Inter (Part-I) Gujranwala Board 2012
Statistics
Paper: I
Time: 20 Minutes
Marks:17
OBJECTIVE

Note: You have four choices for each objective type question as A, B, C and II The choice which you think is correct, rill that circle in front of that question number with marker or pen on the answer book provided. 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 contraction in the babble and hand written answer, bubble option will be considered correct.

1).

• The probability of an impossible event is always:
  

(A) positive    
(B) zero
(C) negative   
(D) 1

• If X and Y are independent, then S.D (X- Y)=

 (A) S.D (X) - S.D. (Y)          
(B) S.D.(X) + S.D(Y)
(C)          
(D)

• When a distribution is symmetrical and has one mode, the highest point on the curve is called:
  

(A) mode        
(B) median
(C) mean        
(D) all of these

• The section of table that contains the column caption is called:
  

(A) box head  
(B) box plot
(C) stub          
(D) body

• The mean of the hyper-geometric distribution is:

(A)          
(B)
(C)
(D)

• When two dice are rolled, the maximum, total on theTwo  faces of the dice will be:

(A) 6               
(B) 36
(C) 12             
(D)

• In fixed base method, the base period should be:

(A) for away   
(B) normal
(C) unreliable 
(D) abnormal

• The hyper-geometric  destruction has____       
  parameters.
  

(A) 2   
(B) 3
(C) 1   
(D)4

• Probability density function is the probability functionOf _____ random variable.
  

(A) continuous          
(B) discrete
(C) qualitative            
(D) none

• Comparisons of changes in variable over___  period are not reliable in the index number.
  

(A) long          
(B) short
(C) fixed        
(D) chain

• Which set has the minimum variation?
  

(A) 46, 48, 50     
(B) 30, 40, 50
(C) 40, 50, 60     
(D) 48, 48, 49

• Mean is affected by the change of:

(A) origin-                   
(B) scale
(C) both A and B       
(D) none of these

• Random numbers are generated from the single digit numbers:
  

(A) {1, 2, 3,….10}     
(B) {0,1, 2, ...,10}
(C) {0,1,2,….:}                 
(D){0,1,2,….9}

• In a binomial probability distribution, the skewness is positive for:

(A)  P˂1/2                    
(B) P˃1/2
(C) np˂npq                    
(D) np≠ 1/2

• A polution of population selected for study is called:

(A) parameter 
(B) statistic
(C) population
(D) sample

• In a symmetrical distribution, the, coefficient of
  skewness will always be:
  

(A) negative     
(B) zero
(C) 1                    
(D) -1

• The smallest and the largest values of data are called:
  

(A) range        
(B) mid-point
(C) extreme values     
(D) arrayed values

Inter (Part-I)
Gujranwala Board 2912
Statistics
 Paper: I
Time: 2.40 Hours 1 
  Marks: 68
SUBJECTIVE

Note: Section I is compulsory. Attempt any three (3) questions from Section II.

(Section – I)

2. Write short answers to any EIGHT questions: (2x8=16)

• Explain inferential statistics.
  
• Write any two sources of secondary data.
  
• Write any, two properties of a good average.
  
• Prove that ∑(y, - )=0
  
• If n1 = 3, n2= 2,  2, = 3,  2= 4, find c
  
• Write two merits of G.M.
  
• Calculate G.M. for 0, 2, 4, 6 and 10.
  
• Write any two uses of index numbers.
  
• Write the formula for Fisher's index number.
  
• What is meant by base year?
  
• Write any two limitations of index numbers.
  
• How do we select commodities for index numbers?
  

3. Write short answers to any EIGHT question: (2x8=16)

• What is an Ogive?
  
• Define the term "Classification."
  
• Define the term "Dispersion."                                               •
  
• What is variance?
  
• What is positive skewness?
  
• If standard deviation of values of X is 10, what is the
  standard deviation of values of 5 X.
  
• Is it possible that first moment 'about mean is 10?
  
• Define the term "Kurtosis."
  
• What is a sample space?
  
• State the difference between simple and compound
  events.          -
  
• Are the events A and B independent if P(A) = 0.5 and
  P(A/B)= 0.4? 
  
• Find the value of P(A ∩ B), if P(A)=0.4 P(B) = 0.7
  and P (A ᴜ B) = 0.3
  

4. Write short answers to any SIX questions: (2x6 = 12)

• Define-random variable.
  
• Differentiate between discrete and continuous random
  variable.
  
• Define probability distribution.
  
• What do you mean by expected value of a random
  variable?
  
• If two coins are tossed and 'X' denotes the number of
  heads, construct probability distribution of X.
  
•  Define binomial distribution.
  
• If n = 10 and q = 0.4, find the mean and variance of
  binomial distribution.              ,
  
• Write down the properties of hypergeometric
  experiment.
  
• Given P(X) = K. ⁴C_x and x = 0.1, 2, 3, 4, Find the value
  of K.

(Section - II)

5).
a) The frequency distribution given below has been
derived from the use of working origin. if D = X - 18,
find arithmetic mean and geometric mean.

b) The class marks for the ages of sales clerks employed
in a departmental store are:
18.5, 28.3, 38.5, 48.5, 58.5 and 68.5. Find the class-
boundaries of this distribution and compute median if
the class frequencies are 7, 12, 23, 35, 25, 8
respectively.

6).
a) Following information regarding the two series are
given below:
n1 = 150, ∑(x1- 100) = 180, ∑(x1 - I 00)2 = 245320
n2 = 200,  ∑(x2 100) = 250, E (x2- 100)2 = 43850
Compare the variability of each series. Also determine
which series shows the consistent performance.

b)       In a moderately skewed distribution, the Pearson's
coefficient of skewness =0.6 mean = 65, and median = 70

7.
a)  Compute chain indices using median as an average:

 b)
(i) There coins are tossed, find the probability that
(a) exactly 3 heads appear
(b) at the most 2 heads appear.
(ii) If A and B are independent events, find P(A ∩ B).
If P(A)=0.6,P(B)=0.8

8).  
a) A continuous random variable X has a density_
function
f(x)= 2/27(x+1)     2≤ x ≤ 6        
Find
(i) P (X <4)
(ii) P (X > 15)

b) Let X be a random variable with probability
distribution as follows:                  4

Find variance of(X).
9).
a) Find mean and variance of (q + p)2

b) A machine produced 7 good and 3 defective items.
Two items are selected randomly without replacement.
If 'X' denotes the number of defective items, then find
expected number of defective items.