RAWALPINDI BOARD 2012
PAPER STATISTICS PART-I
Time: 20 Minutes      
(Objective Part) 
Marks: 17

Note: Four Answers are given against each column A,B,C&D. Select the write answer and only separet answer sheet, fill the circle A,B,Cor D with pen or marker in front of that question number.

• Data obtained from interim sources is

(a) Primary data
(b) Raw data
(c) Secondary data
(d) Fictitious data

• Raw caption of a table is also called:

(a) Title         
(b) Body           
(c) Box head      
(d) Stub

• The graph of frequency distribution is called:

(a) I listorigram
(b) Pie chart       
(c) Histogram
(d) Ogive

• Sum of deviation of observations from mean is:

(a) One           
(b) Zero           
(c) Less than zero
(d) None

• The most frequent value of the data is called:

(a) Mean          
(b) Median         
(c) Mode
(d) Geometric Mean

• The first moment about origin is:

(a) Zero          
(b) One            
(c) Variance
(d) Mean

• The standard deviation is calculated from:

(a) Median        
(b) Mean           
(e) Mode
(d) Combined Mean

• The variance of 2,2,2,2 is:

(a) 2             
(b) 2²             
(c) 0
(d)

• For computing chain index we computer

(a) Price relative
(b) Link relative
(c) Weighted indices                           
(d) Fixed base indices,

• Cost of living index numbers arc:

(a) Simple
(b) Unweighted
(c) Chain                      
(d) Composite

• The probability of an event cannot he:

(a) =0           
(b) 0.5            
(c) >1           
(d) =1

• 9x8x7x6x5 is equal to:

          
(a)            
(b)              
(e)            
(d)

• If X and Y are two independent random variabls, then E(XY) is:

(a) E(X)+E(Y)
(b) E(X)-E(Y)
(c) X E(Y)                   
(d) E(X) E(Y)

• The variable whose values arc obtained by the outcomes of a random experiment is called:

(a) Dependent Variable                    
(b) Random Variable
(c) Standard Normal Variable              
(d) None of these

• A binomial distribution has variance.

(a) np           
(b) npq          
(c)      
(d) nq

• The hionomial distribution is symmetrical, when:

(a) p = y        
(b) p >           
(c) p < q        
(d) np > pq

• The hypergeomctric disribution has parameters:

(a) 3            
(b) 2             
(c) 1            
(d) 4

Time: 2:40 Hours   
(Subjective Part)
Marks: 68
SECTION-I

 2.    Write short answers of any Eight parts.  16

• What is statistics as a subject?
• State any two functions of statistics.
• Define the term average.
• State any two advantaes of median.
• Define Harmonic Mean.                 
• Define "Index Number".
• What are weighted Index Numbers?
• State any two uses of Index Numbers.
• If for any variable X; ∑(X —10) = - 20, ∑ (X - 15) = 0 and ∑(X —20) = - 20 , What is the A.M of the values of X?
• Write down empirical Relation between Mean, Median and Mode.
• What is the difference between simple and composite index numbers.               
• Define Fixed Bases Method.

3.    Write short answers of any Eight parts. 16

• What is scatter plot?
• What is bivariate frcqucnce distrubtion?
• Write down any two properties of variance.
• When does a distribution is platykurtic?         
• Write a note on sample space
• Write a note on co-efficient of variation
• If (A) = 0.82 find P()
• If ∑|Y - Median = 155,n = 30. Find M.D.
• Write down the formula for 4th central moment in terms of raw moments.
• How can we calculate the percentile co-efficeent of kurtosis.
• A card is drawn from a pack of 52 cards. Find the probability that it is a picture card.
• A student solved 109 questions'out of 200 questions. Find his probability.

4.    Write short answers of any Six parts.    12

• Enlist the laws of Expectations.
• Given E(2X)-10 and E(2X)² = 500 , then find S.D.(X).
• What do you understand by rAndom variable'?
• Define probability distribution along with its properties.
• Given a r.v.X with E(X) = 200 and S.D (X)=14, then find E(X2):
• The mean of a binomial distribution is 5 and its S.D. is 3, point out the falacy if any in given statement.
• In a binomial distribution if n=5 and P(X=0)=P(X=1), then compute the probability of success.
• Define the parameters of the hypergcometric distribution.
• Under which circumstances we can apply the binomial distribution and the hypergeometric distribution?

SECTION-II:

Attempt any THREE questions. Each questions carries 8 marks.

 5.
(a) A variable Y is obtained from a variable X by the equation Y=10-2X. Dtermine the Y values when
the X values are -3,-2,-1,0,1,2,3,4,5 and show that  = 10 — 2.         04
(b) Find the Geometric mean from the following frequency distribution.    04

6.
(a) For the following frequency dis ribution find mean-deviation.   04

        
(b) Find co-efficient of skewness of  the data given above in part (a).                                            04

7.
(a) Compute the consumer price index number for the following data for 2010. with 2004 as bases year
use a weight.                          04

(i) The quantities consumed in the bases year.
(ii) The values in the bases year.

  (b)
i. Two good dice are rolled, find the probability if
(a) sum is complete square.
(b) modules difference is 2.                                       04

ii.    Six cards are drawn from a pack of 52 cards, what is probability of getting 3 black cards.

8.
(a) For the following probability distribution.          04

Find (i). µ
(ii). Var(X).

(b) A continous r.v.x has the p.d.f. given by: f(x)=c(4-x) For I < X >3                   04
Sketch Y=f(x) and use the rules of geomatry to find
(i) c
(ii) P(1.2 < X < 2.4) .

9.
(a) Find the mean and variance of the binomial distribution (q + P)3     04
(b) A bowl contains 4 white and 7 plack beads. 5 beads are drawn at random. Determine the probability
distrubution of number of white heads. Also find mean of th distribution.    04