SARGODHA BOARD 2016
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,C or D with pen or marker in front of that question number.

Question#1

• Total group under discussion is called:
  
  (a) Sample
  (b) Population
  (c) Subset
  (d) None
  
  
• Sum of relative frequencies is always:
  
  (a) Zero          
  (b) Less than 1
  (c) Greater than 1       
  (d) I
  
• If K is a constant then is equal to: 1=1
  
  (a) 3 ± K         
  (b) 3 – K         
  (c) 3 K
  (d) None of these
  
  
• Sum of deviations is zero when deviations are taken from:
  
  (a) Mean         
  (b) Median
  (c) Mode        
  (d) All of these
  
  
• If two numbers are 4 and 16 then Geometric Mean is:
  
  (a) 4    
  (b) 16  
  (c) 8    
  (d) 10
  
  
• Difference between the largest and the smallest values is:
  
  (a) Q.D           
  (b) M.D          
  (c) S.D
  (d) Range
  
  
• Mean Deviation (M.D) is least from:
  
  (a) Mean         
  (b) Median
  (c) Mode        
  (d) G.M
  
  
• Variance of 3,3,3,3 is:
  
  (a) 3    
  (b) Zero          
  (c) 9    
  (d) 81
  
  
• An Index number computed for single commodity is called:
  
  (a) Simple Index        
  (b) Composite Index
  (c) Weighted Index    
  (d) None of these
  
  
• Quantity index number is also known as:
  
  (a) Value lndex
  (b) Volume Index
  (c) Both A & B          
  (d) None
  
  
• A coin is tossed three times. Then total number of sample points will be:
  
  (a) 3    
  (b) 32   
  (c) 23    
  (d) 33
  
  
• If A and B are mutually exclusive events then (A (1 B) is:
  
  (a) A U B       
  (b) ᶲ    
  (c) S    
  (d) Undefined
  
  
• Life time of a light bulb is:
  
  (a) Discrete Variable  
  (b) Continuous variable
  (c) Both a & b
  (d) None of these
  
  
• Expected value of a random variable is equal to:
  
  (a) Mean         
  (b) Variance
  (c) Mean Deviation    
  (d) Zero
  
  
• Number of parameters of binomial distribution are:
  
  (a) One           
  (b) Two          
  (c) Three         
  (d) Four
  
  
• Standard Deviation of (q + p)5 is equal to:
  
  (a) 5 p q          
  (b) (5 pq)2       
  (c)        
  (d) Zero
  
  
• In hypergeometric Distribution, the trials are:
  
  (a) Independent         
  (b) Dependent
  (c) Both a & b
  (d) None

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

2. Write short answers of any Eight Parts. 16

• Define the term statistics.  
• Define the primary data.
• What is meant by Statistical average?
• Define Harmonic mean. 
• Define the weighted mean.
• Given u=;∑ fu=100;∑=200. Find arithmetic mean.
• Given ℓ= 60 ; h = 10 ; f = 20 ; n = 80 and c = 30. Find median.
• (viii)Define price index number.
• What are the uses of index numbers (any two).
• Describe the chain base method.
• What is C.P.I?
• Given ∑W = 8500 and ∑WI = 892500 . Construct consumer price index number by family budget method.

3. Write short answers of any Eight Parts. 16

• What is tabulation?
• Define Ogive.
• What is Dispersion?  
• Define Quartile deviation.
• What is Variance?
• Define Kurtosis.
• Write down the formulas of moment ratios b1 and b2.
• If b1= 0 and b2 = 3, what is the symmetry and Kurtosis of the distribution.
• Define Mutually exclusive events?
• What is compound event?
• Make a sample space, if we toss a coin three times.
• If we throw two dice at a time what is the probability of getting the total of '7'.

4. Write short answers of any Six Parts. 12

1. Define continous random variable.
2. Write down two properties of expectation.
3. If E(x2)= 400 and E(x)=10. Find Var(x).
4. If X and Y are independent. Find E(XY).
5. Given

1. Define Binomial frequency distribution.
2. If n=4 , N = 6 , k = 3. Find P (x = 1).
3. If n = 10, p = 0.4. Find Mean and Variance of the Binomial distribution.
4. State any two properties of the Hypergeometric distribution.

SECTION-II

Attempt any THREE question. Each question carries 8 marks.
Question#5
(a) Calculate Harmonic Mean of the data given below.

(b) Calculate Mode and P40 of the data given above.

Question#6
(a) Find coefficient of variation of the following data by using the transformation
as :µ=.

(b) From the marks secured by 120 students in section 'A' and 120 students in section 'B' of a class, the following measures are obtained.

Describe which distribution of marks is more skewed.

Question#7
(a) Compute chain index Numbers for the following data taking 1997 as base.

(b) If Three coins are tossed, What is the probability of getting exactly Two Heads.

Question#8
(a) A coin is tossed times. Let x denote "number of heads". Find probability distribution of “x".
(b) A committee of size 5 is to be selected at random from 3 women and 5 men. Find expected number of women on thecommittee.

Question#9
(a) If 20% of the bolts produced by a machine are defective, determine the probability that of 5 bolts chosen at random
(i) 2 bolts are defectives
(ii) At least 3 bolts are defectives.
(b) From a lot of 10 missiles, 4 are selected at random and fired. If the lot contains 3 defective missiles that will not fire, what is the probability that
(i) All 4 will fire?
(ii) Atleast three wil fire?