SAHIWAL BOARD 2015
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.

• A part of the population selected for study is called a: 
  
  (a) Variance
  (b) Data          
  (c) Sample
  (d) Parameter
  
  
• Graph of a cumulative frequency distribution is called:
  
  (a) Histogram 
  (b) Frequency polygon
  (c) Ogive         
  (d) None of these
  
  
• The average of lower and upper class limit is called:
  
  (a) Class boundary     
  (b) Class limit
  (c) Class mark
  (d) Class frequency
  
  
• Mode of the series 1, 1, 3, 3, 5, 6, 3, 7, 7, is:
  
  (a) 1    
  (b) 3    
  (c) 1    
  (d) None of these
  
  
• Ina symmetrical distribution, the Mean, Median and Mode are:
  
  (a) Always equal        
  (b) Never equal
  (c) Sometimes equal   
  (d) None of these
  
  
• The standard deviation is independent of:
  
  (a) Change of origin   
  (b) Change of scale
  (c) Change of origin and scale
  (d) None of these
  
  
• Standard deviation of 2, 2, 2, 2, is equal to:
  
  (a) 2    
  (b) 8    
  (c) Zero          
  (d) 4
  
  
• In case of positive skewed distribution the extreme value lie in the:
  
  (a) Middle
  (b) Left tail
  (c) Right tail
  (d) Any where
  
  
• Laspeyre's index = 110, Paasche's index = 108 then the Fisher's index is equal to:
  
  (a) 110
  (b) 108          
  (c) 100
  (d) 109
  
  
• Time reversal test is satisfied by:
  
  (a) Laspeyre's index   
  (b) Paasche's index
  (c) Fisher's index        
  (d) M.Edgeworth's index
  
  
• The term "event" is used for:
  
  (a) Time          
  (b) Subset of the sample space
  (c) Probability
  (d) Total number of outcomes
  
  
• If two dice are rolled, the No. of the possible outcomes are: 
  
  (a) 6    
  (b) 36  
  (c) 1    
  (d) Difficult to tell
  
  
• In a discrete probability distribution, the sum of all the probabilities is always equal to:
  
  (a) Zero          
  (b) One           
  (c) Minimum
  (d) Maximum
  
  
• The probability of the impossible events is always equal to:
  
  (a) Zero          
  (b) One           
  (c) E(x)           
  (d) F(x) +1
  
  
• The binomial probability distribution is symmetrical when:
  
  (a) P = q         
  (b) P < q         
  (c) P > q         
  (d) np > npq
  
  
• The parameter of the binomial distribution are:
  
  (a) n and p
  (b) p and q
  (c) np and nq
  (d) np and npq 
  
  
• In hyper geometric distribution successive trials are:
  
  (a) Independent         
  (b) Not independent
  (c) With replacement  
  (d) Not fixed
  
  

Tithe: 2:40 Hours
(Subjective Part)
Marks:8
SECTION-I

2. Write short answers of any Eight Parts. 16

1. Differentiate between parameter and statistic.
   
2. What is a primary data?
   
3. Average of 5 values is 70, Find the sum of values.
   
4. Describe empirical relation between mean, median and mode.
   
5. Define median.
   
6. If mean is 20 median =18. Find Mode.
   
7. Give two properties of arithmetic mean.
   
8. What do you understand by base period?
   
9. Define composite index number.
   
10. If Laspeyre's index number =105.4 and Paasche's index number = 103.2 then find the Fisher's index number.
    
11. Define weighted index number.
    
12. Give two Tim, Ʃ poqo =352, Ʃ p1qo = 422 Find base year weighted index number.

3. Write short answers of any Eight Parts. 16

1. What is ogive?       
   
2. Define pie chart.
   
3. Given Ʃ f =120, Ʃ fx=296 and mode = 2.9. Find coefficient of skewness.       
   
4. Define range.
   
5. Given Ʃ f =100, Ʃ -fx =800 and Ʃ fx =1600 . Find coefficient of mean deviation.
   
6. Define Kurtosis.
   
7. The first moment about x = 15 is 2.5, the second moment about mean is 16. What is the value of standard deviation?
   
8. Give the formula for calculating combined standard deviation for three subgroups.    
   
9. Define combination
   
10. What are exhaustive events?
    
11. State the multiplication law of probability for dependent events.
    
12. Given  = 55,S2=121. Find coefficient of variation.

4. Write short answers of any Six Parts. 12

1. Describe the properties of a discrete probability distribution.
   
2. Define continuous random variable,
   
3. State any two laws of expectation.6 1
   
4. Given x= 0, 1, 2, P(x) =9/16,6/16,1/16 Find E(x).
   
5. If E(x) = 5, Find E (-3x+2).
   
6. What is a binomial experiment?
   
7. What are the parameters of hyper geometric distribution?
   
8. If mean = 20, P = 0.2 binomial distribution, then find n.
   
9. Write the formula of variance of the hyper geometric distribution.

SECTION II

Attempt any THREE Questions. Each Question carries 8 marks.

Question#5
(a) Calculate arithmetic mean using step deviation method from the following data. 04

 (b) Consider the following data: 04

Question#5
(a) Compute Q1 and 7th decile.

(b) The first three moments of a distribution about the value 2 of a variable are 1, 16 and - 40. Show that Mean is 3 and its variance is 15?. 04

Question#7
(a) Taking median as an average. Construct the chain indices for the following data:

(b) Assume that "X" is a number chosen at random from the set of integers between 1 and 15 both Inclusive. What is the probability that "X" is a single digit number? ,

Question#8
(a) Show that f(x)= 2 ≤ x ≤ 4 is a proper density function and find the probability 2 ≤ x ≤ 3.
(b) A pair of dice is rolled. Let X represents the sum of dots on both dices. Find   
(i) range of X
(ii) Probability distribution of X.

Question#9
(a) Let "X" is a binomial r.v with n = 5 and p = 0.2, Find the complete binomial distribution.
(b) Given that "x”  is hypergeometric r.v. with N =10, n = 4, K =  5. Compute
(i) P(x ≤ 3)
(ii) P(x = 4),

SECTION-III
(Practical Part)

10. Attempt any THREE questions.
(A) Find the value of mode to the following data:

(B) Calculate C.V for the data given. 60. 65, 70, 75, 80, 85, 90, 95.
(C) Find index number of prices from the following data taking 1990 as base:

 (D) Given the following probability distribution of discrete random variable:

Show that E (2x+5) = 2E(x) +5
(E) A bag contains 5 green and 4 red balls. 4 balls are selected at random without replacement. Compute the probability distribution of green balls.