4
(b) A random variable 'X' is believed to follow a binomial distribution with b(x;5, p)
If P(x=0)=244/1043 find P(x=3). 4

SECTION-111
(PRACTICALI)

10. Attempt any three parts. 3x5=15
(A) Find the median and mode for the following frequency distribution of 100 students at a certain examination:-

(B) Find the first four moments about mean for the following frequency distribution

(C) Compute the Index Number for 2009 taking 2008 as base year using weighted average of relative method.

(D) A random variable X has the probability distribution given below:-

Find (i) E( X )
(ii) E(x2) and prove that
(iii) E(2x+5)=2E(X )+5
(E) Four dice are rolled 405 times and a throw of 3 or 4 is regarded as a success. Find the expected frequencies for 0, 1, 2, 3 and 4 successes.