Statistics Lahore-Board 2016
Inter Part-I
Time: 20 Min
Objective
Type Marks = 17

Note: Four possible answers A, B, C and D to each question are given. The choice which you think is correct, fill that circle in front of that question with Marker or Pen ink in the answer-book. Cutting or filling two or more circles will result in zero mark in that question.

• A quantity calculated from the sample is called:

(A) Statistic
(B) SaMple
(C) Parameter
(D) None of these

• The grouped data is :

(A) Primary data
(B) Secondary data
(C) Raw aata
(D) None of these

• The graphic representation of the frequency distribution

(A) Frequency curve
(B) Historigram
(C) Ogive
(D) Histogram

• If I (x - 20) = 25 , ∑(x -15) = 0 and ∑ (x - 10)= -10 then arithmetic mean is :

(A) 25
(B) -10
(C) 15
(D) 20

• Geometric mean of 2, 4, 8 is :

(A) Zero
(B) 16
(C) 8
(D) 4

• Second moment about mean is

(A) variance
(B) Standard deviation
(C) Zero
(D) One

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

(A) Negative
(B) Zero
(C)1
(D) -1

• If β₂= 3 then the distribution is called :

(A) Symmetrical
(B) Mesokurtic
(C) Platykurtic
(D) Leptokurtic

• Index number for the base period is always taken as :

(A) 1
(B) Zero
(C) 100
(D) 200

• Laspeyre's index number is :

(A)                                    
(B)  
(C)                                 
(D) 

• The probability of an event cannot be .

(A) Zero
(B) Greater than zero
(C) One
(D) Less than zero

• The probability of selecting a red bard out of 52 playing cards is :

(A)                                          
(B)                                                                    
(C)                                     
(D)                                                                     

• In a discrete probability distribution, the sum of all the probabilities is always equal to :

(A) Minimum
(B) Maximum
(C) Zero
(D) One

• E (X + 2Y) is equal to:

(A) E(X) + 2E(Y)
(B) E(X) + 4E(Y)
(C) E(2X) + E(2Y)
(D) E(X) + E(Y)

• In a binomial distribution p = q = then distribution is :

(A) Symmetrical
(B) Positively skewed
(C) Negatireiy skewed
(D) Biased

• The parameters of the hypergeometric distribution are :

(A) n,p,q
(B) n, N, p
(C) n, N, k
(D) n, N, q

• The hypergeornetric probability distribution is :

(A) Continuous distribution
(B) Simple distribution
(C) Discrete distribution
(D) None of these

Statistics Lahore Board 2016
Inter Part-I
Time: 2.40 hrs
Subjective
Marks = 68

SECTION - I

2. Write short answers to any Eight (8) questions: 16

• Define statistics as a discipline of science.
  
• Define population.
• Write the types of average.
• Write two properties of A.M.
• Define geometric mean with formula.
  
• Given ℓ= 200 , f m₃ = 2 f₁= 20 , f₂= 20 , h = 10, find mode.
  
• Given ∑ fu = 100, ∑ f = 200. Find X .
  
• Define an index number.
  
• Define link relative.
  
• What is the relationship between Laspeyre's Paasche's and Fisher's ideal index number?
  
• Given ∑ p₀q₀ = 1000 and , ∑ p_nq_n = 1360, find current year weighted index.
  
• If Paasche's index number is 105.72 and Laspeyre's index number is 107.22, then find Fisher's index number?

3. Write short notes on any EIGHT (8) questions: 16

• What do you mean by term classification?
  
• Define histogram.
  
• What are the types of dispersion?
  
• What is quartile deviation?
  
• What is the use of coefficient of variation?
  
• What do you ssy about the relative dispersion of 5, 5, 5, 5?
  
• What do you know about kurtosis?
  
• If β₂ = 3 and m₄ = 1875, then what will be the standard deviation?
  
• Define composite event.
  
• What are independent events?
  
• If P(A) = and P(B)= find are independent events?
  A fair die is rolled, what is the probability of getting an odd number?

4. Write short answers to any SIX (6) questions: 12

• Define continuous random variable.
  
• Describe properties of discrete probability distribution.
  
• Explain the term mathematical expectation.
  
• Describe properties of probability density function.
  
• If E(X) = 0.63, var (X) = 0.2331 then find E(X²)?
  
• Define binomial probability distribution.
  
• Describe hypergeometric experiment.
  
• What is mean and variance of hypergeometric distribution with parameters N, n, K?
  
• In binomial distribution mean = 6 and var = -2.4 find parameters of binomial distribution.

SECTION-II

Note: Attempt any THREE questions.

5. (a) A variable Y is determined from a variable X by equation Y = 10 - 4X. Find Y when X = -3 , -2 -1,0

1, 2, 3, 4, 5 and show that = 10 - 4 .

(b) Compute mode of the data given below

6. (a) Find coefficient of quartile deviation from the following data :

(b) For a moderately skewed distribution the mean price is Rs.20 and the median price is Rs.17. if the coefficient of variation is 20%, find the coefficient of skewness of the distribution?

7. (a) Compute Fisher's ideal index numbers from the given data :

(i) ∑p₁q₀ = 8800 ∑ p₀q₀=7800 , ∑ p₁q₁ = 15400 , ∑ p₀q₁ = 13710

(ii) ∑ p₂q₀=11000 , ∑ p₂q₂= 23000 , ∑ p₀q₂ = 16370 , ∑ p₀q₀ = 7800

(b) Two coins are tossed. What is the probability that least one head will appear?

8. (a). A continuous random variable 'X' has density function

f(x) = X = 2 to X = 4. Find P(X 3.5) and P(X = 1.5)

(b) If it rains, a rain coat dealer can earn Rs.500 per day? If it is fair, he can lose Rs. 100 per day? what is expectation if the probability of min is 0.4?

9. (a) A bag contains 4 green and 3 white bails. Three balls are drawn without replacement. Make a probability distribution for white balls.

(b) If 20% of the bolts produced by a machine are defective, determine the probability that out of 4 bolts chosen at random : (i) 0 (ii) 2 bolts are defective?